Annuity TVM

CFA Level I
#1

A mutual fund salesman tells John Q. Public that the Tradem & Weep growth fund is expected to generate an effective annual rate of 15% per year. John decides to invest $500 per month into the fund for the next 25 years and writes the first $500 check to the salesman. If the fund charges an 8% load on each monthly investment to pay the salesman’s commission, how much should John expect his investment to be worth when the investment program ends? a. $1,510,674 b. $1,192,237 c. $1,268,041 d. $1,253,358 - Dinesh S

#2

I am going with C. N=300 I/Y=1.17 PMT=460 CPT FV->1253335.23 1253335.23*1.0117~ 1268000 Since its annuity due. Am I right?

#3

I think it’s A. since this is an annuity due (he writes a check today) plus the fact that 8% of that $500 is going to be deducted every month. Thus, PMT= - 460, N= 25* 12= 300, I/Y= 15/12= 1.25, PV= 0, FV= $1,510,674 Dinesh, what’s the answer pls?

#4

It should be A.

#5

It says 15% is EAR so (1+r)^12 -1 = .15 r = 1.15^(1/12) - 1 = 1.1715% PMT=460, N=300, BGN Mode, FV=? Answer: 1268013

#6

I got A —> If it is C, can someone explain why we are using I/Y = 1.17. I know you are saying it has something to do with them giving us the EAR, but my brain is not connecting the dots on this one…

#7

Yes that is the reason. It says 15% is EAR – so need to get the right rate for that one. CP

#8

I agree, it is C…although i got 1,268,017.96 but that seems close enough.

#9

guys, the answer is C. LongOnCFA and cpk123 (as usual) are bang on target. - Dinesh S

#10

Don’t forget me, sir…i got it in under the wire!!

#11

petetini Wrote: ------------------------------------------------------- > Don’t forget me, sir…i got it in under the > wire!! sure, petetini you are right on target too… actually we posted on the exact same time 9.33.

#12

Bodymore Wrote: ------------------------------------------------------- > I got A —> If it is C, can someone explain why > we are using I/Y = 1.17. I know you are saying it > has something to do with them giving us the EAR, > but my brain is not connecting the dots on this > one… Because 15% is effective annual rate, and to compare apples-to-apples we need to convert it to Periodic Rate (monthly) using… ***************** EAR = (1 + PR)^n - 1 ***************** so we have a Periodic Rate (monthly in this case) of 1.17% - Dinesh S

#13

Thanks Dinesh for explanation of EAR stuffs. Now I got it.

#14

Thanks Dinesh for explaning EAR stuffs. Now I got it.