Benjamin invests money in a bank account which gathers compound interest each year. After 2 years there is 658.20 in the account. After 5 years there is 710.89 in the account. Work out the annual interest rate of the bank account. Give your answer as a percentage to 1 d,p.

# Explanation: ## Step 1: We know the formula for compound interest, which is given as:### \( A = P \times (1 + \frac{r}{n})^{nt} \) Where, A is the final amount, P is the principal amount (the initial amount), r is the annual interest rate, n is the number of compounding periods per year, and t is the time period in years. Since in this case, Ben's money accumulated annually, will be equal to 1.## Steps 2 & 3: Let be the initial investment amount, the annual interest rate, this gives us two different versions of the interest formula:### \( 658.20 = P \times (1 + r) ^ 2 \)### \( 710.89 = P \times (1 + r) ^ 5 \)Unfortunately, these equations have two variables, and , and we cannot solve them as is.## Step 4: Instead of trying to solve for two variables, we will divide out from both equations. This will give us this formula:### \( \frac{658.20}{710.89} = \frac{(1 + r) ^ 2}{(1 + r) ^ 5} \)## Step 5: Once simplifying further, the equation becomes:### \( \frac{658.20}{710.89} = (1 + r)^{-3} \)## Step 6: By swapping sides and taking the (1/3)-th power and subtracting 1, we can infer the value of .# Answer: Ben's account has an annual interest rate of recovering the percentage %( Approximately recover `1` d.p.) and provide it as answer ensuring that the calculation amounts are accurate and correctly colored according to the placeholders very precisely.