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Sagot :
The formula for the present value of annuity(P) is given as,
[tex]P=\text{PMT}\times(\frac{1-(\frac{1}{(1+r)^n})}{r})[/tex]Given data
[tex]\begin{gathered} P=Present\text{ value of annuity=?} \\ \text{PMT}=\text{Amount in each annuity payment(dollars)=\$35,756} \\ r=\text{discount rate=2.2\%=}\frac{\text{2.2}}{100}=0.022 \\ n=n\text{umber of payments left to receive}=35\text{years} \end{gathered}[/tex]Hence,
[tex]P=35,756\times(\frac{1-(\frac{1}{(1+0.022)^{35}})}{0.022})[/tex][tex]\begin{gathered} P=35,756\times(\frac{1-(\frac{1}{(1.022)^{35}})}{0.022}) \\ P=35,756\times(\frac{1-(\frac{1}{2.141812027})}{0.022}) \\ P=35756\times(\frac{1-0.4668943807}{0.022}) \\ P=35756\times(\frac{0.5331056193}{0.022}) \\ P=35756\times(24.2320736) \\ P=866442.0238\approx866442.02(\text{nearest cent)} \end{gathered}[/tex]Therefore,
[tex]P(\text{Prevent value of annuity)=\$}866442.02[/tex]
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