Compound Interest

# Compound Interest

GCSE(F), GCSE(H),

Compound interest is interest which is added to the original amount at the end of one period, and the new amount is then used as the original amount for the next year.

£100 is invested in a savings account with a compound rate of 6%.

Calculate the multiplier as 1 + frac(6)(100) = 1.06.

At the end of the first year, the new amount is £100 X 1.06 = £106.00.

This new value is used as the original value for year 2: £106 x 1.06 = £112.36.

At the end of year three, the new amount is 112.36 x 1.06 = £119.10.

The value at the end of year 3 can also be represented as:

£100 x 1.06 x 1.06 x 1.06 (three lots of 1.06, one for each year) = £100 x 1.063.

This can be written as a formula:

Amount = Principal x (1 + frac(text(interest rate))(100))^text(periods)

or

Amount = P x (1 + frac(text(i))(100))n

where P = Principal (starting amount); i = interest rate and n is the number of periods.

## Examples

1. Joshua is investing £250 for 5 years at a compound interest rate of 3.5% APR. How much will that be worth at the end of that time?

250 x (1 + frac(3.5)(100))5

= 250 x (1.035)5

= 296.92.

2. Bacteria in a petri dish are reproducing at a rate of 65% per hour. There were initially 465 bacteria in the dish: how many will there be after a complete day? Give your answer in standard form to 3 significant figures.

Answer: 7.71 x 107

465 x (1 + frac(65)(100))24 (24 hours in a day)

= 465 x 1.6524

= 77102349