Question

After 5 years, Rachel’s amount in her savings account is $7446.52. Her account earned interest at 4.32% APR and was compounded daily. How much did she invest?

Answer 1

$\bf \qquad \textit{Continuously Compounding Earned Amount}\\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\to &7446.52\\ P=\textit{original amount deposited}\\ r=rate\to 4.32\%\to \frac{4.32}{100}\to &0.0432\\ t=years\to &5 \end{cases} \\\\\\ 7446.52=Pe^{0.0432\cdot 5}\implies \cfrac{7446.52}{e^{0.0432\cdot 5}}=P\implies 5999.92404\approx P$