Question

Hannah wants to have $ 5500 to help pay for a new deck in 10 years. If she wants to put her money into an account earning 5.5% interest compounded continuously, how much should she invest now, so that she will have $ 5500 in 10 years?

Payment amount =

Answer 1

`~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^(rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$5500\\ P=\textit{original amount deposited}\\ r=rate\to 5.5\%\to (5.5)/(100)\dotfill &0.055\\ t=years\dotfill &10 \end{cases} \\\\\\ 5500=Pe^(0.055\cdot 10) \implies \cfrac{5500}{e^(0.055\cdot 10)}=P\implies 3173.22\approx P`