Question

You deposit $2,000 in an account earning 3% interest compounded monthly.

a. How much will you have in the account in 20 years?
b. How much interest will you earn?

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 3\%\to (3)/(100)\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &20 \end{cases}`

`A = 2000\left(1+(0.03)/(12)\right)^(12\cdot 20)\implies A=2000(1.0025)^(240) \implies \boxed{A \approx 3641.51} \\\\\\ 3641.51~~ - ~~2000~~ \approx~~ \stackrel{earned~interest}{\boxed{1641.51}}`