Question

Thane invests $6,000 in an account that earns interest at an annual rate of 4.2% compounded monthly. What is return on his investment after 1 year?

Answer 1

`\text{ROI}=\$256.908`

Step-by-step explanation: The investment of $6,000 earns an annual interest rate of 4.2% and is compounded monthly: this problem can be solved using the compound interest formula, which is as follows:

`\begin{gathered} A=P(1+(r)/(n))^(nt)-P\Rightarrow(1) \\ P=\$6000 \\ r=0.42 \\ n=12 \\ t=1 \end{gathered}`

By plugging this information in equation (1), we get the answer as follows:

`\begin{gathered} A=(6000)\cdot(1+(0.042)/(12))^((12)\cdot(1))-(6000) \\ A=(6000)\cdot(1.0035)^(12)-(6000) \\ A=(6000)\cdot(1.043)-6000 \\ A=\$(6,256.908-6000) \\ A=\$256.908 \\ \therefore\Rightarrow \\ \text{ROI}=A=\$256.908 \end{gathered}`