GCSE(F),

If a Savings Account is opened at a bank or a building society, then the bank will normally pay Compound Interest on the amount that is being saved. Savings rates are normally given as an annual rate, shown as AER or APR (Annual Equivalent Rate, or Annual Percentage Rate). So 5% APR means 5% per year.

If a deposit of £200 is left in a savings account paying 1.5% APR, then at the end of the year the interest added to the account, by the bank, is 200 x `frac(1.5)(100)` = £3.00. The balance on the account becomes £200.00 + £3.00 = £203.00.

If the money is left in the account for a further year, then the interest added to the account is 203 x `frac(1.5)(100)` = £3.05, as the starting amount for the second year was £203.00. The balance at the end of the second year is £206.05.

Interest not using the starting amount for each new year, and calculated using the original amount, is known as Simple Interest. A few specialist accounts, where savings are fixed for several years, behave like this.

1. Arianna is putting £80 into a savings account paying 1.2% APR. How much will that be worth at the end of three years?

Answer: £82.91

Interest earned after year 1 is 80.00 x `frac(1.2)(100)` = £0.96: savings = £80.00 + £0.96 = £80.96

Interest earned after year 2 is 80.96 x `frac(1.2)(100)` = £0.97: savings = £80.96 + £0.97 = £81.93

Interest earned after year 3 is 81.93 x `frac(1.2)(100)` = £0.98: savings = £81.93 + £0.98 = £82.91

You can also use the compound interest formula A = P(1 + `frac(text(i))(100})^{t}:

A = 80(1 + `frac(1.2)(100)`)^{3} = £82.91

2. Chloe has £160 to invest for three years. Is she better off investing £160 into an account paying 1.55% APR at a compound rate of interest; or 1.58% at a simple rate of interest?

Answer: Simple Interest is the better deal.

Using the compound formula A = P(1 + `frac(i)(100)`)^{t}

A = 160 x (1 + `frac(1.55)(100)`)^{3}

A = £167.56

For simple interest:< The same interest is received each year;

For one year = 160.00 x `frac(1.58)(100)` =£2.53

Total interest earned = 3 x £2.53 = £7.59

Total savings = £160.00 + £7.59 = £167.59.

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