Question

What is the present value of $4,100 per year at a discount rate of 9 percent if the first payment is received 5 years from now and the last payment is received 15 years from now?

Answer 1

Solution:-

$4,100 is an ordinary annuity as the amount is received every year starting from the 5th year and till the 15th year.

The number of years from 5th year to 15th year = 11 years.

Using the present value of annuity for r = 9% and n = 11 years(from the present value tables) we get present value factor for an ordinary annuity.

PVIFA_9%,11 = 6.8052

Thus the present value of amounts received as at the beggining of 5th year will be = $4,100 * 6.8052

= $27,901.32

Now above value is the amount as on the beggining of 5th year(or the end of 4th year) we have to further discount for 4 more years.

where r = 9%

n = 4

(Presenet value interest factor)PVIF_9%,4 = 0.7084

THUS THE PRESENT VALUE TODAY WILL BE = present value at the beggining of 5th year*PVIF

= $27,901.32 * 0.7084

= $19,765.29