Peter saved up \( \$ 20,000 \) in an account earning a nominal \( 5 \% \) per year compounded continuously. How much was in the account at the end of two years? Round the answer to nearest dollar.

To find the amount in the account at the end of two years with continuous compounding, you can use the formula: \[ A = Pe^{rt} \] where: - \( A \) is the amount in the account after time \( t \), - \( P \) is the principal amount (\$20,000), - \( r \) is the nominal interest rate (0.05), - \( t \) is the time in years (2), - \( e \) is the base of the natural logarithm (approximately 2.71828). Plugging in the values: \[ A = 20000 \cdot e^{0.05 \cdot 2} \] \[ A = 20000 \cdot e^{0.1} \] Calculating \( e^{0.1} \) gives approximately \( 1.10517 \). So, \[ A \approx 20000 \cdot 1.10517 \] \[ A \approx 22103.40 \] Rounding to the nearest dollar, the amount in the account at the end of two years is approximately **\$22,103**.