Example 4 Tim borrows 5300 at 4.6% /a compounded annually. How much will he have to pay back if he borrows the money for 10 years?

## Step 1: Calculate the annual interest rate as a decimal.### The given annual interest rate is 4.6%. To convert this percentage to a decimal, divide by 100. .## Step 2: Calculate the total amount to be repaid using the compound interest formula.### The formula for compound interest is , where A is the total amount, P is the principal, r is the interest rate per period, and n is the number of periods. In this case, 5300 r = 0.046 n = 10 A = 5300(1 + 0.046)^{10} = 5300(1.046)^{10} \approx 5300(1.5683) \approx 8324$.