Question

Find the principal amount invested if the amount in a monthly compounded account with a 5.1% interest rate is $9,996.32 after 54 months.

Answer 1

again, there are 12 months in a year, so 54 months is 54/12 years


`\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\to &\$9996\\ P=\textit{original amount deposited}\\ r=rate\to 5.1\%\to (5.1)/(100)\to &0.051\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\to &12\\ t=years\to (54)/(12)\to &(9)/(2) \end{cases}`


`\bf 9996=P\left(1+(0.051)/(12)\right)^{12\cdot (9)/(2)}\implies \cfrac{9996}{\left(1+(0.051)/(12)\right)^{12\cdot (9)/(2)}}=P`