Question

Que 4.
A college is paying $200 000 each quarter into a fund which pays 16% per year interest compounded quarterly . How much will have accumulated into the fund
a.) The first year (6 marks)

b.) The sixth year (6 marks)

Answer 1

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\ 200,000\\ r=rate\to 16\%\to \frac{16}{100}\dotfill &0.16\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &\stackrel{first~year}{1} \end{cases}$

$\bf A=200000\left(1+\frac{0.16}{4}\right)^{4\cdot 1}\implies A=200000(1.04)^4\implies A=233971.712 \\\\\\ \stackrel{\textit{for the 6th year, then t = 6}}{A=200000\left(1+\frac{0.16}{4}\right)^{4\cdot 6}}\implies A=200000(1.04)^{24}\implies A\approx 512660.83298$