Benjamin invests money in a bank account which gathers compound interest each year. After years there is 658.20 in the account After 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: <br />## Step 1: <br />We know the formula for compound interest, which is given as:<br /><br />### \( A = P \times (1 + \frac{r}{n})^{nt} \) <br /><br />Where, <br />A is the final amount, <br />P is the principal amount (the initial amount), <br />r is the annual interest rate, <br />n is the number of compounding periods per year, <br />and t is the time period in years.<br /> <br />Since in this case, Ben's money accumulated annually, \( n \) will be equal to 1.<br /><br />## Steps 2 & 3: <br />Let \( P \) be the initial investment amount, \( r \) the annual interest rate, this gives us two different versions of the interest formula:<br /><br />### \( 658.20 = P \times (1 + r) ^ 2 \)<br />### \( 710.89 = P \times (1 + r) ^ 5 \)<br /><br />Unfortunately, these equations have two variables, \( P \) and \( r \), and we cannot solve them as is.<br /><br />## Step 4: <br />Instead of trying to solve for two variables, we will divide out \( P \) from both <br />equations. This will give us this formula:<br /><br />### \( \frac{658.20}{710.89} = \frac{(1 + r) ^ 2}{(1 + r) ^ 5} \)<br /><br />## Step 5: <br />Once simplifying further, the equation becomes:<br /><br />### \( \frac{658.20}{710.89} = (1 + r)^{-3} \)<br /><br />## Step 6: <br />By swapping sides and taking the (1/3)-th power and subtracting 1, we can infer the value of \( r \).<br /><br /># Answer: <br />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.