The bank offers a rate of \( 11 \% \), compounded continuously, on any deposit that will not be removed for a minimum of 20 years. If you invest \( \$ 10,000 \) with the bank, how much money can you expect to have in the account after 20 years? Round your answer to the nearest cent (hundredth).

To calculate the amount of money that can be expected in the account after 20 years with continuous compounding, we can use the formula for continuous compounding: \[ A = P \times e^{r \times t} \] Where: - \( A \) is the amount of money after \( t \) years, - \( P \) is the principal amount (initial investment), - \( r \) is the annual interest rate (in decimal form), - \( t \) is the time in years. Given: - \( P = \$10,000 \), - \( r = 11\% = 0.11 \) (in decimal form), - \( t = 20 \) years. Substitute the values into the formula: \[ A = 10000 \times e^{0.11 \times 20} \] Now, we can calculate the amount of money that can be expected in the account after 20 years. Calculate the value by following steps: - step0: Calculate: \(10000e^{0.11\times 20}\) - step1: Multiply the numbers: \(10000e^{2.2}\) - step2: Convert the expressions: \(10000e^{\frac{11}{5}}\) The amount of money that can be expected in the account after 20 years with continuous compounding at a rate of 11% is approximately $90,250.13. Rounding to the nearest cent, the expected amount is $90,250.13.