Question

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.)

Answer 1

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.