Lincoln Memorial hospital has just been informed that private donor is willing to contribute $5 million per year at the beginning of each year for fifteen years. What is the current dollar value of this contribution if the discount rate is 9 percent?

Answer 1

We have two main annuity formulas

1. PV of annuity = payment [ 1 - (1+i)^-n ]/i
and
2. Amount of annutiy = payment [ (1+i)^n - 1 ]/i

both of these assume that the payments are made at the end of each interest period.
So for this question, we have to separate the first payment from the remaining 14.

PV = 5 million + 5million( 1 - 1.09^-14)/.09
= 5 million + 5million( 7.78615...)
= $43,930,751.94