(1) An investor wants to save money to purchase real estate. He buys an annuity with yearly payments that earn \( 5.4 \% \) interest, compounded annually. Payments will be made at the end of each year. Fnd the total value of the annuity in 17 years if each yearly payment is \( \$ 771 \). Do not round any intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the list of financial formulas. sil

To find the total value of the annuity after 17 years, we can use the future value of an ordinary annuity formula: \[ FV = P \times \frac{(1 + r)^n - 1}{r} \] Where: - \( FV \) = future value of the annuity - \( P \) = payment per period (\$771) - \( r \) = interest rate per period (5.4% or 0.054) - \( n \) = number of payments (17) Now, substituting the values into the formula: \[ FV = 771 \times \frac{(1 + 0.054)^{17} - 1}{0.054} \] \[ FV = 771 \times \frac{(1.054)^{17} - 1}{0.054} \] Calculating \( (1.054)^{17} \): \[ (1.054)^{17} \approx 2.4617 \] Now substituting back into the formula: \[ FV = 771 \times \frac{2.4617 - 1}{0.054} \] \[ FV = 771 \times \frac{1.4617}{0.054} \approx 771 \times 27.0972 \approx 20,910.56 \] So, the total value of the annuity in 17 years will be approximately **\$20,910.56**.