CMM Subject Support Strand: FINANCE Unit 2 Simple and Compound Interest: Text m e p STRAND: FINANCE Unit 2 Simple and Compound Interest TEXT Contents Section 2.1 Simple Interest 2.2 Compound Interest 2.3 Compound Interest Formula 2.4 Savings: Annual Equivalent Rate (AER)
CMM Subject Support Strand: Finance Unit 2 Simple and Compound Interest: Text 2 Simple and Compound Interest 2.1 Simple Interest When money is deposited in a bank or building society account, it commonly attracts interest; in a similar way, a borrower must normally pay interest on money borrowed. The rate of interest is usually (but not always) quoted as a rate per cent per year. At the time of writing a typical rate is 1.5% per annum for money deposited and 1%-2% per annum for money borrowed. Up-to-date rates are available from finance organisations. There are two basic ways of calculating the amount of interest paid on money deposited: simple interest and compound interest. If simple interest is paid, interest is calculated only on the principal £P, the amount deposited (the original capital sum). The interest £I payable after one year years at rate r% per annum is given by the formula I= I x P 100 and the total amount owing can then be calculated by adding I to P. Worked Example 1 Natasha invests £250 in a building society account. At the end of the year her account is credited with 2% interest. How much interest had her £250 earned in the year? Solution Interest = 2% of £250 = 2 × £250 100 £5 Worked Example 2 Alan invests £140 in an account that pays r% interest. After the first year he receives £4.20 interest. What is the value of r, the rate of interest? Solution After one year, the amount of interest is given by r × £140 = £4.20 100 r = 100 × 4.20 = 420 140 140 = 3 So the interest rate is 3%. 1
2.1 CMM Subject Support Strand: Finance Unit 2 Simple and Compound Interest: Text Exercises 1. Calculate (a) the interest payable and (b) the total amount owing on the following deposits at simple interest. (i) £300 borrowed for 5 years at 8% p.a. (ii) £1000 invested for 4 years at 9.5% p.a. (iii) £50 borrowed for 2 years at 18% p.a. (iv) £2500 invested for 6 months at 8.75% p.a. (T = 0.5 years) (v) £45 000 borrowed for 2 weeks at 15.5% p.a. The following questions relate to simple interest. 2. What is the actual rate of interest if £4000 deposited for 3 years attracts interest of £1440? 3. For how long would £500 have to be left in an account paying 4% interest p.a. to give a balance of £600 ? 4. A school's rich benefactor wants to deposit a certain sum in an account paying interest at 10.5% so that it will produce interest of £1200 per year, to pay for scholarships. How much should she deposit? 5. A boy borrows £1.00 from