Savings

## Savings

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 the money is left in the account for a further year, then the interest added to the account is based on the previous year start value.

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.

## Example 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?

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

## Example 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?

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.

Answer: Simple Interest is the better deal.