Question

What is the future value of a 10-year investment of $2000 at an APR of 5% compounded monthly? (Round answer to nearest cent.)

Answer 1

The formula for finding the future value of an investment is given below

`\begin{gathered} FV=PV(1+r)^n \\ \text{Where} \\ FV=\text{Future value} \\ PV=\text{Present value} \\ r=annualyinterest\text{rate} \\ n=nmber\text{ of periods interest} \end{gathered}`

From the question given, the following were given

`\begin{gathered} PV=\text{ \$2000} \\ r=5\text{ \%} \\ r=(5)/(100)=0.05 \\ r_{\text{monthly}}=(0.05)/(12)=0.0041667 \\ n=10 \\ n_{\text{monthly}}=10*12=120months \end{gathered}`

Substitute all the given into the formula as shown below

`\begin{gathered} FV=2000(1+0.00416667)^(120) \\ FV=2000(1.00416667)^(120) \end{gathered}`
`FV=3294.032`

Hence, the future value to the nearest cent is $3294.0