# Perpetuity

I disagreed with the given answer in this question. Wonder what you all think: An investor has decided to set a scholarship. The plan is for the fund to be capable of awarding 25,000 annually in perpetuity. The first scholarship is to be awarded and paid out exactly four years from today. The funds will be deposited into an account immediately and will gorw at a rate of 4% compounded semiannually for forseeable future. How much money must the investor donate today to fund the scholarship. a. 528,150 b. 549,487 Right this is my thinking. The required value for the perpetuity is 25,000 / (1.0404) = \$618,811.88 The answer agrees to that. But the issue is here, I discounted this value to today: 618,811.88 / (1.0404) ^ 4. Because as the question asked the first payment will be in T4. So there are 4 years exactly since then. We need 618,811.88. But the answer divided this value by 1.0404 ^ 3. Anyone can explain this for me?

A perpetuity should always be present valued at n-1…look at every DDM example where there is a perpetuity

because if you discount back with 4…you are going back too far… you are finding the value at time zero…that value is based on the payment in year 1… Make sense?

Well, it is confusing, so i hope they don’t ask stuff like that , but to your question: if periods are like this: 0 1 2 3 4 0=now, and since this is annuity due, first payment is in period 0 , and first scholarship is in 4, so from 0 to 4 is 4 years, so perpetuity discounts to the period (t-1) so perpetuity starting at period 4 will be discounted to 3, and then from 0 to 3 is 3 years, so discount by another 1.0404^3 but i would get this one wrong too if i didnt know the right answer…

mib20 Wrote: ------------------------------------------------------- > A perpetuity should always be present valued at > n-1…look at every DDM example where there is a > perpetuity Aha right. OK that does it. Geez I would totally get this question wrong hadn’t I do this one this evening.

quick question, how did you arrive at .0404?

Semiannual compound. [(.04/2)+1]^2 = 4.04

thanks.