Question

A principal of $4,570 is placed in an account that earns 4. 5% interest. If the interest is compounded annually, how much money will be in the account at the end of 5 years? a. $4,654. 15 b. $4,775. 65 c. $5,638. 75 d. $5,695. 05 Please select the best answer from the choices provided A B C D.

Answer 1

$~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\ 4570\\ r=rate\to 4.5\%\to \frac{4.5}{100}\dotfill &0.045\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A=4570\left(1+\frac{0.045}{1}\right)^{1\cdot 5}\implies A=4570(1.045)^5\implies A\approx 5695.05$