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

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