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BBA/BCOM 2 All right are reserved with CU-IDOL Business Mathematics & Statistics Course Code: BBA102/BCM 102 Semester: 1 SLM Unit: 1,2 e-Lesson: 1 www.cuidol.in Unit 1,2(BBA 102 /BCM 102)

Business Mathematics & Statistics 33 OBJECTIVES INTRODUCTION To make students aware of the uses of In this unit we are going to learn about uses Mathematics in Business. of Mathematics in Business, Simple Interest and Compound Interest. To develop an understanding of simple interest and its uses in business. Under this you will learn how to calculate simple interest and compound interest. To make students understand about compound interest and its uses in business. In this unit you will learn the scope & . compliance of Business Mathematics, Simple Interest and Compound Interest. www.cuidol.in Unit 1,2(BBAA/B1C0o2m/B1C0M2 )102) INSTITUTE OAF lDl ISriTgAhNtCaEreANreDseOrNveLIdNwE iLtEhACRUN-IINDGOL

Topics To Be Covered 4  Introduction of Basic concepts of Business Mathematics  Uses of Business Mathematics  Introduction to Simple Interest and its calculation  Introduction to compound interest and its calculation  Uses of Simple Interest in Business  Uses of compound interest in Business www.cuidol.in Unit 1,2(BBA 102 /BCM 102) All right are reserved with CU-IDOL

Introduction of Business 5 Mathematics Bankers, accountants, and tax consultants all need to become well-acquainted with every aspect of corporate and personal finance in order to deliver appropriate advice and problem solve with customers. Real estate and property professionals also employ business mathematics often when calculating their commission, navigating the mortgage process, and managing taxes and fees upon closing a deal. When it comes to professions that deal more with capital allocation, such as investment consulting and stockbroking, understanding investment growths and losses and making long-term financial predictions is a fundamental part of the daily job. Without business math, none of these jobs could function. www.cuidol.in Unit 1,2(BBA 102 /BCM 102) All right are reserved with CU-IDOL

Mathematical Skills That 6 Will Prepare You for Business Math  Integers Be comfortable reading, writing, and making estimates for whole numbers up to 1,000,000. Be able to add, subtract, multiply, and divide any integers (using a calculator if needed).  Fractions, Decimals, and Percentages Be able to add, subtract, multiply, and divide fractions, simplifying as needed. Be able to calculate percentages. Be able to convert between fractions, decimals, and percentages. www.cuidol.in Unit 1,2(BBA 102 /BCM 102) All right are reserved with CU-IDOL

Continued….. 7  Basic Algebra Be able to solve equations with one or more variables. Be able to calculate proportions. Be able to solve multi-operational equations.  Formulas Be able to correctly apply values and variables to any given formula (e.g. when given the formula for calculating simple interest, I=Prt, be able to input the correct values for P=principal, r=interest rate, and t=time in years to solve for I=interest). These formulas do not need to be memorized.  Statistics Be able to solve for the mean, median and mode of a data set Be able to interpret and understand the significance of the mean, median, and mode.  Graphing Be able to interpret different types of graphs and charts such as bar and line graphs, scatter plots, and pie charts to understand the relationships between different variables. www.cuidol.in Unit 1,2(BBA 102 /BCM 102) All right are reserved with CU-IDOL

Uses of Business Mathematics 10  Measure Business Profits If you want to determine the net profit for a certain time period, you will need to subtract returns, costs to produce an item and operating expenses from your total amount of sales, or gross revenue, during that time. Discounts on products, depreciation on equipment and taxes also must be calculated and subtracted from revenue. To arrive at your net profit, add any interest you earned from credit extended to customers, which is reflected as a percent of the amount each person owes. Your net profit helps you understand if you are charging enough for your product and selling an adequate volume to continue to operate your business or even expand. www.cuidol.in Unit 1,2(BBA 102 /BCM 102) All right are reserved with CU-IDOL

Uses of Business Mathematics  Various application of business mathematics in production 12 1. Cost of manufacturing a product 2. Break-even analysis 3. Quality control 4. Time study 5. Fundamental processes a. Compute break-even point in number of manufactured units b. Compute percent of defective goods c. Use time and study results to compute number of units that can be produced and percent of time on task d. Compute dimensions of packaging containers www.cuidol.in Unit 1,2(BBA 102 /BCM 102) All right are reserved with CU-IDOL

Uses of Business Mathematics 13  Application in purchasing and selling 1. Discounts—trade, chain, cash 2. Selling prices 3. Net profit 4. Fundamental processes a. Compute net price b. Compute trade discount rate c. Compute cash price d. Compute selling price www.cuidol.in Unit 1,2(BBA 102 /BCM 102) All right are reserved with CU-IDOL

Simple Interest 14 When you deposit money in a bank, the bank usually pays you for the use of your money. When you take out a loan from a bank, you have to pay the bank for the use of their money. In both cases, the money paid is called the interest. The Simple Interest Formula is given by Simple Interest = Principal × Interest Rate × Time I = Prt where The Principal (P) is the amount of money deposited or borrowed. The Interest Rate (r) is a percent of the principal earned or paid. The Time (t) is the length of time the money is deposited or borrowed. www.cuidol.in Unit 1,2(BBA 102 /BCM 102) All right are reserved with CU-IDOL

Examples of Simple Interest 15 Example: Sarah deposits Rs.4,000 at a bank at an interest rate of 4.5% per year. How much interest will she earn at the end of 3 years? Solution: Simple Interest = 4,000 × 4.5% × 3 = 540 She earns Rs.540 at the end of 3 years. Example: Wanda borrowed Rs.3,000 from a bank at an interest rate of 12% per year for a 2-year period. How much interest does she have to pay the bank at the end of 2 years? Solution : Simple Interest = 3,000 × 12% × 2 = 720 She has to pay the bank Rs.720 at the end of 2 years. www.cuidol.in Unit 1,2(BBA 102 /BCM 102) All right are reserved with CU-IDOL

Examples of Simple Interest 16 Example: Raymond bought a car for Rs.40, 000. He took a Rs.20,000 loan from a bank at an interest rate of 15% per year for a 3-year period. What is the total amount (interest and loan) that he would have to pay the bank at the end of 3 years? Solution : Simple Interest = 20,000 × 13% × 3 = 7,800 At the end of 3 years, he would have to pay Rs.20,000 + Rs.7,800 = Rs.27,800 www.cuidol.in Unit 1,2(BBA 102 /BCM 102) All right are reserved with CU-IDOL

Examples of Simple Interest 17 Example: Raymond bought a car for Rs.40, 000. He took a Rs.20,000 loan from a bank at an interest rate of 15% per year for a 3-year period. What is the total amount (interest and loan) that he would have to pay the bank at the end of 3 years? Solution : Simple Interest = 20,000 × 13% × 3 = 7,800 At the end of 3 years, he would have to pay Rs.20,000 + Rs.7,800 = Rs.27,800 www.cuidol.in Unit 1,2(BBA 102 /BCM 102) All right are reserved with CU-IDOL

Simple Amount 18 The sum of The simple amount formula is given as the original principal & S  Principal  Interest earned the interest  P  PRT earned  P1 RT  www.cuidol.in where : S = Simple amount P = Principal / Investment R = Rate per annum (year) T = Time in years Unit 1,2(BBA 102 /BCM 102) All right are reserved with CU-IDOL

Difference Between Simple 19 Interest and Compound Interest Simple Interest Compound Interest It is calculated on the total principal amount for the total It is calculated on the principal amount periodically (monthly, tenure. quarterly, half-yearly or annually). The accumulated interest on the principal is not added to the The interest that you accumulate periodically is added to the calculation of interest for the next period. calculation of interest for the next period. The interest earned/paid will not increase even if the The interest earned or paid will increase if the frequency of calculation is done periodically. interest generation or payment is more. The accumulation of interest is slow. The accumulation of interest is fast since you get interest on the growing interest amount as well. Simple interest will not earn you enough for savings and Compound interest will earn you more in savings and investments but will benefit you if you take a loan. investments but will be costlier on a loan. It is not good for wealth creation. It is good for wealth creation. It is beneficial to the borrower but not to the lender. You will It is beneficial to the lender but not to the borrower. You will be paying less on a loan that is taken on simple interest. be paying more on a loan that is taken on compound interest. Simple interest is easy to calculate. Compound interest is complicated to calculate. www.cuidol.in Unit 1,2(BBA 102 /BCM 102) All right are reserved with CU-IDOL

Compound Interest 20  Compound interest (or compounding interest) is interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods on a deposit or loan.  Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one. The total initial amount of the loan is then subtracted from the resulting value. www.cuidol.in Unit 1,2(BBA 102 /BCM 102) All right are reserved with CU-IDOL

Compound Interest Formula 21 • The formula for calculating compound interest is: • Compound Interest = Total amount of Principal and Interest in future (or Future Value) less Principal amount at present (or Present Value) = [P (1 + i)n] – P = P [(1 + i)n – 1] (Where P = Principal, i = nominal annual interest rate in percentage terms, and n = number of compounding periods.) Take a three-year loan of Rs.10,000 at an interest rate of 5% that compounds annually. What would be the amount of interest? In this case, it would be: Rs.10,000 [(1 + 0.05)3 – 1] = Rs.10,000 [1.157625 – 1] = Rs.1,576.25. Using the above example, since compound interest also takes into consideration accumulated interest in previous periods, the interest amount is not the same for all three years, as it would be with simple interest. While the total interest payable over the three-year period of this loan is Rs.1,576.25, the interest payable at the end of each year is shown in the table below. www.cuidol.in Unit 1,2(BBA 102 /BCM 102) All right are reserved with CU-IDOL

Pros and Cons of Compound 22 Interest • While the magic of compounding has led to the apocryphal story of Albert Einstein calling it the eighth wonder of the world or man’s greatest invention, compounding can also work against consumers who have loans that carry very high-interest rates, such as credit card debt. A credit card balance of Rs.20,000 carried at an interest rate of 20% compounded monthly would result in total compound interest of Rs.4,388 over one year or about Rs.365 per month. • On the positive side, the magic of compounding can work to your advantage when it comes to your investments and can be a potent factor in wealth creation. Exponential growth from compounding interest is also important in mitigating wealth-eroding factors, like rises in the cost of living, inflation, and reduction of purchasing power. www.cuidol.in Unit 1,2(BBA 102 /BCM 102) All right are reserved with CU-IDOL

Pros and Cons of Compound 23 Interest • Mutual funds offer one of the easiest ways for investors to reap the benefits of compound interest. Opting to reinvest dividends derived from the mutual fund results in purchasing more shares of the fund. More compound interest accumulates over time, and the cycle of purchasing more shares will continue to help the investment in the fund grow in value. • Consider a mutual fund investment opened with an initial Rs.5,000 and an annual addition of Rs.2,400. With an average of 12% annual return of 30 years, the future value of the fund is Rs.798,500. The compound interest is the difference between the cash contributed to investment and the actual future value of the investment. In this case, by contributing Rs.77,000, or a cumulative contribution of just Rs.200 per month, over 30 years, compound interest is Rs.721,500 of the future balance. Of course, earnings from compound interest are taxable, unless the money is in a tax-sheltered account; it's ordinarily taxed at the standard rate associated with the taxpayer's tax bracket. www.cuidol.in Unit 1,2(BBA 102 /BCM 102) All right are reserved with CU-IDOL

Illustrative Examples 24 Suppose Rs. 9000 is invested for seven years at 12% compounded quarterly. P  9000 r  12%  interestcalculated4 times a year m4 t 7 i  r  12%  3% m4 n  mt  47  28 www.cuidol.in Unit 1,2(BBA 102 /BCM 102) All right are reserved with CU-IDOL

Illustrative Examples 25 • Determine the future value of Rs. 1000 which was invested for : a) 4 years at 4% compounded annually b) 5 years 6 months at 14%compounded semi – annually c) 2 years 3 months at 4% compounded quarterly d) 5 years 7 months at 5% compounded monthly e) 2 years 8 months at 9% compounded every 2 months f) 250 days at 10% compounded daily www.cuidol.in Unit 1,2(BBA 102 /BCM 102) All right are reserved with CU-IDOL

Illustrative Examples 26 r  4%; m  1; t  4 years; i  4%  4%; n  14  4 1 S 10001 4%4  Rs.1,169.86 r  14%; m  2; t  5 years 6 months  5 6  5.5 12 i  14%  7%; n  25.5  11 2 S 10001 7%11  Rs.2,104.85 www.cuidol.in Unit 1,2(BBA 102 /BCM 102) All right are reserved with CU-IDOL

Illustrations 27 1. Calculate the future values for the following investment: • i. Rs 1000 at 7% compounded annually for 8 years • ii. Rs 2500 at 9% compounded semi – annually for 10 years • iii. Rs 42000 at 7.75% compounded quarterly for 8 years • iv. Rs 180,000 at 9% compounded monthly for 6 years and 3 months. • v. Rs 150,000 at 12% compounded daily for 3 years. 2. At what rate compounded semi – annually will Rs 2000 become Rs3500 in five years? 3. Shima invested a certain sum of money in an account that pays 5% compounded quarterly. The account will amount to Rs 1000 in 27 months’ time. Calculate the original principal that was invested. www.cuidol.in Unit 1,2(BBA 102 /BCM 102) All right are reserved with CU-IDOL

Illustrations 28 4. How long will it take for Rs 5000 to grow to Rs 6000 if the investment earns interest at the rate of 12% compounded monthly? 5. How long will it take an investment of Rs 2000 to double if the investment earns interest at the rate of 9% compounded monthly? 6. Calculate the amount to be invested now at 6% compounded monthly so as accumulate Rs 8888 in three years. www.cuidol.in Unit 1,2(BBA 102 /BCM 102) All right are reserved with CU-IDOL

SUMMARY 29  Business Mathematics- Business mathematics are mathematics used by commercial enterprises to record and manage business operations. Commercial organizations use mathematics in accounting, inventory management, marketing, sales forecasting, and financial analysis.  Simple Interest- Simple interest is interest calculated on the principal portion of a loan or the original contribution to a savings account. Simple interest does not compound, meaning that an account holder will only gain interest on the principal, and a borrower will never have to pay interest on interest already accrued.  Compound Interest:-Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest. www.cuidol.in Unit 1,2(BBA 102 /BCM 102) All right are reserved with CU-IDOL

Multiple Choice Questions 30 1.A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is: a) Rs. 120 b) Rs. 121 c) Rs. 122 d) Rs. 123 2.The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is: a) 625 b) 630 c) 640 d) 650 Answers: 1. b) 2. a) Unit 1,2(BBA 102 /BCM 102) All right are reserved with CU-IDOL www.cuidol.in

Multiple Choice Questions 31 3.There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate? a) Rs. 2160 b) Rs. 3120 c) Rs. 3972 d) Rs. 6240 4.What is the difference between the compound interests on Rs. 5000 for 1 years at 4% per annum compounded yearly and half-yearly? a) Rs. 2.04 b) Rs. 3.06 c) Rs. 4.80 d) Rs. 8.30 Answers:3. c) 4. a) www.cuidol.in Unit 1,2(BBA 102 /BCM 102) All right are reserved with CU-IDOL

Frequently Asked Questions 32 Q.1 What do you understand by business mathematics?  Ans: Business mathematics are mathematics used by commercial enterprises to record and manage business operations. Commercial organizations use mathematics in accounting, inventory management, marketing, sales forecasting, and financial analysis. Q.2 What is simple interest and compound interest? Ans: Simple Interest- Simple interest is interest calculated on the principal portion of a loan or the original contribution to a savings account. Simple interest does not compound, meaning that an account holder will only gain interest on the principal, and a borrower will never have to pay interest on interest already accrued. Compound Interest:-Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest. www.cuidol.in Unit 1,2(BBA 102 /BCM 102) All right are reserved with CU-IDOL

REFERENCES 33 1. Evans, Allan (1936). Francesco Balducci Pegolotti, La Pratica della Mercatura. Cambridge, Massachusetts. pp. 301–2. 2. Lewin, C G (1970). \"An Early Book on Compound Interest - Richard Witt's Arithmeticall Questions\". Journal of the Institute of Actuaries. 96 (1): 121–132. 3. Lewin, C G (1981). \"Compound Interest in the Seventeenth Century\". Journal of the Institute of Actuaries. 108 (3): 423–442. www.cuidol.in Unit 1,2(BBA 102 /BCM 102) All right are reserved with CU-IDOL

34 THANK YOU For queries Email: [email protected] www.cuidol.in Unit 1,2(BBA 102 /BCM 102) All right are reserved with CU-IDOL