Question

Hannah wants to have $ 6500 to help pay for a new deck in 16 years. If she wants to put her money into an account earning 4.75% interest compounded continuously, how much should she invest now, so that she will have $ 6500 in 16 years?

Payment amount =

Answer 1

`~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^(rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6500\\ P=\textit{original amount deposited}\\ r=rate\to 4.75\%\to (4.75)/(100)\dotfill &0.0475\\ t=years\dotfill &16 \end{cases} \\\\\\ 6500=Pe^(0.0475\cdot 16) \implies \cfrac{6500}{e^(0.0475\cdot 16)}=P\implies 3039.83\approx P`