An investment banker deposited \( \$ 50,000 \) in an account earning a nominal \( 6 \% \) per year compounded continuously. How much was in the account at the end of three years? Round the answer to nearest dollar. Select the correct answer below:

To calculate the amount in the account at the end of three years with continuous compounding, we can use the formula: \( A = Pe^{rt} \) where: - \( A \) is the amount in the account after time \( t \), - \( P \) is the principal amount (initial deposit), - \( r \) is the annual interest rate (decimal), and - \( t \) is the time in years. Here, \( P = 50,000 \), \( r = 0.06 \), and \( t = 3 \). Plugging these values in: \( A = 50000 \cdot e^{0.06 \cdot 3} \) Calculating this gives approximately: \( A \approx 50000 \cdot e^{0.18} \approx 50000 \cdot 1.1972 \approx 59860 \) Therefore, after rounding to the nearest dollar, the final amount in the account at the end of three years is approximately \( \$ 59,860 \).