QMT 3301 BUSINESS MATHEMATICS REV 00 CHAPTER 7 SIMPLE INTEREST QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS 7.1 Interest REV 00 “Interest ” comes from the Latin word intereo which means “to be lost”. When developed into the concept of borrowing money, the lender is likely to lose his money when he pays back the money with interest. Nowadays, interest is not only paid but gained if we make an investment. QMT 3301 BUSINESS MATHEMATICS

7.2 Simple Interest Formula REV 00 The simple interest amount is calculated by the following formula: I = Prt Where: I = Simple interest P = Principal / Present value r = Interest rate (in decimals) t = Time / Period (in years) QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS Example 1: REV 00 RM 1000 is invested for 2 years in a bank, earning simple interest rate of 8% per annum. Find the simple interest earned. Solution: I = Prt = 1000 x 0.08 x 2 = RM 160 QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS Example 2: REV 00 Raihan invests RM 5000 in an investment fund for three years. At the end of the investment period, his investment will be worth RM 6125. Find the simple interest rate that is offered. Solution: I = RM 6125 – RM 5000 = RM 1125 From I = Prt, we get 1125 = 5000 x r x 3 r = 7.5% QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS Example 3: REV 00 How long does it take a sum of money to triple itself at a simple interest rate of 5% per annum? Solution: Let the original principal be RMK and time taken be t years. Hence interest earned is RM 3K – RM K = RM 2K Then from I = Prt, we get 2K = K x 0.05 x t t = 40 years QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS 7.3 Simple Amount Formula REV 00 Simple amount is the sum of the original principal and the interest earned. Therefore, the simple amount formula is given as: S = P(1 + rt) Where: S = Maturity value / Future value P = Principal / Present value r = Interest rate (in decimals) t = Term / Period (in years) QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS Example : REV 00 RM 10 000 is invested for 4 years 9 months in a bank earning a simple interest rate of 10% per annum. Find the simple amount at the end of the investment period. Solution: From S = P(1 + rt), we get S = 10 000(1 + (0.1 x 4.75)) = RM 14750 QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS 7.4 Four Basic Concepts REV 00 There are four different methods for determining terms (t): 1. Exact time: It is the exact number of days between two given dates. 2. Approximate time: Time computed on the assumption that each month has 30 days. 3. Exact interest: Interest calculated based on 365 days a year or 366 days for a leap year. 4. Ordinary interest: Interest is calculated based on 360 days a year. QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS 7.5 Present Value REV 00 Present value may be debt or an investment amount that is lent or invested today, and that will be mature in a specific time together with interest. By transposing the maturity value formula, we have the present value formula as follows: P = S (1 + rt) OR P = S (1 + rt)-1 QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS Example : REV 00 If Saleh has to pay RM 350 interest for a loan that charges 7% simple interest per annum for 2 and a half years, find the amount of loan. Solution: From P = S (1 + rt)-1, we get P = 350(1 + (0.07 x 2.5))-1 P = RM 297.87 QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS 7.6 Equation of Value REV 00 Every value of money has an attached date, the date on which it is due. An equation that states the equivalence of two sets of dated values at a stated date is called an equation of value or equivalence. The stated date is called the focal date, the comparison date or the valuation date. To set up and solve an equation of value, the following procedure should be carried out: QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS REV 00 1. Draw a time diagram with all the dated values. 2. Select the focal date. 3. Pull all the dated values to the focal date using the stated interest rate. 4. Set up the equation of value and then solve. QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS REV 00 Example : A debt of RM 800 due in four months and another of RM 10000 due in nine months are to be settled by a single payment at the end of six months. Find the size of this payment using a) The present as the focal date, b) The date of settlement as the focal date, Assuming money is worth 6% per annum simple interest. QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS REV 00 Solution: a) Focal date 0 4 6 9 months 800 X 1000 Let the single payment at the end of 6 months be RM X. Amount of the RM 800 debt at the focal date = 800(1 + (0.06 x 4/12))-1 = RM 784.31 QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS REV 00 Amount of the RM 1000 debt at the focal date = 1000(1 + (0.06 x 9/12))-1 = RM 956.94 Amount of the single payment at the focal date = X (1 + (0.06 x 6/12))-1 = RM 0.97087X Setting up the equation of value, we get 0.97087X = 784.31 + 956.94 X = 1741.25 0.97087 X = RM 1793.49 QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS REV 00 b) Focal date 0 4 6 9 months 800 X 1000 Amount of the RM 800 debt at the focal date = 800(1 + (0.06 x 2/12)) = RM 808 Amount of the RM 1000 debt at the focal date = 1000(1 + (0.06 x 3/12)) = RM 985.22 QMT 3301 BUSINESS MATHEMATICS

QMT 3301 BUSINESS MATHEMATICS REV 00 Let the amount of payment at the end of 6 months be RM X. Setting up the equation of value, we get X = RM 808 + RM 985.22 = RM 1793.22 *(It should be noted that the two answers in part a and b are different when the focal dates are different) QMT 3301 BUSINESS MATHEMATICS