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

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

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