1 2 3 4 5 6 An investor wants to save money to purchase real estate. She buys an annuity with monthly payments that earn \( 5 \% \) interest, compounded monthly, Payments will be made at the end of each month. Find the total value of the annuity in 16 years if each monthly payment is \( \$ 58 \). Do not round any intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the list of financial formulas, \( \$ \)

To find the total value of the annuity in 16 years, we can use the future value of an ordinary annuity formula: \[ FV = P \times \frac{(1 + r)^n - 1}{r} \] Where: - \( FV \) is the future value of the annuity - \( P \) is the monthly payment - \( r \) is the monthly interest rate (annual rate / 12) - \( n \) is the total number of payments (years × 12) Given: - \( P = 58 \) - Annual interest rate = \( 5\% \) - Monthly interest rate \( r = \frac{5\%}{12} = \frac{0.05}{12} \approx 0.00416667 \) - Number of payments \( n = 16 \times 12 = 192 \) Now we plug in the values: \[ FV = 58 \times \frac{(1 + 0.00416667)^{192} - 1}{0.00416667} \] Calculating: 1. \( (1 + 0.00416667)^{192} \approx (1.00416667)^{192} \approx 2.21964 \) 2. \( (1.00416667)^{192} - 1 \approx 2.21964 - 1 = 1.21964 \) 3. \( \frac{1.21964}{0.00416667} \approx 292.69729 \) 4. Thus, \( FV \approx 58 \times 292.69729 \approx 16996.25 \) Therefore, the total value of the annuity in 16 years is approximately \( \boxed{16996.25} \).