# This TVM question tricked me

From Schweser Book 6 Exam 3 AM Session. A successful investor has decided to set up a scholarship fund for deserving students at her alma mater. Her 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 grow at a rate of 4% compounded semiannually. How much must the investor donate today to fund the scholarship. A) 528,150 B) 549,487 C) 574,253 D) 618,812 **Discussion re: part of the solution below. Skip if you want to solve on your own** To start, I found the EAR of the 4% compounded semiannually: 4.04%, which I then used to find the amount needed to fund the 25,000 payout to perpetuity. \$25,000/.0404 = \$618,812. I set this as FV, N=4, I=4.04, PMT=0, CPT-> PV This produced \$528,150, which is wrong. The reason is: "Note that since the first scholarship award is paid out in four years, the present value of the perpetuity represents the amount that must be in the account at time t = 3. " So using N=3 produces \$549,487, or B, which is correct. MY question is: Why is this N=3 and not N=4? This doesn’t make sense to me. If payout starts four years from today, you would have four periods in which the amount invested earns interest. The first 25k is paid out AFTER four periods, i.e. the beginning of the fifth period? Maybe I’m just dumb. I did wind up with a 75% though, so I don’t feel THAT dumb. Anyone able to help my mind grasp this?

When you’re calculating the PV of a perpetuity, you’re calculating the PV as of one period prior - i.e. the present value of this stream of cash flows that starts NEXT period. I would suggest going back and solving the qbank problems for the LOS involving calculating the PV or an annuity and an annuity due. This should build up the intuition

I also got tricked but i think he will save for three yrs since "The first scholarship is to be awarded and paid out exactly four years from today’ may be he needs to make three deposits. If you draw a line and put the first with drawal on yr 4 then you will see that he is only depositing three times. i.e. yr 1, 2, and 3 only yr 4 is for with drawal.