What’s the correct answer and how do you get there? A successful investor has decided to set up a scholarship fund for deserving students at her alma matter. Her plan is for the fund to be capable of awarding $25000 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, for the forseeable future. How much money must the investor donate today to fund the scholarship? A $528150 B $549487 C $574253 D $618812
FV = (25000/.04), n = 8, rate = 2% compute PV
That’s what I did, and I get a PV of 533,431 which isn’t one of the answers…
closest to A, pick it and go with it. if its not A, then its a trick question, move on to the next trick one. Exam has 120 of them.
The correct answer seems to be B) 549487 but I’m not sure how they got that answer?
Pepp: totally agree. I’ll read a question, do it properly, get what I think it the right answer, then discover there’s a trick that means I’m wrong. As for this Q, is there any explanation behind the answer?
No explanation provided. I only have the correct choice.
EAY=(1.02)^2=1.0404 since the 1st $25000 should be given out at year 4 from today. so the at beginning of year 3, the minimium principal to genernate $25000 return should be ready,i.e we have 3 years to grow the principal, not 4 year. and the principal is 25000/.0404=618,812 and PV=618,812 PMT=0 I=2 N=6–>PV=549,487 or PV=618,812 PMT=0 I=4.04 N=3–>PV=549,487 same result B
What confuse me is the fact that we have an “annual” perpetuity and “semi-annual” compounded interest. we should consider the interest annually I think
strangedays Wrote: ------------------------------------------------------- > What confuse me is the fact that we have an > “annual” perpetuity and “semi-annual” compounded > interest. we should consider the interest annually > I think yeah you still get A, see annex’s solution. he has found theEAY to be 4.04
Answer is B Find the EAY (1.02)^2-1 = 4.04% Find the PV of the perpetuity>>> 25,000/(0.0404) = 618,812 Remember that this PV is at T=3…not T=4…now discount it back 3 years 618,812 / (1.0404)^3 = $549, 487
nirjraina Wrote: ------------------------------------------------------- > Answer is B > > Find the EAY (1.02)^2-1 = 4.04% > > Find the PV of the perpetuity>>> 25,000/(0.0404) > = 618,812 > > Remember that this PV is at T=3…not T=4…now > discount it back 3 years > > 618,812 / (1.0404)^3 = $549, 487 Can you explain to me why you did: > Find the EAY (1.02)^2-1 = 4.04% where did you get this 2% from?
best to draw a time line in this case, i was sleepy when i did this problem… i pray to god i wont get this wrong on the exam.
Thank you!
This is covered in one of the early quant chapters… Basically when they say 4% compounded semiannually it means (1 + 0.04/2)^2 -1 = 4.04% If its compounded monthly…(1 + 0.04/12)^12 -1 = 4.07%
Also 4% compounded semi-annually is the same as saying it has a BEY of 4%
nirjraina Wrote: ------------------------------------------------------- > This is covered in one of the early quant > chapters… > > Basically when they say 4% compounded semiannually > it means (1 + 0.04/2)^2 -1 = 4.04% > > If its compounded monthly…(1 + 0.04/12)^12 -1 = > 4.07% Ok, so calculate the EAY as we have annual perpetuity. is it correct? Thanks for the explanation
Yeah that’s pretty much it