Question

An investment of $74,500.00 earns 13.3% annual interest, compounded continuously. If no funds are added or removed from this account, what is the future value of the investment after 25 years? Round your answer to the nearest penny.

Answer 1

`~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^(rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$74500\\ r=rate\to 13.3\%\to (13.3)/(100)\dotfill &0.133\\ t=years\dotfill &25 \end{cases} \\\\\\ A=74500e^(0.133\cdot 25)\implies A=74500e^(3.325)\implies A\approx 2071025.40`