Question

If $1500 is deposited in an account that pays 4% interest, what is the difference in the amount after 3 years between the amount earned if the principal is compounded annually and the amount earned calculated using simple interest?

$3.20

$7.30

$9.40

$15.10

Answer 1

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\ 1500\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases} \\\\\\ A=1500\left(1+\frac{0.04}{1}\right)^{1\cdot 3}\implies A=1500(1.04)^3\implies \boxed{A=1687.296}$

$\bf \rule{34em}{0.25pt}\\\\ ~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \ 1500\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &3 \end{cases} \\\\\\ A=1500[1+(0.04)(3)]\implies A=1500(1.12)\implies \boxed{A=1680} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 1687.296 - 1680\implies 7.296$