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.)

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TomShelby TomShelby · Answer 1 · 2020-02-12T08:13:39+01:00

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

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

C 6,800.00

time 22 years (25 - 3)

rate 0.07

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

PV $75,216.4354

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

[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]

Maturity $75,216.4354

time 3.00

rate 0.07000

[tex]\frac{75216.4353825748}{(1 + 0.07)^{3} } = PV[/tex]

PV 61,399.0165

that would be the value of the annuity today.