# Q,TVM

08CMV4-Q20 Rachel Kelly, age 24, is planning for retirement. Kelly’s annual consumption expenditures are currently \$30,000. She assumes her consumption expenditures will increase with the rate of inflation, which she expects to average 3% until she retires at age 68. Given a life expectancy of 83 years and constant expenditures in retirement, the amount Kelly must accumulate by her retirement date, assuming an 8% rate of return on her retirement account, is closest to: A. \$320,000. B. \$423,000. C. \$1,176,000. D. \$1,552,000. my calcualtion is close to C. any thought?

Years to retirement : 44 annuity after retirement: 30,000*1.03^44 =110143.57 PMT=110143.57, I/Y=8, N=15, CPT Pv = 942771.54 C is closest but still far away. Where is my wrong? Also, I am not sure this is annuity due or ordinary annuity. If the former one applies, I would multiple the above result by 1.08.

they want you to gross up \$30,000 by 44 years of inflation and assume that will be the constant yearly expenditure for the 15 years of retirement.Expense become 30,000*(1.03^44)=110,143 at age 68; FV=0 PMT=110,143 I=8% N=15 CPT PV(age68)=\$942,775, which is closest to C but not close enough to convince me this is what they have in mind. here’s my best guess. they made a mistake. the inflation 3% becomes zero after age68 is not reasonable. I assume 3% inflation all life long. Thus the effective annual return=8-3=5%. Expense 30000 become 30000*(1.03^44)=110,143 at age 68. FV=0 PMT=110,143 I=5% N=15 CPT PV(age68)=1,143,252. it is much closer to C 1,176,000. this is a very dirty question.

it doesn’t say if withdraw money at the end or beginning of year. in previous calculation, I used annunity. if it says withdraw money right after birthday or retirement annually, I guess it becomes annunity due, answer is 1,200,415; still C. what’s your opinion?

There’s got to be something missing in the question, because even with the \$1.14M, it’s 3% off. Not that it’s significant, but significant enough to make me doubt my answer…

guys, it seems this is from cfai mock exam - i just reviewed my feedback report - they use in their calculation n=25 instead of 15. life expectancy should be 93 years, so that answer coincide with C

Guys…come on…we must work on this question and make it clear. I am currently working on it…

Indeed, if you change the formula from N = 15 to N = 25, then you do arrive at C. Dear, pashuha00, please explain “feedback report”

there is a hyperlink on the page with results to.pdf feedback report after completion of mock exam. Although this report does not contain the explicit answer (ie ABCD), but provides with explanation/ computation for each question with the reference to los.

Thanks pashuha00!

strangedays, Nothing to work on. They definitely use 25 instead of 15 in their calculations. I dont know if this error is intentional or not, bearing in mind that anyway the answer is C.

thanks pashu!

Pashu this was really a good catch!Good

C. This is what question is asking: What is the PV at t=68 of a constant annuity where PMT = 110143.56 with rate of 8%, and time of 15 yrs. The way to compute the PMT is essentially to find out the FV of the current consumption at T=68 for a given inflation rate of 3%, for n = 68-24 took me 2 minutes to read and do it, i guess i should work on time now.

got C – if n = 15 and got D if n = 25. Good thing is you can change N quickly on the HP calculator and hit PV again to find the answer. The trick is that this is a 2 step TVM problem – step 1 – find the FV to get the PMT step II – plug the PMT in to get the PV where you are essentially discounting back 15 years, because she will not start collecting till age 68 and she is presumably dead @ age 83.

“The Time Value of Money,” Richard A. Defusco, Dennis W. McLeavey, Jerald E. Pinto, and David E. Runkel 2008 Modular Level I, Vol. 1, pp. 190-208 Study Session 2-5-d, e calculate and interpret the future value (FV) and present value (PV) of a single sum of money, an ordinary annuity, an annuity due, a perpetuity (PV only), and a series of unequal cash flows; draw a time line, specify a time index, and solve time value of money applications (for example, mortgages and savings for college tuition or retirement) Kelly expects her consumption spending (currently \$30,000 annually) to increase with the rate of inflation (3%) over the next 44 years until she retires. Her annual consumption spending at the time she retires will be \$110,143.57 (PV = 30,000, %I = 3, N = 44, solve for FV). To support that level of spending for 25 years of retirement, assuming an 8% return on her retirement account, she must accumulate \$1,175,756 by her retirement date (PMT = 110,143.57, ___N = 25___, %I = 8, solve for PV). 21 “Discounted