he bank offers a rate of \( 11 \% \), compoundec 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?

To determine how much money you'll have in your account after 20 years with continuous compounding, we can use the formula for continuous compounding: \[ A = P \times e^{rt} \] Where: - \( A \) = the amount of money accumulated after \( t \) years, including interest. - \( P \) = the principal amount (\$10,000). - \( r \) = annual interest rate (11% or 0.11). - \( t \) = time the money is invested for (20 years). - \( e \) = the base of the natural logarithm (approximately 2.71828). Plugging in the values: \[ A = 10,000 \times e^{0.11 \times 20} \] \[ A = 10,000 \times e^{2.2} \] Calculating \( e^{2.2} \): \[ e^{2.2} \approx 9.0250135 \] Now, multiply this by the principal: \[ A \approx 10,000 \times 9.0250135 = 90,250.135 \] **So, after 20 years, you can expect to have approximately \$90,250 in your account.**