Question

Find the present value that will grow to $22000 if interest is 6% compounded quarterly for 14 quarters

Answer 1

$\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\ 22000\\ r=rate\to 6\%\to \frac{6}{100}\to &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus } \end{array}\to &4\\ t= \begin{array}{llll} \textit{how many years}\\ \textit{14 quarters is 3years and}\\ \textit{6 months} \end{array}\to &\frac{7}{2} \end{cases}$

$\bf A=22000\left(1+\frac{0.06}{4}\right)^{4\cdot \frac{7}{2}}$