# Compound and simple interest rates

## Introduction

If you have a savings account with a bank and deposit some money, the bank will pay you extra money for saving with them.
Similarly if you need to borrow money from a bank the bank will expect you to pay back more than you borrowed from them in the first place!
How much extra depends on the **interest rate** set by the bank.
Banks make their money by charging more for their loans than they give for their savings accounts.

For your GCSE maths exam you need to know about two different types of interest rates,
**simple interest** and **compound interest**.

**Simple interest** is where the amount of interest earned is fixed over time.
For example, if you saved £1000 at 4% simple interest you would earn £40 per year, every year.
*The amount of interest earned stays the same when dealing with simple interest.*

**Compound interest** is where interest is paid on the amount already earned leading to greater and greater amounts of interest.
For example £1000 at 4% compound interest would earn you £40 in the first year but in the second year you would
earn 4% on the new amount of £1040 which would be £41.60.

Compound interest is by far the most common type of interest use in real life. It is the reason why small amounts saved can turn into retirement nest eggs and why small loans taken out can spiral into huge debts very quickly. Try this compound interest calculator for some examples to show how the interest is calculated.

## How to work out simple interest

### Example 1

You deposit £400 in to a bank account paying 5% simple interest per year. How much interest would you have earned after 3 years?

First we need to find 5% of £400.

10% of £400 = £40 so 5% is £20.

As the bank pays simple interest this amount stays the same. So after 3 years you will have earned 20 + 20 + 20 = £60.

### Example 2

You deposit £345 in to a bank account paying 7% simple interest per year. How much would interest would you earn after 5 years?

This time the amounts are not nice round figures so we will solve it using a calculator method.

First find 7% by multiplying £345 by 0.07 to work out our interest of £24.15 per year.

So the interest earned after 5 years which will be 5 x 24.15 = £120.75.

## How to work out compound interest

### Example 3

You take out a loan of £800 and the bank charges you 15% compound interest per year. If you don't pay off any of the loan in 4 years, how much would you owe the bank?

This time we are dealing with compound interest so the interest earned gets added to the original amount each year.

After 1 year you would owe the bank £800 x 1.15 = £920.

To work out how much is owed after four years we would then have to multiply this amount by 1.15 a further 3 times. This can be done quickly on a calculator using the power keys: £800 x 1.15\(^4\) = £1399.21 (to the nearest penny).

### Example 4

You invest £4000 in a fund which earns an 11% compound return per year. How much would the fund be worth after 10 years?

To increase an amount by 11% on a calculator we multiply by 1.11.

As we are investing for 10 years we the sum on our calculator will be £4000 x 1.11\(^{10}\) = £11357.68 (to the nearest penny).

## Worksheets to practise solving simple and compound interest problems

Try these worksheets to practise your skills.