Question

What is the value that will grow to 24000 if intetest is 8% compounded quarterly for 15 quarters?

Answer 1

bearing in mind that a year has 4 quarters, so 15 quarters is really 15/4 years.

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\to &\ 24000\\ P=\textit{original amount deposited}\\ r=rate\to 8\%\to \frac{8}{100}\to &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\to &4\\ t=years\to &\frac{15}{4} \end{cases}$

$\bf 24000=P\left(1+\frac{0.08}{4}\right)^{4\cdot \frac{15}{4}}\implies 24000=P(1.02)^{15} \\\\\\ \cfrac{24000}{1.02^{15}}=P\implies 17832.35\approx P$