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+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$200,000\\ r=rate\to 16\%\to (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+(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+(0.16)/(4)\right)^(4\cdot 6)}\implies A=200000(1.04)^(24)\implies A\approx 512660.83298`