MATH SOLVE

4 months ago

Q:
# You invest $600 an an annual rate of 7% for fifteen years. How much more interest would you earn in year 11 with compound vs. Simple interest and for the whole 15 years?

Accepted Solution

A:

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount \underline{for 11 years}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$600\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &11 \end{cases}[/tex][tex]\bf A=600\left(1+\frac{0.07}{1}\right)^{1\cdot 11}\implies A=600(1.07)^{11}\implies \boxed{A\approx 1262.91} \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \textit{Simple Interest Earned Amount \underline{for 15 years}} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$600\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years\dotfill &15 \end{cases}[/tex][tex]\bf A=600(1+0.07\cdot 15)\implies A=600(2.05)\implies \boxed{A=1230} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{earnings difference}}{1262.91 - 1230\implies 32.91}~\hfill[/tex]