Question

How much should you invest in a continuously compounded account at an annual interest rate of 6% if you want exactly $8000 after four years? (Round to the nearest cent)

Answer 1

`~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^(rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$8000\\ P=\textit{original amount deposited}\\ r=rate\to 6\%\to (6)/(100)\dotfill &0.06\\ t=years\dotfill &4 \end{cases} \\\\\\ 8000=Pe^(0.06\cdot 4)\implies 8000=Pe^(0.24)\implies \cfrac{8000}{e^(0.24)}=P\implies 6293.02\approx P`