Question

How much would $300 invested at 4% interest compounded monthly be worth after 2 years? Round your answer to the nearest cent.

Equation: A(t)=P(1+r/n)^nt

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 &\$300\\ r=rate\to 4\%\to (4)/(100)\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &2 \end{cases}`

`A=300\left(1+(0.04)/(12)\right)^(12\cdot 2) \implies A=300\left( (301)/(300) \right)^(24)\implies A \approx 324.94`