Question

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

Find the principle and interest

Please help

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 (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}`