TVM Question

An investor plans to retire 8 years from today. To maintain her standard of living, she needs to have $2.5 mill accumulated when she retires. Her portfolio is currently valued at 1.2 mill and is expected to return i/y = 7% annually. The minimum amount she must save at the beginning of each of the next 8 years to a achieve a retirement accumulation of 2.5 million is closest to: a) 0. b) 31,875. c) 39,914. d) 42,708.

D. PV = 1.2 I/Y=7 N= 8. CPT future value = 2.061823 So she needs a FV of 0.438177 FV= .438177 I/y = 7 N =8 (since she is depositing at beginning of 8 years) PMT=42708

c. 39914


C is the correct answer. D would be the answer it the payments were made at the end of the year. Note how D/C is equal to 1.07, which is equal to one plus the interest rate. That’s because these beginning/end of year questions can usually be arrived at by getting the answer assuming ordinary end of year payments, then adjusting by the interest rate. Looking for the two answers separated by the interest rate is also a hint that one of those answers is likely correct.

Answer is C. What did you do after you figured out she’s $255k short today? Is that the PV of the annuity due? I don’t get C when I calc for PMT and can’t figure out where I’m screwing up.

The most straightforward method is simply to punch in the following to the HP12C in “BEG” mode: N=8, PV = -1,200,000, FV = 2,500,000, i=7; solve for PMT = 39,914. If you would prefer not to risk having your calculator in BEG mode for test, do it the normal way and then divide the answer by 1.07.

nm, got it. Thanks.

I just did the ol plug and chug Set clac to BGN mode I = 7 N = 8 PV = 1.2MM FV = 2.5MM CPT PMT = 39,914,10

thanks, bud. I guess I was doing it the hard way :wink:

BGN N=8 I/Y=7 PV=-1.2 FV=+2.5 CPT—>PMT = 0.03991410 = C? EDIT: oops, sorry bud already posted ahead of me…

easy way > hard way > CFAI way :wink: Gonna make me a flash card of that one.

i hope we dont miss out on these small lil things like beginning of each month … etc., on the exam day most of the times i read least likely as most likely…n end up choosing the first statement that seems likely. :frowning:

Make sure you switch your calculator back into END mode!!

Coneptually, it seems like the following reflects what’s being described in the passage. You start with 1200, add something to it at the start of the year, grow it 7%, then start over next year. Whatever something gives you 2500 at the start of year 8 is what you’re looking for. This method yields answer C instead. Year_____Open Bal_____Saved_____7% Earned_____Close Bal 0________1200_______39.914________87_________1327 1________1327_______39.914________96_________1462 2________1462_______39.914________105________1607 3________1607_______39.914________115________1763 4________1763_______39.914________126________1929 5________1929_______39.914________138________2106 6________2106_______39.914________150________2297 7________2297_______39.914________164________2500 8____>>__2500_______39.914________17_________2718