RPEB Workbook

46. (b) Interest is paid to be calculated 47. (c) 48. (b) 49. (d) 50. (c) The Rule of Partial Withdrawal from PPF A/c.: Anytime after the expiry of five years from the end of the financial year in which the initial subscription is made 51. (a) 52. (b) 53. (c) 54. (b) 55. (c) 56. (c) 57. (b) 58. (b) 59. (a) 60. (a) 61. (c) 62. (b) Social Security System 63. (b) 64. (c) Whole Life Plan 65. (a) 66. (d) Funds from Tier I account can be transferred to Tier II account 67. (c) 25% of the eligible balance and 3 years 68 (c) Employee- Nil, Employer- 8.33%, Central Government- 1.16% 69. (c) Risk Appetite 70. (b) Any advice that would be in conflict with financial products/services industry's business interests 71. (c) It decreases the debt servicing burden of forex loans of a nation. 72. (c) Financial Planner Code of Ethics and Professional Responsibility 73. (b) Market capitalization and liquidity 43

74. (b) Referring the client to other professionals for certain duration with transfer of liability 75. (b) owe the client all due services meant to be fairly provided, without prejudices and with proper balance of interests 76. (d) she should withdraw the amount as the PPF account is non-transferable, nor a nominee can continue the account 77. (d) higher tax liability 78. (a) Higher than expected inflation 79. (d) increased standard of living 80. (a) concentrating on maximizing returns from corpus after retirement to leave a sizable estate 81. (b) A rising trend in the interest rates 82. (c) Take an analysis of the minimum amount with which all other goals can be achieved so that maximum sums can go towards retirement goal 83. (d) maintain the same standard of living in the future by utilizing investments 84. (b) Higher rate of interest due to higher inflation would give better compounding effect and hence a sustainable corpus. 85. (b) 86. (a) 87. (d) wages last drawn by him 44

SECTION–1 1. Raman is 40 years old. His annual family expenses are ₹7 Lakh. He will retire at age 62. During this period, average inflation is expected to be 6% p.a. He wishes to provide for 35 years after retirement. If the inflation in the post retirement period is 4% p.a. and expected return on investments is 7% p.a. how much corpus is required for retirement?(3 marks) a) ₹5.00 crores b) ₹4.69 Crores c) ₹5.67 crores d) ₹5.98 crores 2. A retired couple estimates that they may live another 20 years after retirement and would like to have an annual income of ₹2, 40,000. If the rate of return on investments is assumed to be 8% per annum, what amount of should they have at retirement to provide for their needs? (2 marks) a) 2544864 b) 2456789 c) 3456987 d) 2765433 3. Ramesh is 35 years old and started a program of depositing ₹40,000 at the beginning of every year in a deferred annuity scheme as part of his retirement plan. How much amount will he accumulate for his retirement needs? The rate of return on investments is 9.5% p.a. and the rate of inflation is 5.5% p.a. He will retire at age 55. (2 marks) a) ₹2546789 b) ₹23,70,554 c) ₹30,00,000 d) ₹2567345 4. The current household expenses of Mr. X, aged 30, are estimated to be ₹400000 p.a. If the inflation rate is assumed to be 6% p.a. calculate the household expenses of Mr. X at the time of his retirement, if he plans to retire at age60 and will require only 75% of the last spend? (3 marks) a) 2297396 b) 2017058 c) 3044902 d) 1723047 45

5. Mr. Mansukh aged 30 years is working as a senior analyst with an annual salary of ₹800000. He bought a house with a loan amount of ₹3000000 to be paid in next 16 years with an interest rate of 8% p.a. reducing monthly. Assume he pays EMI in the end of the month. Compute the amount of EMI on housing loan and total interest paid by him? (3 marks) a) 27563.99, 2292286 b) 17747.75, 2327568 c) 27748, 2327568 d) 28856,2345678 6. Mr. Y retired from XYZ Ltd. after completing 30 years 9 months. Salary at the time of retirement is ₹11500 p.m. Actual gratuity received is ₹455000. Average salary for previous 10 months is ₹9350. Calculate the exempted amount of gratuity if XYZ Ltd. is not covered under Payment of Gratuity Act? (3 marks) a) ₹10,00,000 b) ₹140250 c) ₹144925 d) ₹161827 7. Mr. Pawar is a 30 year old, self-employed person is saving ₹30,000 per annum in PPF account. He has been saving for the last 5 years. He is willing to look at a lifestyle after retirement that fits into a fixed ₹3lakhs p.a. spend for 15 years. What is the spending opportunity for him, at the time of his retirement of age 60 given his savings and assume a rate of 6% on his funds after retirement. (Compounded annually, assume beginning; assume the return on PPF account to be 8%). (4 marks) a) 14,26,890 b) 20,81,345 c) 24,94570 d) 18,54,425 8. Mr. Ashay 35 years wants to retire at 60; he has a life expectancy of 75 years. Current expenses are ₹300000 annually. He estimates no reduction of expenses post retirement. How much should he save per annum to achieve his target, if inflation is 6% and yield from investment is 10%. He does not wish to leave an estate. (4 marks) a) ₹139523 b) ₹143789 c) ₹153475 d) None 46

9. Mr. Manish is working with A ltd from October 1st 2003. He is entitled to a basic salary of ₹6000per month. DA is 40% of basic salary. He retired on Jan 1st 2017. Benefits received Gratuity ₹98000, Pension from Jan 1st ’17 ₹2000pm. Payment from recognized PF ₹300000. Encashment of earned leave for 150 days ₹36000. He was entitled to 40 days leave for every completed year of service. Got 50% of his pension commuted in lump sum w.e.f. March 1st ’17. What amount of leave encashment is eligible for tax exemption for Manish? (4 marks) a) Actual encashed b) Nil c) 10 months average salary d) None of the above 10. If nominal rate of interest is 12% and compounding is done monthly what would be the effective rate of return? (1 mark) a) 12.58% b) 12.61% c) 12.68% d) 12.75% 11. Nisha opened a PPF account on 1st April 2010. She had a balance of ₹4,95,564 on 31st March 2013. The amount outstanding in her account at the end of preceding FY was ₹6,45,293. What amount can she withdraw from PPF account and from which date? (2 mark) a) He cannot withdraw any amount from PPF account b) ₹247,782 from 1st April 2016 in the year 2016-17 c) ₹322,647 from 1st April 2014 in the year 2014-15 d) ₹247,782 from 1st April 2013 in the year 2013-14 12. If a person wants a sum of ₹42000/- pm at a replacement ratio of 70%, what should his normal earning be at the time of retirement?____ (3marks) a) 4.2 lakh b) 5.6 lakhs c) 6.4 lakhs d) 7.2 lakhs 13. Jatin is 40 yrs. old. He earns ₹2.8lakhs a year currently. If his earnings rise 8% for the next 15 years & he wants a replacement ratio of 80%, what will be his requirement at the time of retirement? (3 marks) a) 701555 b) 710566 c) 710655 d) 701655 47

14. The current income of a person is ₹4lakhs p.a. He wants a sum of ₹5lakhs at the replacement ratio of 80% in 5 years’ time. By what rate should his income increase to provide such a benefit? (3 marks) a) 7.33% b) 8.33% c) 9.33% d) 10.33% 15. Shinde invested ₹72000 at the rate of interest of 5%. After 7 yrs. The ROI is 5%compounded half yearly. After 3 yrs. ROI is 6% compounded quarterly. What will he get after 15 years? (3 marks) a) 140000 b) 155000 c) 148251 d) 158242 16. Mira aged 30 saves ₹15000 per year (at the end) in Bank FD earning 8.25% p.a. compounded annually until she retires at 58. Life expectancy is 80 yrs. Calculate the Corpus on the date of retirement? What amount she can withdraw at the beginning of each year inflation adjusted until 80 in case she wishes to exhaust her corpus completely? Inflation rate is 5% p.a. (4 marks) a) 1424894, 89458 b) 1348974, 87498 c) 1491655, 137767 d) 1491655, 91655.75 17. Mr. Goyal has just retired from Govt. Service with a lump sum of ₹35,85,650 as retirement benefits in total. Currently he is 59 and life expectancy for him is 80 years. He intends to take a world trip soon, for which he would require an amount of ₹4,00,000 and he also wants to buy a car of ₹3 lakhs immediately. Calculate what amount will be available to him for post- retirement living expenses in the beginning of every month, considering inflation at 5.5% and rate of return is 8.5% p.a? (3 mark) a) 16337.5 b) 17000.5 c) 15133.5 d) 15535.6 18. What is the present value of an investment that will be worth ₹10000 in 10 years based on an inflation rate of 4% p.a.? (2 mark) a) 3855 b) 5584 c) 6756 48

d) 8203 19. The current yield of a bond with coupon rate of 11.5% is 10.773%. How much is the price of this bond? (2 marks) a) 100 b) 106.75 c) 107.76 d) Nil 20. Aman 25 yrs old, working with a Pvt. Ltd Co. since 2009. He receives ₹80,000/- towards leave encashment in 2012 which is equal to 1 mths salary. What is the taxable component? (2 marks) a) 4000 b) 12500 c) 20000 d) 80000 21. Jagan is 30 years of age and is currently earning ₹350000 per annum. He expects an annual increment of 8% for the next 15 years and wants a replacement ratio of 75% at the time of retirement. According to you this amount will be ____? (2marks) a) ₹832694 b) ₹710566 c) ₹823980 d) ₹710655 22. Kulkarni has estimated present expenses of ₹300000 per annum. If inflation is 6% for first 10 years, 5% for next 10 years and 7% for the balance term. What would if the household expenses required by him at the age of 60 years if he requires only 80% as replacement ratio. He is currently 30 years old and has a life expectancy of 75 years. (2 marks) a) 15.77 lakh b) 13.77 lakh c) 12.89 lakh d) None of the above 23. Sudarshan is retiring at 58 and has accumulated a corpus of ₹25 lakh. If inflation is 5% and interest rate is 8% p.a. calculate the rate of growth. (2 marks) a) 3% b) 3.29% c) 2.86% d) 2% 49

24. If the inflation rate is 4.9% and the tax rate is 30%, evaluate the required rate of return to maintain the value of the investment? (1 mark) a) 8.33% b) 6.37% c) 7% d) 10% 25. The current yield of a bond, with coupon rate of 8.5% and market price of ₹110 is ____ (2 marks) a) 7.143% b) 7.77% c) 7.27% d) 7.73% 26. The current yield of a bond with coupon rate of 9% is 12%. What is the worth of this bond? (3 marks) a) 100 b) 75 c) 108 d) None of the above 27. Determine the present value of an investment that will be worth ₹10000 in 8 years based on an inflation rate of 5%p.a.? (3 marks) a) 6768 b) 6756 c) 10000 d) Nil 28. Mr. Ankur aged 65 years just retired and has no source of income after retirement. He owns a self-occupied house which is valued at ₹95 lakh. His financial planner has advised to take the benefit of reverse mortgage scheme. An approved lending institution agrees to provide periodic monthly payments under the scheme considering a loan to value ratio of 80% and at a rate of interest of 12.50% p.a. If the retiree opts for a 15-year term of reverse mortgage, what fixed periodic monthly payments he stands to receive under the scheme? (3 mark) a) 92,206 b) 93,671.67 c) 14355.48 d) 14505.01 50

29. A promises to pay B a sum of ₹200000 at the end of 3 years and another ₹400000 at the end of 5 years from now. What cash amount should be accepted now in lieu of the above two amounts if interest rate is 5% p.a.? (2 marks) a) 486178 b) 486523 c) 465789 d) None of the above 30. Reema aged 40 spends ₹350000 p.a. as ALC. (Annual living costs).She expects her expenses to go up by 3% every year till her son settles in his career in 7 years’ time. After that her expenses will stabilize. Inflation rate is 6% p.a. Calculate the amount required by her at age: (2 marks)  47  60 a) 526270, 1122497 b) 639814, 1364677 c) 526270,1613441 d) None of the above 31. Neha has received an inheritance of ₹2.5 lakh. She wants to withdraw equal amounts at the beginning of each month for the next seven years. She expects to earn an annual interest of 10% compounded monthly on her investments. What amount can she receive each month? (2 mark) a) ₹4150 b) ₹4116 c) ₹2266 d) ₹26265 51

SOLUTIONS 1. (c) 5.67 crores Solution: Current age of Raman 40 years Retirement age 62 years Annual family expenses ₹7,00,000 p.a. Inflation during pre-retirement period 6% Expenses required on Retirement ₹25,22,476 { FV of 7,00,000 @ 6% for 22 years Expected Return 7% Inflation post retirement 4% Expenses required for 35 years Corpus to be accumulated for retirement ₹56715936 (rate 2.8846% (real rate), 35 N, -2522476 PMT, Bgn, Compute PV= 56715936 2. (a) Solution 240000 Pmt. Bgn 8=I 20=N Compute PV = 2544864 3. (b) Solution 40000 =Pmt Bgn 9.5 =I 20 =N Compute FV = ₹23,70,554 4. (d) 1723047 (FV of ₹4,00,000 @6% after 30 years is 2297396. But he requires only 75% of the last spend. 5. (c) ₹27748 and ₹2327568 (First compute EMI and then go to AMRT, PM 1=1, PM2=192, N=192, Rate = 8%/12, PV=-3000000, PMT= 27747.75, Sum INT Solve 6. (b) 140250 7. (c) Solution: Pmt = -30000, n=35, I =8%, mode = begin, FV = 5583064.439 Pmt = 300000, n =15, I =6%, mode = begin, PV = 3088495.176 52

5583064.439 – 3088495.176 = 2494569 8. (a) Solution: End/Begin 25 Step-1: Calculate the FV of expenses 6% Set 300000 N 0 I PV (solve) = 1287561.216 PMT 1 FV 1 P/Y C/Y Step-2:Calculate the corpus required Begin 15 (75-60) Set 3.77358% ((10-6)/1.06) N (Solve ) = -15093801.73 I -1287561.216 PV PMT 0 FV 1 P/Y 1 C/Y Step-3: Annual Savings needed to accumulate the required funds for retirement Set Begin N 25 (60-35) I 10% PV 0 PMT FV (solve) = 139522.5974 P/Y 15093801.73 C/Y 1 1 53

9. (d)Solution: Least of 10 x 8400 =84000 Actual received = 36000 Statutory limit =300000 13 x 40 = 520days, actually taken 150 days, 520 – 150 = 370, As per act 13 x 30 = 390, therefore balance 390 – 370 = 20, 8400 x 20/30 =5600. 10. (c ) 11. (b) ₹247,782 from 1st April 2014 in the year 2014-15 The Rule of Partial Withdrawal from PPF A/c:Anytime after the expiry of five years from the end of the financial year in which the initial subscription is made, the subscriber can partially withdraw but not more than fifty percent (50%) from the balance that stood to his / her credit at the end of the fourth financial year immediately preceding the year of withdrawal or at the end of the preceding financial year whichever is lower, less the loan amount (if any). Only one withdrawal is allowed per financial year. Time Rule: Initial Subscription Date1st April, 2008(year of initial subscription: 2008-09) Expiry of 5 years from the end of FY of initial subscription31st March 2014 Hence, Year of withdrawal to be 2014-15 Amount Rule: Balance at the end of 4th FY ₹4,95,564 preceding 2014-15, i.e. at the end of year 2010-11 or as on 31st March 2011 50% of this balance (1) ₹247,782 Balance at the end of preceding FY, ₹6,45,293 50% of this balance (2) 322,647 Lower of [1] and [2] ₹247,782 From 1st April, 2014 in the year 2014-15 12. (d) Solution 42000 x 12/ 70% = 7.2 lakhs 54

13. (b) Solution Mode = end, n = 15, I = 8%, PV = -280000, FV = 888207.3520, 80% x 888207.3520 = 710566 14. (c) Solution FV =500000/80% = 625000 Mode = end/begin, n = 5, PV = -400000, FV = 625000, I = 9.33% 15. (d) Solution: Mode = begin, PV = -72000, n = 7, I =5%, FV = 101311.2304, P/Y= 1, C/Y=1 After 7 years when investment is made for 3 years PV = -101311.2304, n = 3, I = 5%, FV (solve) = 117489.9671, P/Y= 1; C/Y=2 Amount accumulated at the end of 15 years, PV = -117489.9671, n = 5, I = 6%, FV (solve) = 158241.9504, P/Y= 1; C/Y=4 16. (d) Solution Mode = end, pmt = -15000, i= 8.25%, n =28, FV = 1491655, Mode = begin, n =22, I = 3.09..%, PV = -1491655, pmt = 91655.75 17. (c) Solution: Net retirement corpus available = ₹28,85,650 RRR =2.84360{(8.5-5.5)/1.055} Monthly amount available for post-retirement living expenses Set Begin; N=252 {21(80-59)*12};I= 2.8436; PV=-28,85,650; PMT (solve) = 15133.57, P/Y=12; C/Y=1 18. (c) 19. (b) Solution 11.5 / 10.773 = 1.06748 X 100 = 106.75 20. (d) Leave encashment during service is fully taxable 21. (a) 22. (b) 13.77 lakh 23. (c)Real rate is to be calculated 55

24. (c) 7% Let us suppose the required rate of return is X% X * (1-0.30) = 4.9% Post tax return of 0.7% (1-0.30) should match the inflation (4.9%) to maintain the value of investment X=4.9/0.7 = 7% Hence, the required rate of return to maintain the value of investment = 7% 25. (d) 26. (b) 27 (a) 28. Solution (c) Value of house = ₹95 lakh Loan eligible = ₹76,00,000 (95,00,000*.80) Rate of interest =12.50% N = 15 years Monthly payments under reverse mortgage = ₹14355.48 (Set = begin, n=180 (15*12), i=12.50, PV = 0; FV=-76,00,000; PMT (solve)=14355.4754; P/Y=12; C/Y=12) Note: 1. Calculation: We generally see in mortgage formula, the loan amount is usually considered with negative sign in PV while FV is 'Nil'. In Reverse Mortgage case, the admissible loan amount is taken with negative sign under FV while PV is 'Nil'. Also, 'begin mode' is considered 2. The annuity period is 15 years. Though the annuity payment stops after 15 years, the loan is not payable as long as the mortgagor survives. After the death of the mortgagor and his/her surviving spouse, the lending institution sells the house and recovers loan amount with interest and the balance, if any is paid to the heirs. 29. (a) 30. (b) 31. (B) 4116 Set Begin, N= 84 (7*12), I=10, PV=250,000, PMT (solve) = 4115.99604, FV=0; P/Y=12, C/Y=12 56

SECTION–II 1. A person has availed a housing loan of ₹28 lakh at 9.25% rate of return. Cost of the house is 40 lakhs. The tenure of loan is 18 years. He has present investments worth ₹12 lakh. He will start saving ₹50, 000 per quarter beginning a quarter from now. Investment will generate return of 9% p.a. What will be his net worth 5 years from now? Net worth does not include the house in which he lives. (3 marks) a) ₹3.45 lakh b) ₹13.56 lakh c) ₹6.68 lakh d) ₹7.45 lakh 2. Mr. X has taken a loan of ₹3 lacs today at 11.25%p.a for a period of 60months from a nationalized bank. The first EMI’s will be payable end of every month. The bank has a prepayment penalty clause by which he can prepay the whole outstanding amount by paying a prepayment charge of 2.5%. He intends to prepay his loan after paying 36 installments and wants to know what amount he has to pay towards the foreclosure of this loan.(ignore taxes and any other charges, if applicable) (3 marks) a) ₹149238 b) ₹181105 c) ₹154514 d) ₹143913 3. Mr. Verma is 40 years old. Current household expenses are ₹3,00,000 p.a. Inflation rate is 7% and increase in living standard will be at 1.75% up to retirement. Retirement age is 63 years and Life expectancy is 75 years. He starts investing ₹30,000 p.a. increasing at the amount at a rate of 20% per year. Return on investments is 10% p.a. If after retirement, requirement is 80% of the last spend, what maximum inflation would sustain his corpus till he survives if corpus is invested at 7% p.a.? (4 marks) a) 1.86% b) 4.00% c) 6.07% d) 7.90% 4. Ms. Mamta is 30 and plans to retire at 58 years. Her CFP says that Mamta will require inflation adjusted ₹75000 in the first month after retirement. Inflation is 4%p.a. & return on investment is 6%p.a. What is the retirement corpus required to meet such expense? Will Mamta’s corpus be enough to fund her retirement if she saves ₹2lakhs p.a.(end of year)? Life expectancy 75 years. (4 marks) a) Yes, ₹13,080,232 57

b) Yes, 13,705,622 c) Yes, ₹17,48,948 d) No, ₹15,78,498 5. Sudhakar decides to accumulate 50 lakhs when he retires. He is 30 years old and wants to retire at 55. Interest rate is 9% p.a. & inflation is 5% p.a. compounding to be done on annuity certain basis. If Sudhakar could save only ₹45000 p.a for the first 10 years how much does he need to save for the next 15 years to meet his retirement nest egg? (3 marks) a) ₹71,417p.a. b) ₹85477p.a. c) ₹98450 P.a. d) ₹77,844 p.a. 6. Mr. Laxman, NRI working in USA for 5 years. He is aged 40, and saving ₹8lakhs at beginning of every year for the past 5 years and hopes to save for the next 10 years. He would like to return to India 10 years from now. Life expectancy is 70 years. If the estimated spend is ₹90000 pm. for the family. If inflation is 4% how long will his savings last? Investments earn 6% p.a.? (3 marks) a) The funds will last until Laxman is 81 years old. b) The funds will not be adequate to fund his estimated life span of 70 years. c) The funds will last until Laxman is 72 years old. d) The funds will exhaust before Laxman is 71 years old. 7. A 30 year old person plans to retire at age 50. He has Financial assets worth ₹18 lakhs. His current expenses are ₹27,000 p.m. Post retirement money is required for 30 years and provision to be made for purchase of inflation linked annuity. Average inflation is 7% and annuity is expected to yield 8% p.a. You advise him to invest his current financial assets at 9.5% p.a. If she invests ₹250000 per year at the beginning of the year, what return should be generated on his investment? (3 marks) a) 11.10% b) 19.65% c) 15.41% d) 12.61% 8. Mr. Swapnil will start receiving a pension of ₹12000 pa., exactly 10 years from now. He will receive this pension for 20 years every year end. If interest rate is 12% what is the present worth of his pension? (3 marks) 58

a) ₹32323 b) ₹28860 c) ₹83667 d) ₹32257 9. Ram aged 35 saves ₹30000 per year (at the end) in Bank FD earning 7% p.a. compounded annually until he retires at 60. Life expectancy is 70 yrs. Corpus on the date of retirement? What is the fixed amount he can withdraw at the beginning of each yr. until 70. Presuming he wishes to leave his heirs an estate of ₹150,000. Inflation rate is 5% p.a. (3 marks) a) 1897471, 197970 b) 2147854, 214598 c) 1745897, 192712 d) 1945875, 199145 10. Ms. Madhuri is 40 yrs old to retire at 65. Life expectancy is 75 yrs. She will require ₹15000 in 1st month after retirement. Inflation 4% p.a., rate of return 7%. What is the corpus required to meet the expenses after retirement. Will the corpus be enough to fund her retirement if she saves up to ₹30,000 pa (at the end of the year) (4 marks) a) 1562027, Yes b) 1687498,No c) 1984571, No b) 1568545.961,Yes 11. Niraj wants to retire at 45 and he wants to maintain his present standard of living. He spends 325000 a year. He is expected to live up to 85. Inflation 4% expected return 7% p.a. How can he achieve this? He is at present 30 yr. What is the nest egg required at age 45 and what amount shall he save every year to meet this plan? His present investment is ₹10, 00,000. (4 marks) a) Nest egg and saving required will be 25100065 and 541093 resp. b) Nest egg and saving required will be 12773065 and 438300 resp. c) Nest egg and saving required will be 14182819.48 and 424864.82 resp. d) Nest egg and saving required will be 14773065 and 740530 resp 12. Your client Kalpesh’s current monthly expenditure is ₹25,000. He is 35 years old and expects to retire at the age of 55. His annual expenses are estimated to rise by 5% p.a. and his life expectancy is 75 years. He wishes to maintain the same standard of living after retirement. The rate of return expected on investments before retirement is 10% p.a. and after retirement is 8% p.a. How much does he need to save every month in order to maintain the same standard of living after retirement? 59

a) 16830.64 b) 16964.86 c) 66332 d) 16046.44 13. Mr. X purchased a flat worth ₹50 lakh in February 2007 by availing a housing loan of ₹35 lakh for 15 years tenure at a rate of 9% p.a. The value of this flat as on Feb 2013 has appreciated to ₹90 lakh. What approximate value of home equity can he consider in his flat towards his unencumbered interest after also setting aside 15% of the appreciation value towards taxes and other costs to be discharged on selling the unit? (4 marks) a) ₹52 lakh b) ₹75 lakh c) ₹57.79 lakh d) ₹67.79 lakh 14. Krishna aged 30 saves ₹10000 per year (at the end) in Bank FD earning 8% p.a.comp annually until he retires at 60. Life expectancy is 80 yrs. Corpus on the date of retirement? What amount he can withdraw in the beginning of each year inflation adjusted until 80. Presuming he wishes to leave his heirs an estate of ₹200,000. Inflation rate is constant at 6% pa.(4 marks) a) 1105694, 61375 b) 1132832, 12787 c) 1054875, 108423 d) 1132832, 64709 15. Deepak invested ₹40,00,000 in a 25-year fixed monthly annuity providing a yield of 9.5%. If the start date of the monthly annuity is deferred by 5 years, calculate the amount of monthly annuity? a) 55016.285 b) 52916.54 c) 54584.16065 d) 52532.33 16. Harinder has heard that changes in inflation rate might have a significant impact on his real saving. Currently he can buy the car of his dreams for ₹3 Lakh. He wants to estimate the amount he may need to buy the car in 8 yrs time. The inflation rate for the period are expected to be 5% p.a. for 1st four year, 4% p.a. for next four years value of the car is expected to fall by 10 % every 4 yrs. If he buys the car in 8 yrs then what would be the same real amount that he would need to have saved. (4 marks) a) 345539 b) 400000 c) 383932 60

d) 426591 17. You have been appointed as financial planner of Mr. Ranjit. He is 35 yrs old at present and would be retiring at age 60 yrs. He expects to live up to 80 yrs. You have to plan in such a way that Ranjit starts getting 25000 pm from the very day he retires and keep receiving till his survival. If an expected return is 7%p.a, what is saving required per year to meet his retirement needs? (4 marks) a) 47646, b) 50982, c) 47924, d) 48723.96 18. Mr. Sunil’s present age 25 yrs, wants to retire at 55 yrs.Life expectancy is 70 yrs. He estimates that he will require 35000 pm after retirement. Inflation is 4.5% and return on investment is 6.5%.What will be saving required per annum? (4 marks) a) 63534.35 b) 59656.67 c) 63358, d) 82689, 19. Mr. Bhandari presently 30 yrs old, wants to retire at 45 yrs. He wants to maintain present standard of leaving .He is currently spends around ₹3,25,000 p.a. He expects to survive upto 85 yrs .Inflation is 4% and expected return on investments are 7%. What will be nest egg required at age 45 yrs? What amount, he needs to save every year to meet his plan of retirement. His present savings are around 10 lacs. (4 marks) a) 14182819.49, 454605.35 b) 12773065, 438300 c) 14182819.49, 424864.82 b) 14773065, 740530 20. Amar is 30 years old wants to retire at 45 years. He deposits 25000 p.a. at the year-end for 15 years, earning an interest rate of 5%. He wants 75000 p.a. post retirement. How long will his corpus suffice him? (2 marks) a) 8 years b) 9 years c) 8.59years d) 7 years 61

21. Ritesh who is 32 years old spends annually ₹8.5 lakh towards his household expenses. He expects to retire at 55 years. During this period inflation is expected to be on an average 6% p.a. He wants to cover 30 years’ living expenses for self and spouse. If the inflation in the post- retirement period moderates to an average of 5% p.a. and he expects to generate a return of 8% from his accumulated corpus, what corpus should he accumulate for a comfortable retirement? a) 5.67 crore b) 6.67 crore c) 6.48 crore d) 5.90 crore 22. Sundar is a 30 year-old self-employed youth with a life expectancy of 75 years. He has been saving ₹30,000 per year providing a compounded return of 8% p.a. for last 5 years. Sundar wants to retire after total 25 years of saving. His post retirement funds are expected to earn 6% pa returns and expenses after retirement are fixed at ₹3 lakh per year. He wants to know what rate of return should he get on his current accumulated fund as well as his future yearly saving of ₹30,000 pa till retirement. To fund his retirement needs and leaving Nil estate behind. (Assumption: All computations for interest spend and savings compound annually, assuming beginning of the period investment). a) 11.72% b) 11.69% c) 10.61% d) 13.20% 23. You advise your client aged 31 years to accumulate corpus for retirement. The client already has in Balanced MF scheme ₹1.60 lakh which you advise to extend to achieve this goal. You advise him to start SIP of ₹15,000 per month till his age of 56 years. You advise him to switch outstanding Balanced MF portfolio to Liquid schemes from age 57 until retirement at age 60. How much of the retirement corpus would he be able to accumulate?(Rate of return Balanced MF 9% p.a., Liquid MF 5.5% p.a.) a) 2,22,18,594.65 b) 1,73,59,320 c) 10,001,947 d) 1,89,21,658.80 62

SOLUTIONS 1. (c) Solutions: ₹6.68 lakh Housing loan liability 28,00,000 Tenure18 years Rate of interest 9.25% Financial assets 12,00,000 Annual Savings 2,00,000 Rate of investment growth in assets 9% EMI on housing loan 26,659 (Set End; N=18*12; I= 9.25%; PV -28, 00,000, P/Y =c/Y=12, PMT = Solve) After 5 years Outstanding loan amount 24,14,624 (Amortization: PM1 = 1, PM2 =60, N= 13*12, Rate=9.25%/12, PV=-2800000, PMT 26659.33, Balance Solve (-2414624) Financial Assets30,82,962(Go to CMPD,Set END, N=5*4, I= 9, PV= -12,00,000,PMT= -50000; P/Y=4, C/Y=1, FV Solve ₹3082962) Net Worth of the individual after 5 years 668338 (3082962-2414624) 2. (d) ₹143913 (First compute EMI, Go to AMRT, PM1= 1, PM2=36, N=60, Rate=.9375, PV=- 300000, PMT=6560.19, Bal Solve= ₹140403.08 Add 2,5% penalty to it to foreclose the loan) 3. (c) 6.07% Solution: Present age 40 years Retirement Age 63 years Post Retirement survival period 12 years (75 – 63) Corpus accumulated on Retirement 18906713 Growing annuity with PMT of ₹33000 (30000*1.10) Rate on investment= 10%, Growth rate is 20%. Number of years 23)(30000*(1+10%)*((1+10%)^(63-40)-(1+20%)^(63-40))/(10%-20%)) Current expenses 3, 00,000 Inflation 8.75% Expenses on retirement 20,65,353 (Set End, i=8.75%, n=23 (63-40), PV=3,00,000, FV=solve, P/Y=C/Y=1) 80% of last spend 16,52,283 (80% of 20,65,353) Expected (real) rate of return for inflation-linked annuity = 0.88% (Set = begin, n=12, PMT= - 1652283, PV=18906713, I =solve)) 63

Returns from corpus post-retirement 7.00% p.a. Maximum Inflation for a 12 years' inflation-linked annuity 6.07% p.a. (1+7%)/(1+0.88%)-1 4. (a) Solution: Current Age 30 years Retirement Age 58 years Life expectancy 75 years Post Retirement Period 17 years Expenses in the first month of 75,000 retirement Inflation 4% Investment return 6% Real Rate of return 1.9230769% (6%-4%)/1.04= 1.9230769 Corpus required 13,080,231.62 Set Begin; N= 204 (17 * 12); I=1.9230769; PV = Solve; PMT = -75,000; P/Y= 12 Funds that can be 13,705,622.32 C/Y=1; PV = Solve accumulated on saving ₹2,00,000 p.a. Set End ; N=28, I=6%;PMT = -2,00,000; 5. (a) Solution Step-1: Calculate the amount accumulated by saving ₹45,000 p.a. for 10 years Set Begin N 10 I 9 PV 0 PMT FV (solve) -45000 P/Y 745,213 C/Y 1 1 Set Begin N 15 I9 PV -745,213 64

PMT (solve) -71416.60 FV 50,00,000 P/Y C/Y 1 1 6. (c) Solution Begin Step-1: Amount accumulated by saving ₹8,00,000 15 6% Set N -800,000 I 19738022.46 PMT FV (SOLVE) Step 1 Amount accumulated by saving ₹8,00,000 Set Begin N 269.3 I (6%-4%)/1.04 =1.923076923 P/Y 12 PMT -90000 PV -19738022 Time the corpus will last is = 269.3 months= 22.44 years Amount needed starting from age = 50 years Corpus will last until = 50 +22.44 = 72.44 years 7. (d) 12.61% Solution : Current age= 30, Retirement age = 50, Retirement period =30 years. Current expenses= ₹27000 p.m. or ₹324000 p.a. Annuity rate expected is 8%, Inflation is 7%, FV of present expenses= PV=-27000, N= 20, Rate=7% FV=104481 Corpus required >Pmt= 104481, Begin, Real Rate= .93% N=30 *12, p/y =12 Compute PV=32833476 Current investments ₹18,00,000 invested at 9.5% will become ₹11054902 in 20 years Balance corpus to be accumulated is ₹21778574 (32833476-11054902) (FV =21778574, N= 20, Begin mode, -250000 Pmt , Compute Rate= 12.61% 65

8. (b)Solution Mode = end, I = 12%, n = 20, pmt = 12000, PV = 89633, Mode = end, I =12%, n = 10, FV = 89633, pv= 28859.5 9. (a) Solution: set = end, n = 25 (60-35), I = 7%, PMT= -30,000; FV = 1897471, First we need to discount + 1,50,000 for 10 yrs. @ 7% p.a. As inflation is constant at 5% during pre and post retirement phase, calculate real rate of return ( ) , RRR = (7-5)/1.05 =2/1.05 =1.90476% Set: Begin; n=10 (70-60), I = 1.90476; PV = (-1897471 – 76252), PMT = 197970. 10. (d) Solution: Calculate the retirement corpus accumulated by saving ₹30,000 p.a. (end of year) Set = End; N= 25; I =7%; PMT = -30,000; FV (solve) = 1897471.131; P/Y=C/Y=1 Calculate the retirement corpus required Set = begin; N=10*12; I=2.8846 {7-4)/1.04}; PMT= 15000; PV (Solve)=1568545.961 P/Y=12; C/Y=1 11. (c) Solution: Step-1: Calculate the inflation adjusted expenses at retirement (age 45) Set Begin; N=15; I =4%; PV=-325000, FV (solve) = 585306.64 Step-2: Calculate the amount of retirement corpus (nest egg) required Set Begin; N= 40 (85-45); I= 2.8846 {7-4)/1.04}; PMT = -585306.64;PV (solve) = 14182819.48 Step-3: Calculate the amount of savings required per year Set begin; N= 15 (45-30); I= 7%; PV= -10,00,000; FV = 14182819.48; PMT(Solve) = 424,864.82 12. (a)Solution: Step-1: Calculate the inflation adjusted expenses at retirement Set Begin; N=20; I=5%; PV=25,000; FV (solve) = 66332.44263 Step-2: Calculate the retirement corpus required Set = Begin; N=240 (75-55)*12; I=2.85714 {(8-5)/1.05}; PMT= 66332.44263; PV(solve)= 12185166.66 ; P/Y=12; C/Y=1 Step-3: Calculate the amount of monthly savings required per year to build the retirement corpus Set=Begin; N=240 (55-35)*12; I=10; FV=12185166.66; PMT (solve)= 16830.65; P/Y=12 C/Y=1 66

Monthly savings required to build corpus = 16830.65 13. (c)₹57.79 lakh Solution: EMI on housing loan ₹35499 (Set End; N=180 (15*12); I=9%-PV= 35,00,000, PMT(solve)=35499; P/Y=C/Y=12) Instalments paid till Feb 2013 Outstanding loan amount till Feb 2013 ₹2621249 (Go to Amortization (AMRT), PM1=1, PM2=72, N=180, I=.75%, PV=-3500000, PMT=35499.33, Bal Solve=2621249) Current Value of the flat ₹90,00,000 Appreciation Value of the flat ₹40,00,000 Amount towards taxes ₹600000(15% of ₹40 lakh) Home equity in the flat ₹5778751 (9000000-2621249-600000) 14. (d) Solution: Mode = end, n = 30, I =8%, pmt = -10000, FV = 1132832. We need to calculate the Pv of state () Mode = begin, n =20, I = 1.88%, PV = -(1132832-42910), Pmt = 64709 15. (b) Solution Amount of investment = 40,00,000 Interest rate = 9.5% Deferment period = 5 years Amount available at the time of the start of annuity = 6296954.96 (set begin/end; n=5, I=9.5%; PV = 40,00,000; FV (solve) = 6296954.964; P/Y=C/Y=1) Period of monthly annuity =300 months (25*12) Amount of monthly annuity =(set begin; N=300; I=9.5, PV= 62,96,954.964; PMT (solve) = 52916.546; P/Y=12, C/Y=1) 16. (a) Solution: Mode = end, PV = -300000, n = 4, I = 5%, Fv = 364651.8750 PV = - 364651.8750 x 0.90, n = 4, I = 4%, FV = 383932, Amount needed as value of car will reduce by 10% = 345539 17. (d) Solution Mode begin, n = 20 x 12, I = 7%, pmt = -25000, PV (solve) = 32,97,465.633; P/Y =12; C/Y=1 Mode = begin, n = 25, I = 7%, FV = 3243372.611, pmt (solve) = 48723.96; P/Y=C/Y=1 67

18. (b) Solution: Step-1: Calculate the amount of retirement corpus required Set Begin; N= 180 (70-55)*12; I= 1.91387 {(6.5-4.5)/1.045; PMT =-35000; PV (solve)=5487771.318; P/Y=12; C/Y=1 Step-2: Calculate the amount of savings required to build that corpus Set = Begin; N=30 (55-25); i= 6.5%; FV=5487771.318; P/Y=C/Y=1; PMT (solve) = 59656.67 19. (c) Solution: Step-1: Calculate the inflation adjusted expenses at retirement Set Begin, n= 15 (45-30), I= 4%, PV=-3,25,000, FV(Solve)=585,306.64; P/Y=C/Y=1 Step-2: Calculate the retirement corpus required (nest egg required at age 45) Set Begin, n= 40 (85-45), i=2.8846{(7-4)/1.04}; PMT = 585,306.64, PV (solve) =14182819.49; P/Y=C/Y=1) Step-3: Calculate the amount of savings required per year Set Begin, n=15 (45-30), i=7%, PV=-10,00,000, FV=14182819.49, P/Y=C/Y=1; PMT(solve)=424864.82 20. (c)Mode = end, n = 15, pmt = -25000, FV = 539464.09 Mode = begining, I = 5%, pmt = 75000, PV = -539464.09, N =8.59 years 21. Solution (B) Step 1: Calculate the amount of inflation adjusted expenses during retirement Current household expenses = ₹8.5 lakh Inflation in pre-retirement period = 6% Inflation adjusted expenses expected on retirement =32,46,787.212 (set Begin, n= 23 (55-32), i=6%; PV=8.5 lakh, FV(solve) = 32,46,787.212 ;P/Y=C/Y=1) Step 2: Calculate the amount of retirement corpus required Real Rate of Return = 2.8571 {(8-5)/1.05} Retirement corpus required = 6.67 crore (Set Begin, n= 30; i= 2.8571 {(8-5)/1.05}, PMT = 32,46,787.212; PV(Solve) = 666,82,152.88; P/Y=C/Y=1) 68

22. Solution (b) Pre-retirement investment rate = 8% Post retirement investment rate = 6% Fixed expenses during retirement = ₹3,00,000 Retirement Age = 50 years [he wants to retire after 25 years of saving and he has been saving since last 5 years, he is current 30 years, so retirement age =50 (30+20)] Retirement corpus required = ₹40,65,107.25 Set Begin; N= 25 (75-50), i=6%, PMT = 3,00,000; FV=0 (he doesn’t want to leave any estate); PV (solve) = -40,65,107.25; P/Y=C/Y=1 Amount accumulated by saving ₹30,000 p.a. for last 5 years = {Set Begin; N=5, I=8; PMT=30000; FV(solve)= 190077.8711; P/y=C/y=1} Rate of return required: Set – Begin, n = 20, Pv = -190077.8711, Pmt = - 30000 Fv = 4065107.25, I = Solve = 11.69% 23. Solution (a) Step 1 Calculate the amount of corpus accumulated at the end of age 56. Amount currently accumulated in balanced MF scheme = ₹1,60,000 Rate of return on balanced MF scheme = 9% Accumulated amount in balanced MF scheme at the end of age 56 =1,73,59,320 Set Begin; N= 300 (56-31)*12; I = 9; PV = 1,60,000; PMT =15,000; FV(Solve)= 1,73,59,320; P/Y=12; C/Y=1 Balance at the end of age 57 (amount to be switched to Liquid Fund) =1,89,21,658 (17359320 *1.09) Amount accumulated at the end of age 60 years in Liquid scheme = 2,22,18,594.65 Set Begin; N=3, i=5.5; PV=1,89,21,658; FV(solve) =2,22,18,594.65 69

SECTION–III 1. Navneet is 42 years old, earns and spends ₹8,50,000 annually to maintain his family. He expects his expenses to rise by 8% every year. He has not saved anything for his retirement so far. He has a second house which will start generating rental income of ₹2,60,000 p.a. immediately. The rental income also increases by 8% every year. If he starts investing annual rental income in an investment yielding 10% p.a. at the end of every year, how many years do you think his corpus will last taking the received rents post retirement in to account? He retires at age 60. (4 marks) a) Over 4 years b) Over 9 years c) Over 8 years d) Over 3 years 2. Manoj 30 yrs employee earning salary of ₹300000. He started saving 10 % of his salary, at the end of the year, in a saving plan which yields 6% interest p.a. His salary increases by 5% pa. If Manoj intends to prepone his retirement to the age of 55 yrs. and needs to have the same amount of accumulated saving as at the age of 60 yrs. What percentage of his salary should he start saving to achieve his goal? (4 marks) a) 14.04% b) 3.56% c) 15.70% d) 6.70% 3. Mr. Sharma invested annually ₹2,00,000 towards his retirement in an aggressive fund from his age 40 onwards. After initial high returns, the fund could generate return of just 3.5% p.a. in 10 years. He can direct a higher amount towards retirement goal in the remaining 10 years of retirement. You advise him to switch half of the accumulated funds along with yearly investment in a debt fund with indicative return of 8% p.a. in the future. To achieve a target corpus of ₹1.2 crore. What revised amount should be invested every year if the future expectation from aggressive fund is 11% p.a.? (4 marks) a) ₹5.00 lakh b) ₹4.87 lakh c) ₹1.06 lakh d) ₹3.79 lakh 4. An annuity product is designed in such a way that it gives first cash flow at 8% of the corpus at the end of first year and thereafter every year in the form of growing annuity at the rate of 70

5%. If the cash flows are guaranteed for 15 years, what rate of return is obtained on the corpus invested? a) 6.80% b) 6.41% c) 5.07% d) 5.80% 5. Mr. Thapar has just retired and has accumulated ₹1.65 crore as retirement corpus. His current monthly expenses are ₹85,000 which he needs inflation adjusted for 25 years. If he considers average inflation to be 5% p.a. from now onwards, what rate of return from a 25 year annuity, payable annually and deferred by one year, should meet his goal? a) 3.67% b) 8.67% c) 9.76% d) 8.86% 6. A retired couple has fixed pension of ₹35,000 and their current living expenses are ₹45,000 p.m. They do not have any other source of income. They have consulted you (financial planner) and you advise them to avail a loan under reverse mortgage which is an eligible lump sum of ₹50 lakh for 15 years at 12.5% p.a. interest. The annual interest is calculated after every 12 months on the pre-standing balance and added to the outstanding loan amount. You invest the available amount after withholding the excess normal expenses for the first year and considering 6% inflation thereafter at the beginning of every year. If the investment yield is 9% p.a., by what amount outstanding loan would exceed investment after 8 years. a) 56.40 lakhs b) 53.25 lakhs c) 33.54 lakhs d) 71.88 lakhs 7. Mr. Gupta purchased a 25-year immediate annuity plan which provides an annual stream of income, increasing year-on-year at 5%. He is due to receive 5th installment of ₹4.50 lakh which is 6% of the balance corpus remaining in annuity. He wants the term of the annuity to increase. He estimates that ₹3.75 lakh would be sufficient for his current living expenses. He proposes this to the annuity provider with other terms remaining as originally agreed. If the yield of the annuity is 7.5% p.a., how many more installments would get added in the restructured annuity than the original? 71

a) 3.59 installments b) 6.36 installments c) 5.59 installments d) 7.39 installments 8. Mr. Ahuja just retired has accumulated ₹55 lakh. He invests this corpus in an investment instrument giving return of 8% p.a. His current annual household expenses are ₹6.5 lakh, escalating at inflation of 6% p.a. He would rent out his other fixed property at an expected annual rent of ₹2.20 lakh, the rentals increasing at 6% p.a. The balance expenses are met by withdrawing from the invested corpus. The commercial property, currently valued at ₹60 lakh, is expected to appreciate at 8% p.a. He expects to sell the property after 15 years to create a fresh corpus for his living expenses. How long the total funds available are expected to last after 15 years? a) 16 years 8 months b) 16 years 1 month c) 15 years 2months d) 15 years 8 months 9. Rohit, aged 29 years, have contacted you for planning his retirement. His monthly household expenses are ₹40,000 p.m. Rohit wishes to retire at his age 58 and sustain 70% of pre- retirement household expenses, inflation adjusted, till his lifetime of 75 years. He has two children for whom he wishes to have a provision of gifting ₹50 lakh per child and an additional ₹25 lakh towards charity to an Old Age Home at Rohit’s age of 70 years. The sums are at absolute values then. He also wish to provide in the corpus an additional ₹10,000 per month (current costs) towards healthcare after Rohit’s age of 70 years. You estimate the required corpus, considering the same shall be invested in investment yielding 7% p.a., to be _________(consider inflation at 5.5% p.a.). a) 3.19 crore b) 4.03 crore c) 2.90 crore d) 5.12 crore 10. Ms. Bhawna, aged 34 years, has plans to retire early from service at her age of 55 years. Her current household expenses are ₹70,000 p.m. Her retirement corpus has been estimated considering her current living expenses, her life expectancy as 85 years, investment rate of 7% p.a., inflation at 5.5%p.a. pre-retirement and an average inflation of 5% p.a post retirement. How much curtailment of expenses in the first year of retirement is needed, if provision is made for 5 more years of expected life and investment rate of return is considered to be 6%? a) 23% curtailment b) 12% curtailment 72

c) 14% curtailment d) 10% curtailment 11. A retiree of age 60 wants to enter into the reverse mortgage scheme by mortgaging his self- occupied house which is valued at ₹80 lakh. An approved lending institution agrees to provide periodic monthly payments under the scheme considering a loan to value ratio of 80% and at a rate of interest of 13.75% p.a. If the retiree opts for a 15- year term of reverse mortgage, what fixed periodic monthly payments he stands to receive under the scheme? a) ₹13,379 b) ₹10,703 c) ₹10,826 d) ₹13,532 12. A retiree of age 65 has fixed pension of ₹15,000 per month. His household expenses have exceeded his pension of late and are ₹16,000 per month now. He has approached an approved lending institution under Reverse Mortgage Scheme. He is offered fixed monthly payments for 15 years at a rate of interest of 13.75% on ₹64 lakh eligible value of his home. He meets his annual expenses as increased by 6% inflation every year and invests the excess amount from his two fixed annuities, fixed pension and reverse mortgage stream, in an investment yielding 10% p.a. at the end of every year starting from this year onwards. You assess at the end of five years thus accumulated fund against the total liability under Reverse Mortgage and find that ______. a) ₹3.34 lakh net liability due to Reverse Mortgage Loan b) ₹3.10 lakh net liability due to Reverse Mortgage Loan c) ₹3.51 lakh net liability due to Reverse Mortgage Loan d) ₹66,097 net liability due to Reverse Mortgage Loan 13. An annuity product AA at ₹8640 per annum per Rs.1.00 lakh of purchase value offers annuity for life with a provision of 50% of the annuity payable to spouse during his/her lifetime on death of the annuitant. Another annuity product BB at ₹7010 per annum per Rs.1.00 lakh of purchase value (with return of purchase price), offers annuity for life with a provision of 100% of the annuity payable to spouse during his/her lifetime on death of last survivor. Today your client and his spouse have respectively 20 and 25 years more expected life. You estimated returns from product AA & BB product, to arrive at a right selection for your client. a) BB; it offers 48 basis points/ annum better than AA b) AA; it excess cash flow invested at conservative 8% p.a. c) AA; if offers 41 basis points/ annum better than BB d) BB; it offers 84 basis points/ annum better than AA 73

14. Sundar is a 30 year-old self employed youth with a life expectancy of 75 years. He has been saving ₹30,000 per year providing a compounded return of 8% p.a. for last 5 years. Sundar wants to retire after total 25 years of saving. His post retirement funds are expected to earn 6% pa returns and expenses after retirement are fixed at ₹3 lakh per year. He wants to know what rate of return should he get on his current accumulated fund as well as his future yearly saving of ₹30,000 pa till retirement to fund his retirement needs and leaving Nil estate behind. (Assumption: All computations for interest spend and savings compound annually, assuming beginning of the period investment). Interest rate : equity MF 14% p.a. Debit MF=9% p.a. risk free 7.5% p.a. a) 11.72% b) 11.69% c) 10.61% d) 13.20% 74

SOLUTIONS 1. (b) 9 years. Solution: Current expenses 850000 Rate of increase of expenses 8% Rent received from renting 260000 second house Rate of increase of rent 8% Investment yield from investing 10% rent Accumulated value of investment 20330671.59 FV of ₹260000 with growing at age 60 annuity formula} =260000*(((1.1)^18- (1.08)^18))/2% Expenses required at age 60 (3,396,616.57) Set Begin, N= 18, I=8%,PV=850000, FV(Solve) Expenses covered by rent (1,038,965.07) Set Begin, N= 18, received at age 60 I=8%,PV=260000, FV(Solve) Balance expenses to be drawn (2,357,651.50) = 3,396,616.57- 1,038,965.07 from corpus Number of years the corpus 9.293919418 Set Begin, n=solve, would last i=RRR (10-8)/1.08)=1.8519%; PMT=(-)2,357,651.50; PV=20330671.59 2. (c) Solution: = 30000 x [(1.06)^30 – (1.05)^30] / (0.06 -0.05) = 4264646.395 4264646.395 = x [(1.06)^25 – (1.05)^25]/ (0.06 – 0.05) =47096.32336 47096.32336 / 300000 = 15.698% Solution: (B) 3. (d) Solution: Accumulated value of investments ₹2428398 (FV of 2,00,000 PMT, @3.5% for 10 years at the beginning of the year) Initial Corpus shifted from aggressive fund in debt fund ₹1214199 Remaining corpus in aggressive fund ₹1214199 Accumulated corpus in aggressive fund ₹3447623(FV of 1214199 @11% for 10 years) 75

Total targeted corpus ₹12000000 Remaining to be accumulated through debt funds ₹8552377 (12000000-3447623) We need to compute PMT (FV=8552377, Rate=8%, N=10, Bgn Mode, PV=-1214199 Compute PMT=379087) 4. (a) Suppose the corpus invested = ₹100 Cash flow at the end of first year = 8% Annuity is growing at the rate of 5% every year Guaranteed period of annuity = 15 years Corpus invested= 100 Using Cash Editor Function 1 -100 9 11.2568 28 10 11.81964 3 8.4 11 12.41063 4 8.82 12 13.03116 5 9.261 13 13.68271 6 9.72405 14 14.36685 7 10.21025 15 15.08519 8 10.72077 16 15.83945 IRR (solve) = 6.8034% 5. (d) Amount of annual current expenses = ₹10,20,000 Rate of return from annuity =3.67292117 (Set= end, n=25; PMT= -10,20,000; PV = 1,65,00,000; FV=0; P/Y=C/Y=1) here we have taken set as end as it is mentioned in the question that annuity is deferred by one year. Rate of 25 years level annuity of which level payment pre-5% growth is ₹1,020,000. Then, Annual Growth of 5% built into this annuity to make it growing annuity of which first payment is ₹1,020,000. So, real rate of return (RRR) = 3.67292117% (inflation adjusted return) The formula for RRR =[ To calculate the nominal rate = {(1+RRR) * (1+inflation rate)}-1 = (1.03673 * 1.05 )-1 = 8.8567% 6. Solution: (a) 76

Current annual living expenses = 45,000 * 12 = 5,40,000 Step-1: PV of 6% of escalated expenses discounted at 9% for 8 years = ₹39,25,989.40 (set begin, n=8, i= 2.830188679 (9-6)/1.06, PMT=-540,000; PV (solve) = 39,25,989.40; P/Y=C/Y=1) Annual pension = 35000*12 = 420,000 Step-2: PV of fixed pension discounted at 9% for 8 years = ₹25,33,840.191(set begin, n=8, i= 9, PMT=-420,000; PV (solve) = 25,33,840.191; P/Y=C/Y=1) Step-3: PV of additional expenses recovered from RM loan disbursed =Step 1 – Step 2 = 39,25,989.40 - 25,33,840.191= 13,92,149.209 Loan eligible under reverse mortgage = 50,00,000 Step-4: Balance loan amount to be invested for 8 years at 9% p.a.= 50,00,000 - 13,92,149.209(Step 3) =36,07,850.79 Step-5: Accumulated value after 8 years = 7188868.701(Set begin, n=8, i=9, PV= -36,07,850.79; FV (solve) =7188868.701; P/Y=C/Y=1) Since the annual interest is calculated after every 12 months on the pre-standing balance and added to the outstanding loan amount, Step-6: The outstanding loan amount at the end of 8 years = 1,28,28,922.57(Set end, n=8, i=12.50%; PV=-50,00,000; FV(solve)=1,28,28,922.57; P/Y=C/Y=1) Step-7: Difference between loan liability and investment =Step 6 – Step 5 = =1,28,28,922.57 - 7188868.701 = 56,40,053.869 7. (c) 5.59 installments 5th cash flow stream due to receive = ₹4,50,000 (which is 6% of balance amount) Balance corpus remaining in annuity =₹75,00,000 (450,000/6%) Revised withdrawal amount of 5thinstallment = ₹3,75,000 Interest rate = 7.5% Growth in annuity as agreed = 5% Outstanding corpus after paying 5thinstallment (out of 25) = 75,00,000 – 3,75,000 = 71,25,000 Real rate of return = (7.5-5)/1.05 = 2.38095 Number of years the corpus to last beginning 6thinstallment =25.59(set begin; i=2.38095; PV=- 71,25,000*1.075; PMT=3,75,000*1.05; P/Y=C/Y=1; N(solve)=25.59) Total installments including already 5 paid = 25.59+5 = 30.59 Increase in installments = 5.59 installments (30.59-25) 8. Solution: (d) 15 years 8 months Step-1: PV of 6% increasing expenses for 15 years at 8% interest rate = 7946409.548 (set end, n=15, i=1.8867924 {(8-6)/1.06}; PMT =-613207.5472 (-6,50,000/1.06); P/Y=C/Y=1; PV(Solve) = 7946409.548) 77

Step-2: PV of 6% increasing rental for 15 years at 8% discount rate = 2689554.001 (set end, n=15, i=1.8867924 {(8-6)/1.06}; PMT =-207547.17 (-2,20,000/1.06); P/Y=C/Y=1; PV(Solve) = 26,89,554.001) Drawn from corpus in 15 years = 7946409.548 (step 1) - 26,89,554.001(step 2) = 52,56,855.547 PV of balance corpus (on investing) = 55,00,000 – 52,56,855.547 = 243,144.453 Accumulated investment after 15 years = 7,71,295.3241(set end, n=15, i=8%, PV=243144.453, FV(solve)=; P/Y=C/Y=1)-------------------------------------------(A) Value of commercial property now = 60,00,000 Valuation of commercial property after 15 years = 1,90,33,014.6(set end, n=15, i=8%, PV=60,00,000, FV(solve)=; P/Y=C/Y=1)--------------------------- (B) Total fresh (revised)corpus after 15 years =(A) + (B) =771295.3241 + 19033014.60 = 19804309.92 Expenses (inflation adjusted) required after 15 years = (set end, n=15, i=6%, PV=-6,50,000; FV(solve)= 1557762.826 ; P/Y=C/Y=1) Period up to which the revised corpus would last = 15.6957 (15 years 8 months) (set end; i=1.8867924 {(8-6)/1.06}; PMT= 14,69,587.572 (1557762.826/1.06); PV(Solve)= 19804309.92; P/Y=C/Y=1; N(SOLVE) = 15.6957) Period upto which the revised corpus would last = 15 years 8 months 9. (a)3.19 crore Current age of Rohit = 29 years Retirement age of Rohit = 58 years Pre- retirement period = 58-29 = 29 years Post retirement period (considering Rohit’s Life expectancy) = 75-58 = 17 years Current monthly household expenses (in today’s value) =40,000 p.m. Monthly Household expenses (inflation adjusted) on retirement (at Rohit’s age 58) = 132275.48(set begin, n=29, i=5.5, Pv=28000 (40,000 *70%), FV(solve) =132275.48; P/Y=C/Y=1) Real rate of return = (7-5.5)/1.055 = 1.42180 Retirement corpus required to provide for expenses (till age 75) =24004385.80(set begin, n=204 (17*12), i=1.42180, PMT= 132275.48; PV(solve) =24004385.80; P/Y=12; C/Y=1)………….Corpus (1) Corpus required to provide for gifting and old age home charity =55,50,149.491(set begin, n= 12 (70-58), i=7, FV=1,25,00,000(50L+50L+25L); P/Y=C/Y=1; PV (solve) = 5550149.491)…………………………Corpus (2) Inflation adjusted health care expenses at age 70 = 89815.4075 (set end, n= 41 (70-29); i=5.5; PV=10,000; P/Y=C/Y=1; FV(solve)=89815.4075 78

Corpus required to proviefor Rohit’s healthcare expenses for 5 years (at age 70) =5206182.89(set begin, n=5*12 (75-70); i=1.42180; PMT=89815.4075; P/Y=12; C/Y=1; PV (solve) =5206182.89 Corpus (at age 58 of Rohit) for expenses required from age 70 to 75 of Rohit= 23,11,607.465 (set begin, n=12 (70-58); i=7%; FV=5206182.89; P/Y=C/Y=1; PV (solve) = 23,11,607.………………………………Corpus (3) Total retirement corpus required at Rohit’s age 58 = Corpus (1) + Corpus (2) + Corpus (3) = 24004385.80 + 5550149.491 + 2311607.465 = 31,866,143 10. (a) 23% curtailment Current annual living expenses= 70,000 *12 = 840,000 Inflation adjusted expenses estimated at retirement = 25,85,716.688 (set begin , n= 21(55-34); i=5.5; PV=-840,000, FV(solve)=25,85,716.688 ;P/Y=C/Y=1) Retirement corpus estimated (considering her life expectancy as 85 years) Inflation expected post retirement = 5% Post retirement period (considering life expectancy as 85 years) = 30 (85-55) Real rate of return = 1.90476 {(7-5)/1.05} Estimated retirement corpus = 59794131.10 ((set begin, n= 30; i=1.90476; PV(solve) =- 59794131.10,PMT=25,85,716.688 ;P/Y=C/Y=1) Retirement corpus required if provision is made for 5 more years of expected life and investment rate is 6% Post retirement period (considering life expectancy as 90 years) = 35 (90-55) Real rate of return = 0.952380 {(6-5)/1.05} Estimated retirement corpus = 77384779.17 ((set begin, n= 35; i=0.952380; PV(solve) =- 77384779.17,PMT=25,85,716.688 ;P/Y=C/Y=1) Curtailment of expenses required on retirement if provision is made for 5 more years of expected life and investment rate is 6%= 23%{1-(59794131/77384779)} 11. Solution: (b) Set Begin(In Reverse Mortgage case, begin mode is considered) N=180 (15*12) I= 13.75 PMT(solve)= 10,703.21 FV=- 64,00,000 (80,00,000*.80) P/Y=12 C/Y=12 Fixed periodic monthly payments he stands to receive under the reverse mortgage scheme = ₹10,703.21 79

12. (c) ₹3.51 lakh net liability due to Reverse Mortgage Loan Value of Reverse Mortgage Loan Eligible = ₹6,400,000 Rate of Interest = 13.75% p.a. Term = 15 years Monthly payments under reverse mortgage = ₹10,703 (set begin, n=180, I=13.75, FV=- 64,00,000; P/Y=12; C/Y=12) Fixed pension =15,000 ₹p.m. Current household expenses = 16,000 ₹p.m. End of year 1 Excess funds available for investment: End of year 1 = 116,439 ₹((10703+15000)-16000)*12 End of year 2 Household expenses in the 2nd year = 16,960 p.m. (16000*(1+6%) Excess funds available for investment: End of year 2 = 233,001 ((10703+15000)- 16960)*12+116439*(1+10%) End of year 3 Household expenses in the 3rd year = 17,978 ₹= 16960*(1+6%) Excess funds available for investment: End of year 3 349,008 ₹((10703+15000)- 17978)*12+233001*(1+10%) End of year 4 Household expenses in the 4th year = 19,056 (17978*(1+6%) Excess funds available for investment: End of year 4 = 463,673 ((10703+15000)- 19056)*12+349008*(1+10%) End of year 5 Household expenses in the 5th year = 20,200 {19056*(1+6%)} Excess funds available for investment: End of year 5 = 576,083((10703+15000)- 20200)*12+463673*(1+10%) Mortgage Loan and interest outstanding: End of Year 5 = 926,830 (Set= begin, n=60(5*12); i=13.75; PMT=-10,703; FV(Solve)=926,830.3029; P/Y=12; C/Y=12) Net Liability due to Reverse Mortgage Loan = 350,747 (926830-576083) 13. (a) BB; it offers 15 basis points/ annum better than AA Annuity from product AA. 80

Cash Flow Value Year -100000 1 8640 2 8640 3 8640 4 8640 5 8640 6 8640 7 8640 8 8640 9 8640 10 8640 11 8640 12 8640 13 8640 14 8640 15 8640 16 8640 17 8640 18 8640 19 8640 20 8640 21 4320 22 4320 23 4320 24 4320 25 4320 26 Calculate IRR = 6.53% 81

Annuity from product BB. Value Cash Flow -100000 7010 Year 7010 1 7010 2 7010 3 7010 4 7010 5 7010 6 7010 7 7010 8 7010 9 7010 10 7010 11 7010 12 7010 13 7010 14 7010 15 7010 16 7010 17 7010 18 7010 19 7010 20 7010 21 7010 22 7010 23 100000+7010 24 25 82 26 Calculate IRR = 7.01%

Difference in yield offered by both the product: 0.48 (7.01 – 6.53) 14. 11.69% Step 1: Calculate the amount currently accumulated after saving ₹30000 p.m. for last 5 years. Set Begin, N=5, I=8, PV = 0, PMT= -30000, FV (solve) = 190077.8711; P/Y=1, C/Y=1 Step 2: Calculate the retirement corpus required Set Begin, N=25(75-50), I=6, PV (solve) = 40,65,107.258, PMT= -300000, FV = 0; P/Y=1,C/Y=1 Step 3: Calculate the rate of return Set Begin, N=20, I (solve) = 11.69, PV= -190077.8711, PMT = -30000, FV=40,65,107.258, P/Y=C/Y=1 83

ADDITIONAL PRACTICE QUESTIONS 1. A person at age 57 has accumulated ₹50 lakh towards retirement funds and opts for premature retirement. He purchases an immediate annuity for a total term of 20 years, a fixed monthly amount for the initial period of 10 years and a provision to double the monthly amount in the second 10-year period. If the minimum yield guaranteed in the annuity is 8% p.a., what monthly amount he is expected to receive in the subsequent 10-year period? 2. Anamika, age 42, would retire at age 60years. She wants to accumulate a fund exclusively for retirement, considering her life expectancy to be 75 years. Her current monthly household expenses are ₹39,000. She wants to get an inflation adjusted monthly income (assume inflation rate as 6%p.a.) to extent of 60% of her present monthly expenses and would not leave any estate in the end. You have advised her to invest monthly in Debt MF and Equity MF in the ratio of 30:70 till she completes 55 years. You have further advised her to rebalance the portfolio from the beginning of 56 years in the ratio of 60:40 along with further monthly investment to be in the said revised ratio till she retires. The accumulated funds at the time retirement would be invested in a risk free investment. How much amount should she invest monthly starting from onwards? ( Roi in equity 14% p.a., debt fund 9% p.a. and risk free 7.5% p.a. ) 3. Priya, aged 38 years, is a spinster by choice and a freelance journalist for past 12 years in media industry. Being a freelancer she is more worried about her retirement and ongoing monthly expenses. Now she wants to make an arrangement so that one-third of her present living/personal monthly expenses of ₹30,000 per month can be met for the next 17 years till she stops earning at the age of 55 years, and thereafter the whole of her current living/personal monthly expenses all adjusted to inflation till she is alive. She wants to know what approximate lump sum amount she is required to invest in risk free instruments in order to ensure- such cash flows from the beginning of next month. (Assume Inflation rate as 5% p.a., Risk Free rate as 7.50% p.a and Life expectancy as 75 years). 4. Ankit, aged 29 years wishes to retire at age 58. He wants to supplement his retirement corpus by regularly investing in his PPF A/c ₹15,000 every quarter till its maturity after 4 years, as well as throughout its four extensions each of 5-year blocks. The amounts are proposed to be invested in the first five days of April, July, October and January every financial year beginning immediately. Ankit wants to know the approximate maturity amount of his PPF A/c after the proposed four block period extensions, if the current PPF balance is 290,000. The same would be _______. ( PPF ROI 8.1% p.a. ) 5. You advise your client aged 31 years to accumulate corpus of for retirement. The client already has in Balanced MF scheme ₹1.60 lakh which you advise to extend to achieve this goal. You advise him to start SIP of ₹5,000 every month till his age of35 years, thereafter increase the same to ₹7,500 p.m. till his age 40 years, ₹10,000 p.m. between 40 – 50 years, and ₹15,000p.m. between 50 – 56 years. You advise him to switch 25% of outstanding Balanced MF portfolio every year to Liquid schemes from age57 until full redemption on retirement at age 84

60. How much of the retirement corpus would he be able to accumulate? (Rate of return Balanced MF 9% p.a., Liquid MF 5.5% p.a.) 6. You suggest your client Mr. Chand to limit his annual investment in the PPF A/c in such a way that he invest just ₹150,000 in the beginning of April every in his PPF A/c for remaining 5 years to its maturity excluding this. The current financial year’s deposit of ₹150,000 was done on 1-Dec. The PPF balance as on 31st March of the current FY is 4.27 lakhs. Consider 8% rate of interest effective April 2016, you estimate the gross corpus on maturity after 6 years from now to be ________________. 7. A person invested ₹45 lakh in a 30-year fixed monthly annuity providing a yield of 9% p.a. What will be the amount of monthly annuity if the start date is deferred by 3 years? 8. A 28 year old starts to save for his retirement at the age of 60. You advise him to take maximum advantage of equity in initial stage. The strategy is to invest ₹5,000 per month in equity scheme. After 5 years, start another monthly investment of ₹5,000 in a debt scheme while continuing with equity scheme till 60. At his age of 40, switch 50% of accumulated equity investments to debt scheme while increasing debt investment by ₹10,000 p.m.. At the age of 60, the entire investment is redeemed to buy an inflation adjusted annuity expected to yield 6.5% p.a. If his current expenses are ₹22,000 per month, roughly how many years his corpus will last? Equity - 9.5%, Inflation - 5.5% and Debt - 7.5% 9. A research organization instituted scholarship amounting to ₹10 Lakh / year (End of each year) on a perpetual basis 3 years ago. They set aside a designated corpus for the same in investment yielding 7.5% pa. They want to raise the amount of annual scholarship by ₹5 Lakh per annum while the expected annual yield depressed by 1%. What additional funds need to be infused in the corpus? (End mode to be used) 10. A client invests ₹1 lakh per annum in equity & debt portfolios in 60:40 from his age 36 years. He plans to retire at 60 years. He rebalances the portfolio every 8 years by 10 points in favour of debt. He wants to buy an annuity product for a term of 20 years post retirement yielding 6.5% pa. You estimate the inflation-adjusted annuity in the beginning of each year with equity returns at 10% and Debt at 7.5%. Inflation post retirement is 4.5%? 11. A 25 year old lady plans to retire at 60. Her life expectancy is 85 years and living expenses estimated on her retirement are ₹35000 per month at current cost. Such expenses would be required in line with inflation which is estimated @ 5.5% pa. throughout. The retirement corpus is supposed to be invested in an asset allocation yielding 7.5% pa., If she is starting today with an investment horizon returning on an average 8.5% pre-retirement. What monthly investment is required to achieve this goal? 12. Kapil, age 45 years, wishes to retire at age 60. His currently monthly household expenses are ₹40,000 p.m. He expects his post retirement household/living monthly expenses to be 75% of pre-retirement expenses and he expects to live till the age of 80 years. You advise him to invest the retirement corpus in a pension scheme of a mutual fund yielding 10% p.a. during post retirement period to get such inflation adjusted monthly expenses. What approximate corpus Kapil should have for his retirement 15 years hence to accommodate his post 85

retirement household/living expenses? (Assume this pension scheme would make monthly payments in annuity due mode and inflation is 5.5%). 13. A public sector employee expects to retire after 5 years. He today has a dedicated corpus of 60 Lakh at 9.25% p.a. to fund his 30 years post retirement living expenses. He expects to receive lump sum retirement benefits of ₹20 Lakh and a life long fixed monthly pension of ₹20,000. His current monthly expenses are ₹42,000. If he can contribute towards retirement fund ₹20,000 per month till retirement and expect inflation rate to be 6% p.a. from now onwards. You assume the variability annuity rate of 1.5% over and above inflation for 30 years period post retirement to assess additional corpus required. The same is ____________ 14. A client has 600,000 as salary per year and he starts planning for retirement. He saves 10% of his annual salary in a fund, which would yield 8.5% p.a. He would set aside 2% of his salary every year to take strategic advantage and expects a return of 12% pa and the money from such fund is redeemed and invested in the retirement portfolio every 5 years. What is he expected to retire with 15 years from today. 15. Mr. A has invested annually ₹2.00 lakh towards his retirement in an aggressive fund from his age of 40 onwards. After initial period of investment, the fund could generate return of just 3.5% p.a. in past 10 years. He can direct a higher amount towards retirement goal in the remaining 10 years to retirement. You advise to switch half of the accumulated funds along with fresh investment in a debt fund with indicative return of 8% p.a. in the future. To achieve a target corpus of ₹1.2 crore, what revised amount should be invested every year in debt fund? The future expectation from aggressive fund is 11% p.a.? 16. Om prakash, aged 49 years wishes to retire at age 62. His current annual household expenses are ₹780,000. Post-retirement, he would require 70% of his current personal annual expenses adjusted for inflation in the beginning of first year of his retirement till his life expectancy of 80 years. He wants to leave ₹50 lakh, at then prices, for his children as estate. He wants to know what monthly amount towards his retirement corpus and estate is required to be invested in an Equity oriented MF from today onwards till his retirement. In the distribution phase, the corpus is invested in a Pension fund yielding 100 basis points above risk free rate. Assumption: • Inflation rate @ 5.5% p.a. • Risk free rate of return @ 6% p.a. and Equity mutual fund return is @ 12% (CAGR) p.a. 17. A 30 years old lady plans to retire at 50. She already has financial investments amounting to ₹18 lakh. Her current expenses are ₹27,000 per month. She wants to cover 30 years post- retirement expenses inflation- adjusted by a suitable annuity. Average inflation is considered at 7% p.a. and the annuity is expected to yield 8% p.a. You advise to invest her current financial investments at. 9.5% p.a. If she can incrementally invest ₹2.50 lakh annually, you optimize average rate of return to achieve this goal. The same’ is _____________. 86

18. Your Client started investing for his retirement goal late at age 45. On reaching 55 today he has accumulated ₹35 Lakh which he finds insufficient on reaching age 60 if he draws 5 Lakh pa. Inflation adjusted from his accumulated corpus for 30 years post retirement if the corpus is invested @ 7.5% pa. with inflation of 5.5% pa. If prior to retirement the growth rate is 9.5% is considered for investing already accumulated funds and fresh annual investments of Rs.3.5 lakh, you estimate the period of delay retirement beyond 60 years to be? 19. Mr. X is entitled to a basic salary of Rs.50000 p.m. and dearness allowance of Rs.10000 per month, 40% of which forms part of retirement benefits. He is also entitled to HRA of Rs.20000 p.m. He actually pays Rs.20000 p.m. as rent for a house in Delhi. Compute the taxable HRA. 20. X is employed at Delhi as the Finance Manager of R Company Ltd. The particulars of his salary for the previous year 2016-17 are as under: i) Basic Salary - Rs.30000 ii) Dearness Allowance (forming part of basic salary) - Rs.10000 iii) Conveyance allowance for personal purpose – 5000 p.m. iv) Commission @2% of the turnover achieved which was Rs.2250000 during the previous year and the same was evenly spread -Rs. 45000 v) House Rent Allowance – 15000 p. m. The actual rent paid by him is Rs.10000 p.m. for an accommodation at Noida till 31.12.2016. From 1.1.2017 the rent was increased to Rs.20000 p.m. Compute taxable HRA. 21. R retires on 4.1.2017 after serving XY Company Ltd. For a period of 16 years and 11 months. At the time of retirement his basic salary was Rs.44000 p.m. and he was also entitled to Dearness Allowance of Rs.8000 p.m. On his retirement, he received Rs.600000 as gratuity. Compute the amount of gratuity exempt from tax and the amount to be included in gross salary. He is covered under the payment of gratuity act. 22. R joined the service on 1.6.1998. He retired from his services on 17.11.2016 and received gratuity Rs.1120000. at the time of retirement his basic salary was Rs.70000 p.m. and dearness allowance Rs.35000 p.m.(60% of which was part of salary). Compute the amount of gratuity exempt from tax and the amount to be included in gross salary. He is covered under the Payment of Gratuity Act. 23. An employee, drawing a salary of Rs.5000 p.m. retires from service and becomes entitled to receive pension of Rs.3000 p.m. He gets half of his pension commuted and receives Rs.60000 as lumpsum payment. Henceforth, he shall be entitled to a pension of Rs.1500 p.m. Compute the exemption available under section 10(10A) in respect of the commuted pension. He is also entitled to get gratuity. 24. A retired on 15.4.2016 from B company Ltd. He was entitled to a pension of Rs.4000 p.m. At the time of retirement he got 75% of the pension commuted and received Rs.120000 as commuted pension. Compute the taxable portion of the commuted pension if – a. He is also entitled to gratuity 87

b. He is not entitled to gratuity 25. E, an employee of XYZ Pvt. Ltd. Retired from the company on 30.11.2016. At the time of his retirement, he received Rs.144000 as leave salary from his employer. The following information provided by the employee- 1 Salary at the time of retirement (per month) Rs.9000 2 Period of service 20 years & 8 Months 3 Leave encashment Rs.144000 4 Leave availed while in service 14 months 5 Balance unavailed leave at the time of 16 months retirement 6 Avg. salary for the months of Feb,2016 to Rs.8800 Nov,2016 7 Leave entitlement 1.5 month for completed year of service Compute the amount of taxable leave encashment. 26. R an employee of XYZ Ltd. Retired from services w.e.f. 1.1.2017 after serving for 16 years and 7 months. At the time of retirement he received a sum of Rs.50000 as leave encashment for unavailed leave of 300 days. He was untitled to 40 days leave for each year of completed service. He was getting a salary of Rs.5000 per month at the time of the retirement. He received increment of Rs.500 w.e.f. 1.7.2016. Compute the amount of leave encashment. 27. Businessman wants to achieve the goal of marriage of his daughter after 10 years. The funds required would be Rs. 25 lakh at then costs. He wants to invest monthly for the goal. You suggest an asset allocation strategy where he should invest monthly in equity and debt in ratio 65:35 for 9 years, and shift the entire accumulated amount in these funds to liquid fund in the last year. If the returns expected from equity, debt and liquid funds in this period are 12 % p.a., 9 % p.a. and 5 % p.a., respectively, what approximate amount per month is required to be allocated to equity and debt schemes? 28. You have suggested smith to set aside 10% of his equity MF portfolio(Rs.2500000) for the purpose of his abroad trip after 10 years. Current cost of abroad trip is Rs.1000000 and inflation rate is 5.5% p.a. In addition, you have advised to start monthly investments today in a ratio of 50%: 50% in balanced fund and debt fund for seven years. At the beginning of 8th year, new investment allocation will be in ratio of 30%: 70% and portfolio to be rebalanced in line with new asset allocation for balance term. Calculate monthly investment required for 10 years.(equity MF:11%, balanced MF:9% debt MF:7%) 88

SOLUTIONS 1. In order to calculate the expected annuity to receive in the subsequent 10- year period, we will do reverse calculation. For this we take following assumption. Step-1: For the 1st Ten year if you are likely to receive monthly annuity (PMT) of ₹100, then what is the present value (Today) of the entire cash flow series discounted @ 8%. BGN, N=10*12, I=8, Pmt= 100, PV= Solve (-8,397), P/y=12, C/y=l Step-2: In the subsequent term of Ten year period, if you are likely to receive monthly annuity (PMT) of ₹200 (Annuity amount will be doubled), then what is the present value of the entire cash flow series discounted @ 8%. BGN, N=10*12, I=8,Pmt= 200, PV= Solve (-16,793), P/y=12, C/y=l Step-3: The PV of ₹16,793 is value as on Beginning of second 10 year period which will be further discounted @ 8% to get value as on Today’s date. BGN, N=10, I=8, FV= 16793, PV= Solve (-7,779), P/y=l, C/y=l Step-4: Total value of investment or rather lump sum amount required to invest Today in order to earn monthly annuity of Rs.100 in the 1st 10 year and Doubled annuity of ₹200 in the subsequent 10 year period is ₹16,176 (8397 + 7779). Then with Lump sum investment of ₹50.00 Lakhs today, how much annuity can be earned on monthly basis? Will be as follow: Amount Annuity to earn 16,176 100 50,00,000 Solve (₹30911) (50,00,000 * 100) / (16176) The answer or annuity amount of ₹30,911 indicates monthly annuity to be earned during 1st l0 year period. So as per question language, the annuity amount to be earned in the subsequent 10 year period will be doubled. Then annuity amount in subsequent 10 year period will be ₹61,822 {30,911 * 2). 2. ₹15,143 per month Step-1: Set = BGN, N= 60-42, I = 6, PV = -39000*.60, FV = Solve (66792), P/Y = 1, C/Y=1 Step-2: Set = BGN, N= (75-60)*12, I = ((1.075/1.06)-1)*100, PMT = 66792, PV =' Solve (1,08,46,318), P/Y = 12, C/Y = 1 Step-3: Finding out regular investment (Based on asset allocation) Part 1 of Step 3: Between age 42 to 55 the allocation between Debt: Equity is (30:70) respectively. So in this case we will find future value of each asset class separately. 89

We will consider base of ₹100 per month Future value of Debt instrument with 30% allocation: Set = BGN, N = (55-42)*12, I =9, PMT = 100*0.30, FV= 8,660.75, P/Y = 12, C/Y = 1 Future Value of Equity instrument with 70% allocation: Set = BGN, N = (55-42)*12,1 =14, PMT = 100*0.70, FV= 28,957, P/Y = 12, C/Y = 1 Combined future value of Debt and Equity = 8660.75 + 28957.61 = 37,618.36 Part 2 of Step 3: Between age 56 to 60 (i.e. 5 years, as investment are taking place at the start of the period on monthly basis), portfolio will be rebalanced in ratio between Debt (60%) and Equity (40%). It means that combined value of Debt and Equity of part 1 (Rs.37618.36) will be rebalance between Debt (60%) n Equity (40%) for future calculation. Future value of Debt instrument with 60% allocation: Set = BGN, N = 5*12, I =9, PMT = 100*0.60, PV =- 37618.36 * 0.60, FV= 39,244.60, P/Y = 12, C/Y = 1 Future value of Equity instrument with 40% allocation: Set = BGN, N = 5 *12, I =14, PMT = 100*0.40, PV = = - 37,618.36 * 0.40, FV= 32,381.01, P/Y = 12, C/Y = 1 Combined future value of Debt and Equity = 39,244.60 + 32,381.01 = 71,625.6182 Part 4: In order to calculate monthly starting from onwards will do the following: Monthly Investment Future Value 100 71,625.6182 1,08,46,318 (Required Amount) 100 * 1,08,46,318 / 71,625.6182 = ₹15,143 3. ₹55.40 Lakhs Part-1: Finding out present value of ₹10,000 till retirement age Set BGN Nper 17*12 I ((1.075/1.05)-1)* 100 PV 1,683,002 (A) PMT -10,000 FV P/Y 12 90

C/Y 1 Part-2: Step-1- Finding out future value of Rs.30,000 till retirement age Set BGN Nper 17 I 5.00 PV -30,000 PMT 0 FV 68,761 P/Y 1 C/Y 1 Step-2: Finding out present value of the cash flow at retirement age Set BGN Nper 20*12 I ((1.075/1.05)-1)*100 PV 13,176,129 PMT 68,761 FV 0 P/Y 12 C/Y 1 Step-3: Finding out present value of the cash flow in today’s time (i.e. age 38) Set BGN Nper 17 I 7.50 PV 3,853,399 (B) PMT FV 13,176,129 P/Y 1 C/Y 1 91

Total amount required to fulfill her requirement at age 38 1,683,002 Present value under A 3,853,399 Present value under B 5,536,401 Total amount required to fulfill her requirement (A+B) 4. ₹6145810.151 Current PPF account balance = ₹2,90,000 Amount Invested Quarterly = ₹15,000 Rate of Interest on PPF = 8.1% p.a. Years till due maturity of account = 4 years Number of years in extension blocks = 20 years (4 extensions each of 5-year blocks) Total no. of years for which investment will be made = 24 years Please note that ―PPF interest is calculated monthly on the lowest balance between the end of the 5th day and last day of month, however the total interest in the year is added back to PPF only at the year-end.‖ The approximate maturity amount of Ankit’s PPF account will be: Set End n 24 I 8.1 PV -290000 PMT -63037.5 (:. A) FV (Solve) 6147811.96 P/Y 1 C/Y 1 A:- Balance end of year one if saves 15000 per quarter = 15000 x 4 + 15000 x ( + ) = 63037.5 5. Current Amount in Balanced MF sch. 160,000 Rate of Return of Balanced MF scheme 9.00% % p.a. Balance at the end of age 35 (investing ₹5000 per month for 4 years) = 513,441 (Set Begin, N=48 (4*12), I=9%, PV=-160,000, PMT= -5000, FV(Solve) = 513,441 , P/Y=12, C/Y=1) 92