Let's solve the problem step by step. ### Given: - Principal (\(P\)) = \$18,941 - Annual interest rate (\(r\)) = 6.55% = 0.0655 (as a decimal) - Number of times compounded per year (\(n\)) = 365 (daily) - Number of years (\(t\)) = 13 ### Formula for Compound Interest: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \(A\) = the amount after \(t\) years - \(P\) = principal - \(r\) = annual interest rate (decimal) - \(n\) = number of times interest applied per year - \(t\) = number of years --- ### Step 1: Plug in the values \[ A = 18,941 \left(1 + \frac{0.0655}{365}\right)^{365 \times 13} \] --- ### Step 2: Calculate \(\frac{0.0655}{365}\) \[ \frac{0.0655}{365} \approx 0.0001794521 \] --- ### Step 3: Add 1 \[ 1 + 0.0001794521 \approx 1.0001794521 \] --- ### Step 4: Calculate the exponent \[ 365 \times 13 = 4745 \] --- ### Step 5: Raise to the power \[ \left(1.0001794521\right)^{4745} \approx 2.408179 \] --- ### Step 6: Multiply by the principal \[ A = 18,941 \times 2.408179 \approx 45,624.17 \] --- ## **Final Answer** \[ \boxed{\$45,624.17} \] You will have **\$45,624.17** in your savings account after 13 years.

The compound interest formula calculates the future value of an investment by accounting for interest earned on both the principal and accumulated interest over time. When interest is compounded daily, the interest is applied multiple times per year, increasing the total amount accumulated.