Question

Mr. and Mrs. Williams hope to send their daughter to college in twelve years. How much money should they invest now at an interest rate of 8.5% per year,

compounded continuously, in order to be able to contribute $9000 to her education?

Answer 1

`~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^(rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$9000\\ P=\textit{original amount deposited}\\ r=rate\to 8.5\%\to (8.5)/(100)\dotfill &0.085\\ t=years\dotfill &12 \end{cases} \\\\\\ 9000=Pe^(0.085\cdot 12)\implies 9000Pe^(1.02)\implies \cfrac{9000}{e^(1.02)}=P\implies 3245.35\approx P`