Question

An investment of $2,000 is earning interest at the rate of 6.2% compounded

annually over 5 years. Approximately how much interest is earned on the
investment?

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 &\$2000\\ r=rate\to 6.2\%\to (6.2)/(100)\dotfill &0.062\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases}`

`A = 2000\left(1+(0.062)/(1)\right)^(1\cdot 5)\implies A=2000(1.062)^5 \implies A \approx 2701.80 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{earned interest}}{2701.80~~ - ~~2000} ~~ \approx ~~ \text{\LARGE 701.80}`