Simple and compound interest

Interest is money that is paid regularly at a particular percentage, usually when money has been lent or borrowed. For example, a bank will give its customers interest to reward them for saving money with them, but it will also charge interest to anyone who has borrowed money from them.

Simple interest

As the name suggests, simple interest is a quick way of calculating interest. Simple interest is worked out by calculating the percentage amount and multiplying it by the number of periods that the money will be invested for.

Example

Calculate the interest on borrowing £40 for 3 years if the simple interest rate is 5% per year.

First, work out the amount of interest for 1 year by working out 5% of £40, which is £2.

The money is being loaned for 3 years, so multiply this amount by 3:

\pounds 2 \times 3 = \pounds 6

So the amount of interest on borrowing £40 for 3 years is £6, which makes the total amount payable £46.

Compound interest

Compound interest means that each time interest is paid onto an amount saved or owed, the added interest also receives interest from then on.

Put simply, compound interest changes the amount of money in the bank each time and a new calculation has to be worked out.

Examples

Calculate the interest on borrowing £40 for 3 years if the compound interest rate is 5% per year.

  • Year 1: \pounds 40 + 5 \% = \pounds 40 + \pounds 2 = \pounds 42
  • Year 2: \pounds 42 + 5 \% = \pounds 42 + \pounds 2.10 = \pounds 44.10
  • Year 3: \pounds 44.10 + 5 \% = \pounds 44.10 + \pounds 2.21 = \pounds 46.31

As this is a problem involving money, all rounding should be done to 2 decimal places to represent the pence.

Note that the example above is exactly the same as the example for simple interest, but the answers are different as compound interest changes the amount each period.