Question

Tony Ring wants to attend Northeast College. If he deposits $37,644 today, how much will he have 4 years from now at 12% interest compounded semiannually?

Answer 1

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\ 37644\\ r=rate\to 12\%\to \frac{12}{100}\to &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\to &2\\ t=years\to &4 \end{cases} \\\\\\ A=37644\left(1+\frac{0.12}{2}\right)^{2\cdot 4}\implies A=37644(1.06)^8$