Question

Ethel wants to have $70000 in 20 years. How much does she need to invest today at 5.46% cc?

Answer 1

$\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill&\ 70000\\ P=\textit{original amount deposited}\\ r=rate\to 5.46\%\to \frac{5.46}{100}\dotfill &0.0546\\ t=years\dotfill &20 \end{cases} \\\\\\ 70000=Pe^{0.0546\cdot 20}\implies 70000=Pe^{1.092}\implies \cfrac{7000}{e^{1.092}}=P \\\\\\ 23488.13 \approx P~\hfill \stackrel{~\hfill \textit{the earned interest will be}}{70000-23488.13\implies 46511.87}$