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.<br />### The given annual interest rate is 4.6%. To convert this percentage to a decimal, divide by 100. $4.6\% = \frac{4.6}{100} = 0.046$.<br /><br />## Step 2: Calculate the total amount to be repaid using the compound interest formula.<br />### The formula for compound interest is $A = P(1 + r)^n$, 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, $P = \$5300$, $r = 0.046$, and $n = 10$. Substituting these values into the formula: $A = 5300(1 + 0.046)^{10} = 5300(1.046)^{10} \approx 5300(1.5683) \approx 8324$.