Question

What is the present value of $2,625 per year, at a discount rate of 6.9 percent, if the first payment is received six years from now and the last payment is received 20 years from now?

Answer 1

Solution

Present value of annuity at the end of fifth year==Annuity payment*((1-(1/(1+r)^n))/r)

where

r-discount rate per period-6.9%

n-number of periods -15

Annuity payment-2625

Putting values in formula

Present value of annuity at the end of fifth year=2625*((1-(1/(1+.069)^15))/.069)

=24060.02

Now Present value of this Present value of annuity at the end of fifth year=Present value of annuity at the end of fifth year/(1+r)^m

where m-number of discounting periods=5

Putting values

Present value =24060.02/(1+.069)^5

=$17234.85

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