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 (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`