CHAPTER 2 SIMPLE INTEREST DDG 1113 BUSINESS MATHEMATICS

2.1 INTEREST “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. DDG 1113 BUSINESS MATHEMATICS

2.2 SIMPLE INTEREST FORMULA The simple interest amount is calculated by the following formula: I = Prt Where: I = Simple interest P = Principal r = Interest rate (in decimals) t = Time / Period (in years) DDG 1113 BUSINESS MATHEMATICS

2.3 SIMPLE AMOUNT FORMULA 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 P = Principal r = Interest rate (in decimals) t = Term / Period (in years) DDG 1113 BUSINESS MATHEMATICS

Example 1 pg 22 RM 10000 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 if the investment period. Example 2 pg 23 Raihan invested RM 5000 in an investment find for three years. At the end of the investment period, his investment will be worth RM 6125. find the simple rate that is offered. DDG 1113 BUSINESS MATHEMATICS

Example 3 pg 23 Twenty four month ago, a sum of money was invested. Now the investment is worth RM 12000. if the investment is extended for another twenty four months, it will become RM 14000. Find the original principle and the simple interest that was offered. Example 4 pg 24 Muthu invested RM 10000 in two accounts, some at 10% per annum and the rest at 7% per annum. His total interest for one year was RM 820. find the amount invested at each rate. DDG 1113 BUSINESS MATHEMATICS

2.4 FOUR BASIC CONCEPTS REV 00 There are four different methods for determining terms (t): 1. Exact time : It is the exact number if 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 a year. DDG 1113 BUSINESS MATHEMATICS

Example 1 pg 25 Find a) exact time, b) approximate time From 15 March to 29 August of the same years. Example 2 pg 25 RM 1000 was invested on 15 March 2005. if the simple interest rate offered was 10% per annum, find the interest received on 29 August 2005 using a) Exact time and exact simple interest. b) Exact time and ordinary simple interest. c) Approximate time and exact simple interest. d) Approximate time and ordinary simple interest. DDG 1113 BUSINESS MATHEMATICS

REV 00 2.5 PRESENT VALUE 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 DDG 1113 BUSINESS MATHEMATICS

REV 00 2.6 EQUATION OF VALUE 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: DDG 1113 BUSINESS MATHEMATICS

1. Draw a time diagram with all the dated values. 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. DDG 1113 BUSINESS MATHEMATICS

Example 1 pg 26 Find the present value at 8% simple interest of a debt RM 3000 due in ten months. Example 2 pg 27 A debt of RM 800 due in four months and another of RM 1000 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. DDG 1113 BUSINESS MATHEMATICS

a) the present as the focal date Example 3 pg 28 A debt of RM 500 due two months ago and RM 900 due in nine months are to be settled by two equal payments, one at the end of three months and another at the end of six months. Find the size of the payment using a) the present as the focal date b) the end of six months as a focal date Assuming money is worth 10% per annum simple interest. DDG 1113 BUSINESS MATHEMATICS