# Annuity TVM

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

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?

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?

It should be A.

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

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…

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

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

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

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

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.

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

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

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