Question

Sandra has a savings account which gathers compound interest each year. She opened the account with a deposit of £2500. After 4 years there is £2937.91 in the account. Work out the annual interest rate of the savings account. Give your answer as a percentage to 1 d.p.​

Answer 1

4.1%

Explanation:

You want the annually compounded interest rate that results in £2500 growing to £2937.91 in 4 years.

Compound interest

The amount in an account earning compound interest is ...

A = P(1 +r)^t

where P is the principal invested at rate r for t years.

Rate

Solving for r, we find ...

(A/P)^(1/t) = 1 +r

r = (A/P)^(1/t) -1 = (2937.91/2500)^(1/4) -1 ≈ 0.0412 ≈ 4.1%

The annual interest rate of the savings account is about 4.1%.

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