First City Bank pays 5 percent simple interest on its savings account balances, whereas Second City Bank pays 5 percent interest compounded annually. If you made a deposit of \( \$ 11,500 \) in each bank, how much more money would you earn from your Second City Bank account at the end of 12 years? Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., \( \mathbf{3 2 . 1 6} \). Difference

To determine how much more you would earn from the **Second City Bank** account compared to the **First City Bank** account after 12 years, we'll calculate the final amounts for both banks and then find the difference. ### 1. First City Bank (Simple Interest) **Simple Interest Formula:** \[ \text{SI} = P \times r \times t \] - \( P = \$11,500 \) (principal) - \( r = 5\% = 0.05 \) (annual interest rate) - \( t = 12 \) years **Calculation:** \[ \text{SI} = 11,500 \times 0.05 \times 12 = 11,500 \times 0.6 = \$6,900 \] **Total Amount After 12 Years:** \[ \text{Total} = P + \text{SI} = 11,500 + 6,900 = \$18,400 \] ### 2. Second City Bank (Compound Interest) **Compound Interest Formula:** \[ A = P \times (1 + r)^t \] - \( P = \$11,500 \) - \( r = 5\% = 0.05 \) - \( t = 12 \) years **Calculation:** \[ A = 11,500 \times (1.05)^{12} \] First, calculate \( (1.05)^{12} \): \[ (1.05)^{12} \approx 1.795856326 \] Now, multiply by the principal: \[ A \approx 11,500 \times 1.795856326 \approx \$20,652.35 \] ### 3. Difference Between the Two Banks \[ \text{Difference} = \$20,652.35 - \$18,400 = \$2,252.35 \] ### **Conclusion** At the end of 12 years, you would earn **\$2,252.35** more from your **Second City Bank** account compared to your **First City Bank** account. **Answer:** \$2,252.35