Del Monty will receive the following payments at the end of the next three years: \(2,000, \)3,500, and \(4,500. Then from the end of the 4th year through the end of the 10th year, he will receive an annuity of \)5,000 per year. At a discount rate of 9 percent, what is the present value of all three future benefits?

Time value of money is a concept of valuing the future amount at present or valuing the present amount in future. TVM compares the money value at two different point of time by compounding or discounting one value with respect to other.

$\begin{array}{c}\mathbf{Present}\mathbf{}\mathbf{value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{second}\mathbf{}\mathbf{payment}\mathbf{=}\mathbf{Amount}\mathbf{\times }\frac{\mathbf{1}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{discountrate}\mathbf{)}}^{\mathbf{Numberofyears}}}\\ \mathbf{=}\mathbf{\$}\mathbf{3}\mathbf{,}\mathbf{500}\mathbf{\times }\frac{\mathbf{1}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{09}\mathbf{)}}^{\mathbf{2}}}\\ \mathbf{=}\mathbf{\$}\mathbf{2}\mathbf{,}\mathbf{945}\mathbf{.}\mathbf{88}\end{array}$

$\begin{array}{c}\mathbf{Present}\mathbf{}\mathbf{value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{third}\mathbf{}\mathbf{payment}\mathbf{=}\mathbf{Amount}\mathbf{\times }\frac{\mathbf{1}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{discountrate}\mathbf{)}}^{\mathbf{Numberofyears}}}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{500}\mathbf{\times }\frac{\mathbf{1}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{09}\mathbf{)}}^{\mathbf{3}}}\\ \mathbf{=}\mathbf{\$}\mathbf{3}\mathbf{,}\mathbf{474}\mathbf{.}\mathbf{83}\end{array}$