**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.

To solve these questions, you can either work out the amount on a year-by year basis, taking the amount at the end of one year as the start amount for the second year; or

use 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.

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.

Answer: £296.92

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.

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

= 465 x 1.65^{24}

= 77102349

Answer: 7.71 x 10^{7}

See also Repeated Percentage Change

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