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netineya [11]
3 years ago
9

What is the value today of an annuity of $6,800 per year, with the first cash flow received three years from today and the last

one received 25 years from today? Use a discount rate of 7 percent. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
Business
1 answer:
erma4kov [3.2K]3 years ago
5 0

Answer:

PV   $61,399.0165

Explanation:

First, we solve for the present value of the annuity:

                 3rd year  > Annuity Start                    25th year end

<-----/----/----/----/----/----/----/----/----/......----/----/----/----/----/---->

     ^ Present day

C \times \frac{1-(1+r)^{-time} }{rate} = PV\\

C 6,800.00

time 22 years (25 - 3)

rate 0.07

6800 \times \frac{1-(1+0.07)^{-22} }{0.07} = PV\\

PV $75,216.4354

Now, as this is 3 years from now so we make an additional discount from this lump sum:

\frac{Maturity}{(1 + rate)^{time} } = PV  

Maturity  $75,216.4354

time  3.00

rate  0.07000

\frac{75216.4353825748}{(1 + 0.07)^{3} } = PV  

PV   61,399.0165

that would be the value of the annuity today.

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