Question

Rochelle deposits $4,000 in an IRA. What will be the value (in dollars) of her investment in 25 years if the investment is earning 8% per year and is compounded continuously? (Simplify your answer completely. Round your answer to the nearest cent.)

Answer 1

`~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^(rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$4000\\ r=rate\to 8\%\to (8)/(100)\dotfill &0.08\\ t=years\dotfill &25 \end{cases} \\\\\\ A = 4000e^(0.08\cdot 25) \implies A=4000e^2\implies A \approx 29556.22`