Question

If $850 is invested in an account that earns 2.6% yearly interested compounded quarterly, then which of the

following is the worth of this investment after 5 years?
(3) $967.60
(4) $968.25
(1) $960.50
(2) $966.40

Answer 1

`~~~~~~ \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 &\$850\\ r=rate\to 2.6\%\to (2.6)/(100)\dotfill &0.026\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &5 \end{cases} \\\\\\ A = 850\left(1+(0.026)/(4)\right)^(4\cdot 5)\implies A=850(1.0065)^(20) \implies A \approx 967.60`