Question

How much would you have to deposit in an account with a 7.5% interest rate, compounded continuously, to have $2500 in your account 8 years later? Round to the nearest cent.

Answer 1

`~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^(rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 2500\\ P=\textit{original amount deposited}\\ r=rate\to 7.5\%\to (7.5)/(100)\dotfill &0.075\\ t=years\dotfill &8 \end{cases} \\\\\\ 2500 = Pe^(0.075\cdot 8)\implies \cfrac{2500}{e^(0.075\cdot 8)} \implies 1372.03\approx P`