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 1.06^{3}.

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.

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?

Answer: £296.92

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 10^{7}

465 x (1 + `frac(65)(100)`)^{24} (24 hours in a day)

= 465 x 1.65^{24}

= 77102349

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