Compound Interest

*Example:*

A man invests £2000 in a bank for 6 years earning 7% interest per annum. How much does he have at the end of the 6 years?

How do you calculate the question? You will do as follows.

6 x 7% is 42%.

42% of £2000 is £840.

£2000 + £840 is £2840.

He has £2840.

*That is wrong. The last method used is to solve problems with *

**simple interest**

*.*

*If the question changes to:*

*A man invests £2000 in a bank for 6 years earning 7% interest of his original investment per year. How much does he have at the end of the 6 years?*

This is the problem we would be solving with the last method.

So, how do you calculate ** compound interest ** in I/GCSE Mathematics?

A man invests £2000 in a bank for 6 years earning __7% interest per year__. How much does he have at the end of the 6 years?

Which is the same as..

2000 x 1.07 x 1.07 x 1.07 x 1.07 x 1.07 x 1.07

or more simply,

2000 x 1.07^{6}

Reverse Percentage

*Example 1:*

A woman buys a painting from a car boot sale. She sells it for £129.75- 73% more than she bought it for. How much did she buy it for?

Buying price is 100% of original x

Current price is 173% of original (+73%) £129.75

1% of original is £129.75 ÷ 173 £0.75

New price is 100% è £0.75 x 100

The price she paid was £75.

*Example 2:*

A man buys a car that decreases in value by 18%. After one year, the car is worth £8,200. How much was it worth new?

New price is 100% of original x

Current price is 82% of original (-18%) £8,200

1% of original is £8,200 ÷ 82 £1,000

New price is 100% è £1,000 x 100

The new price of the car was £10,000

That's all