Question

Use the future value formula to find the indicated value.FV = 10,000; i = 0.02; PMT = $800; n= ?

Answer 1

Step 1

State the formula for the future value.

`FV=\text{PMT(}((1+i)^n-1)/(i))`

where;

`\begin{gathered} FV=10,000 \\ i=0.02 \\ \text{PMT}=800 \\ n=\text{?} \end{gathered}`

Step 2

Plug in the given values

`\begin{gathered} 10000=800(((1+0.02)^n-1)/(0.02)) \\ (800\left(\left(1+0.02\right)^n-1\right))/(0.02)(0.02)=10000(0.02) \end{gathered}`
`\begin{gathered} 800\mleft(\mleft(1+0.02\mright)^n-1\mright)=200 \\ (1+0.02)^n-1=(200)/(800) \\ (1+0.02)^n-1=0.25 \\ (1+0.02)^n=0.25+1 \\ (1+0.02)^n=1.25 \\ \ln (1+0.02)^n=\ln (1.25) \\ n\ln (1+0.02)=\ln (1.25) \\ n=(\ln 1.25)/(\ln (1.02)) \\ n=11.26838111 \\ n\approx11\text{ to the nearest integer} \end{gathered}`

Hence, approximately to the nearest integer, n=11