Question

Dan invests $8.911 in a retirement account with an interest rate of 7.71%

compounded continuously. What will the account balance be in 20 years.

Answer 1

`~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^(rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$8911\\ r=rate\to 7.71\%\to (7.71)/(100)\dotfill &0.0771\\ t=years\dotfill &20 \end{cases} \\\\\\ A=8911e^(0.0771\cdot 20)\implies A=8911e^(1.542)\implies A\approx 41649.38`