Moneysaver's Bank offers a savings account that earns \( 3 \% \) interest per year, compounded continuously. If Josh deposits \( \$ 2700 \), how much will he have in the account after five years, assuming he makes no withdrawals? Do not round any intermediate computations, and round your answer to the nearest cent.

To calculate the amount in Josh's savings account after five 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 (initial deposit), - \( r \) is the annual interest rate (in decimal), - \( t \) is the time in years, - \( e \) is the base of the natural logarithm (approximately equal to 2.71828). Plugging in the values: - \( P = 2700 \), - \( r = 0.03 \) (which is \( 3\% \) expressed as a decimal), - \( t = 5 \). \[ A = 2700 \times e^{0.03 \times 5} \] Calculating \( 0.03 \times 5 = 0.15 \). Now, find \( e^{0.15} \): Using a calculator, \( e^{0.15} \approx 1.161834 \). Now multiply: \[ A \approx 2700 \times 1.161834 \approx 3134.79 \] Thus, after rounding to the nearest cent, Josh will have approximately **\$3134.79** in his account after five years.