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Del Monty will receive the following payments at the end of the next three years: $5,000, $8,000, and $10,000. Then from the end of the 4th year through the end of the 10th year, he will receive an annuity of $11,000 per year. At a discount rate of 9 percent, what is the present value of all three future benefits

Respuesta :

Answer:

Present value of all future benefits  = 19,042.58 + 55362.48 = $74,409.24

Explanation:

Given data:

Next three payment at end of next three year are $5000,$8000 and $ 10,000

Amount received at the end of 10th year $11,000 per year.

discount rate = 9%

Present cash of flow is calculated as

[tex]PV = \frac{ FV_1}{(1+r)^1} +\frac{ FV_2}{(1+r)^2} + \frac{ FV_3}{(1+r)^3}[/tex]

[tex]PV = \frac{5000}{(1+0.09)^1} + \frac{8000}{(1+0.09)^1} + \frac{10,000}{(1+0.09)^1}[/tex]

PV = $ 19,042.58

Present value of annuity [tex] = FV \times \frac{1 -(1+r)^{-n}}{r}[/tex]

                                     [tex] = 11,000 \times \frac{1 -(1 +0.09)^{-7}}{0.09}[/tex]

Present value of annuity = 55,362.48

Present value of all future benefits  = 19,042.58 + 55362.48 = $74,409.24