Question

Suppose Carla has $12000 to invest. Which investment yields the greater return over 2 years: 9% compounded quarterly or 8.85% compounded monthly?

Answer 1

`\bf \qquad \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}\to &\$12000\\ r=rate\to 9\%\to (9)/(100)\to &0.09\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four times} \end{array}\to &4\\ t=years\to &2 \end{cases} \\\\\\ A=12000\left(1+(0.09)/(4)\right)^(4\cdot 2)`






`\bf \qquad \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}\to &\$12000\\ r=rate\to 8.85\%\to (8.85)/(100)\to &0.0885\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve times} \end{array}\to &12\\ t=years\to &2 \end{cases} \\\\\\ A=12000\left(1+(0.0885)/(12)\right)^(12\cdot 2)`