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, \( \$ \)

Let the monthly interest rate be \[ r = \frac{0.05}{12} \] and the total number of periods be \[ n = 16 \times 12 = 192. \] The formula for the future value \( FV \) of an annuity (with payments made at the end of each period) is \[ FV = P \cdot \frac{(1+r)^n - 1}{r}, \] where \( P \) is the periodic payment. Substitute \( P = 58 \), \( r = \frac{0.05}{12} \), and \( n = 192 \) into the formula: \[ FV = 58 \cdot \frac{\left(1+\frac{0.05}{12}\right)^{192} - 1}{\frac{0.05}{12}}. \] Now, calculate \( r \): \[ r = \frac{0.05}{12} \approx 0.004166666667. \] Next, compute the accumulation factor: \[ \left(1 + r\right)^{192} = \left(1.004166666667\right)^{192}. \] Taking logarithms or using a calculator yields: \[ \left(1.004166666667\right)^{192} \approx 2.220939. \] Then, \[ (1+r)^n - 1 \approx 2.220939 - 1 = 1.220939. \] Now, compute the fraction: \[ \frac{1.220939}{0.004166666667} \approx 293.02536. \] Finally, multiply by the periodic payment: \[ FV = 58 \times 293.02536 \approx 16995.475. \] Rounded to the nearest cent, the total value of the annuity is \[ \$16,\!995.48. \]