Future Value of an Ordinary Annuity
[tex]FV=\text{PMT}\cdot\frac{(1+i)^n-1}{i}[/tex]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:
[tex]\frac{FV\cdot i}{\text{PMT}}=(1+i)^n-1[/tex]Adding 1:
[tex]\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}[/tex]Substituting values:
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