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Maths

Percentages - Higher

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# Cumulative increase and decrease

## Compound Interest

Here the interest is added to the principal at the end of each year. So the next year the interest is worked out on a larger amount of money than what was originally borrowed.

This means paying interest on the interest of previous years (unlike simple interest, where you only pay interest on the original amount).

This is how it is calculated:

£400 is borrowed for 3 years at 5% compound interest.

Principal at the start = £400

Interest in the 1st year = 5/100 × 400 = £20

Principal after 1 year = £420

Interest in the 2nd year = 5/100 × 420 = £21

Principal after 2 years = £441

Interest in the 3rd year = 5/100 × 441 = £22.05

Principal after 3 years = £463.05

The total interest charged under compound interest will be £63.05.

This is different to the simple interest worked out above.

## Four types of question

In percentage questions, read the question carefully and decide what you are being asked to do. You may need to:

• Find a given percentage of an amount.
• Work out a percentage when given 2 amounts.
• Work backwards from a percentage increase or decrease (reverse percentages).
• Find a cumulative change.

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