CHAPTER 2 SIMPLE INTEREST 23 Learning Objectives By the end of this chapter, you should be able to explain the concept of simple interest; use the simple interest formula to calculate interest, interest rate, time and dates with data provided; use the simple amount formula to calculate the present and future values of some investments; identify four concepts of exact simple interest, ordinary simple interest, exact time and approximate time; apply Banker s Rule to some investments and loan problems, and use the concepts of equation of values to solve some investment and loan problems. 2.1 Introduction The word interest originates from the Latin word intereo, which means to be lost. Interest is then developed from the concept that lending money results in loss to the lender. The word usury is usually associated with lending at an excessive rate. The study of interest is very important and fundamental to the understanding of the economy of a country. For instance, when interest rates fall, stock prices will increase, and when interest rates increase, stock prices will fall. 2.2 Interest Interest can be defined in two ways. Definition 1: Interest is money earned when money is invested. For example, you deposited RM1,000 in a bank for a year and you find that at the end of year 1, you have RM1,050 in your account. The additional amount of RM50 is the interest you earned when you invested RM1,000. Definition 2: Interest is charge incurred when a loan or credit is obtained. For example, you borrowed RM1,000 from the same bank for a year and you paid back RM1,080 at the end of that year. The additional amount of RM80 is the charge or interest you need to pay when you borrow RM1,000. Interest (unless stated otherwise) is usually expressed as per cent per annum. There are two types of interest: simple interest and compound interest. In this chapter, we shall discuss simple interest.
32 BUSINESS MATHEMATICS Quick Check 2B 1. A loan of RM3,000 was made on 20 March 2009 at a simple interest rate of 6% per annum. Find the accumulated amount on 14 June 2009. (Use Banker s Rule). [Modified exam question] 2. On 27 July 2008, Samsiah puts RM2,000 in a savings account that offers a simple interest rate of 2.0% per annum. Find the amount in her account on 1 November 2008 using Banker s Rule. 3. On 10 March 2009, Kalmah deposits RM800 into a savings account which pays 4.8% simple interest per annum. Eight months later, she withdraws RM200 from the account. Find the amount left in the account after the withdrawal. 4. On 1 May 2008, Azizi takes a loan from a bank that charges a simple interest rate of 5.5% per annum. On 28 October 2008, he pays RM14,320.84 to settle the loan. Using Banker s Rule, find (a) the term of the loan in exact number of days, and (b) the loan. 5. On 12 February 2009, Adnan invested RM2,000 in a bank and receives an amount of RM2,040 on 23 June 2009. Calculate the simple interest rate offered by the bank. (Use Banker s Rule). [Modified exam question] 6. A debt of RM6,000 on 25 April 2008 became RM6,180 on 9 June 2008. (a) What was the simple interest rate charged using the Banker s Rule? (b) What would be the value of the debt after 1 1 2 years? 7. A loan was given out on 20 August 2008 at 7% simple interest. It was paid up on 31 December 2008 with a payment of RM9,299.25. Find the loan amount using the Banker s Rule. 8. A sum of money was deposited on 3 March 2008 in an investment fund which offered 7% simple interest. On 12 June 2008, RM2,800 was withdrawn from the fund. Find the initial deposit using Banker s Rule. FOCUS ON EXAM 1. Samy borrowed RM5,000 from a bank on 30 March 2012. If the accumulated amount is RM5,021.67 and the simple interest rate is 6% per annum, find the date of repayment using Banker s Rule. Strategy Interest can first be calculated by subtracting the principal from the amount given. Time can then be calculated using the simple interest
36 BUSINESS MATHEMATICS 2. If the period is given in terms of two dates, then we have (a) exact time = exact number of days between the two given dates (b) approximate time = number of days between the two given dates assuming that 1 month = 30 days (c) ordinary simple interest which uses 360-day year (d) exact simple interest which uses 365/366-day year 3. The simple amount formula is S = P(1 + rt). S 4. Present value, P = or P = S(1 + rt) 1 1 + rt 5. Equation of value: At the focal date, value of debts = value of payments. REVIEW QUESTIONS 2 1. Explain (a) interest, (b) exact and approximate time, (c) exact and ordinary simple interests, (d) Banker s Rule, (e) the letters in the formula S = P(1 + rt). 2. Find i. simple interest earned, ii. simple amount, for the following investments. (a) RM10,000 for 5 years at 12% per annum (b) RM20,000 for 4 years 6 months at 11% per annum (c) RM15,000 for 5 1 years at 9% per annum 4 (d) RM7,000 for 45 months at 8% per annum (e) RM10,000 for 40 weeks at 4% per annum 3. Calculate the exact and ordinary number of days (a) from 12 February 2012 to 26 August 2012, (b) from 8 February 2009 to 21 November 2009, (c) from 19 November 2009 to 1 May 2010, (d) from 12 February 2009 to 1 January 2010. 4. On 4 May, RM5,000 was saved at 8% per annum simple interest. Find the interest earned on 15 July of the same year, using (a) exact time and exact simple interest,
CHAPTER 5 TRADE AND CASH DISCOUNTS 113 FOCUS ON EXAM 1. (a) Find the net price of an item after discounts of 12%, 8% and 5% if the list price is RM2,800. What is the single discount that is equivalent to the trade discounts given? (b) A retailer receives an invoice dated 20 June 2009 for RM3,500. This amount includes a handling charge of RM23. The trade discounts offered are 10%, 5% and the cash discount terms are 4/10, 2/20 and n/60. If the invoice is paid on 28 June 2009, find the amount paid. Strategy As net price is required, the formula NP = L (1 r 1 )(1 r 2 )(1 r 3 ) should be used while single discount equivalent, r, can be found by using r = 1 (1 r 1 )(1 r 2 )(1 r 3 ). In (b), first find the number of days from date of invoice to the date of payment so that the cash discount rate (c%) can be determined. Then subtract the handling charge from the invoice amount to determine the list price of the items. Finally, determine the net amount using net amount = L(1 r 1 )(1 r 2 )(1 c). Solution (a) List price = RM2,800 Trade discounts = 12%, 8% and 5%. Net price = L(1 r 1 )(1 r 2 )(1 r 3 ) = RM2,800(1 0.12)(1 0.08)(1 0.05) = RM2,153.54 Single discount equivalent = 1 (1 0.12)(1 0.08)(1 0.05) = 23.088% (b) 20 June 2009 to 28 June 2009 = 8 days. Therefore 4% cash discount is valid. List price of items purchased = RM3,500 RM23 = RM3,477 Trade discounts offered = 10%, 5%. Total amount paid = L(1 r 1 )(1 r 2 )(1 c) = RM3,477(1 0.1)(1 0.05)(1 0.04) + RM23 = RM2,853.92 + RM23 = RM2,876.92 2. Halimah, a furniture shop owner, buys a new set of furniture worth RM8,260. She receives an invoice dated 26 October 2009 with trade discounts of 7%, 2% and is offered cash discount terms 3/15, 2/30, n/60. (a) Calculate the single discount equivalent to the trade discounts given. (b) Calculate the last day to receive the 2% cash discount.
116 BUSINESS MATHEMATICS Summary 1. Trade discount = List price Net price Or Net price = List price Trade discount 2. Net price, NP = L (1 r) where, L = list price r = trade discount 3. For chain discounts r 1, r 2, r 3, net price, NP = L (1 r 1 )(1 r 2 )(1 r 3 ) 4. Single discount equivalent, r, for a chain discount of r 1, r 2 and r 3 is r = 1 (1 r 1 )(1 r 2 )(1 r 3 ) 5. Cash discount 2/10, 1/30, n/60 means 2% of the net price may be deducted if the invoice is paid within ten days of the invoice date; 1% may be deducted if the invoice is paid between the 11th and 30th day; and the full amount must be paid by the 60th day. 6. Borrowing to take advantage of the cash discount: Amount saved = Cash discount Interest Interest = (Invoice amount Cash discount) r Credit period 7. Partial payment of invoice: Amount paid = Credit given (1 Discount rate) Amount outstanding = Invoice amount Credit given REVIEW QUESTIONS 5 1. Find the trade discounts and the net prices for the following. List price Rate of trade discount (a) RM250 15% (b) RM45 20% (c) RM180 45% (d) RM2,850 26%