Question

Use the future value formula to find the indicated value.

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FV = 2,000; i = 0.02; PMT = $200; n=?

Answer 1

Future Value of an Ordinary Annuity

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

Where.

FV = Future Value of the investment

PMT = Regular payment (annuity)

i = Interest rate

n = Number of periods of the investment

We are given the data:

FV = 2,000, i = 0.02, PMT = $200

It's required to find the value of n. We are going to solve the equation for n as follows:

Multiply by i and divide by PMT:

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

Adding 1:

`\begin{gathered} \frac{FV\cdot i}{\text{PMT}}+1=(1+i)^n \\ \text{Taking logarithms:} \\ \ln \mleft(\frac{FV\cdot i}{\text{PMT}}\mright)=n\ln (1+i) \\ \text{Dividing by }\ln (1+i)\text{:} \\ n=\frac{\ln \mleft(\frac{FV\cdot i}{\text{PMT}}\mright)}{\ln (1+i)} \end{gathered}`

Substituting values: