Question

How much money needs to be deposited now into an account to obtain $1,500 in 7 years if the interest rate is 5% per year compounded continuously?

Answer 1

`~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^(rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$1500\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to (5)/(100)\dotfill &0.05\\ t=years\dotfill &7 \end{cases} \\\\\\ 1500=Pe^(0.05\cdot 7)\implies \cfrac{1500}{e^(0.35)}=P\implies 1057.03\approx P`