an investor is celebrating his 50th birthday today and want to start saving for his anticipated retirement at age 65. he wants to be able to withdraw $15,000 from his savings on each birthday for 20 years following his retirement, with the 1st withdraw being made on his 66th birthday. after extensive research, the investor determines that he can deposit his money into an account that offers 5% interest per year (compounded quarterly). he wants to make equal annual payments on each birthday into the account-- 1st payment on his 51 birthday, and last one on his 65th birthday. in addition, the investor’s employer will contribute $100 to the account at end of everymonth as part of company’s profit-sharing plan(total 180 contributions.) what smount must the invest deposit personally each year on his birthday to enable him to make the desired withdrwals at retirement? a. 7,305 b.9,411 c.12,667 d. 15,549 answer is A.7,305
I got 7,293, close enough to pick the right one I guess.
Shabadoo1 Wrote: ------------------------------------------------------- > I got 7,293, close enough to pick the right one I > guess. what’s your calculation?
- Compute PV of $15,000 annual payments taken for 20 years using annualized int of 5.0945 (5.00 comp quarterly) = 185,444.36 2) Subtract FV Employer monthly contribution (180 pymts) of $100 mthly contributions at 5.0945/12 = -26,940.86 3) Leaves a FV of 158,503.50 for the investor to fund over 15 years. n=15; i=5.0945; FV = 158,503.50: CMPT PYMT = 7,293.33 I might be missing something as it’s off a bit to the given answer or it may be rounding. Shab
How long did you take to do this? IS this the difficulty level expected in the real exam? If yes, I seriously need to look at calculations.
I probably went about 3 to 4 minutes on this one. It took me a bit to consider annualizing the 5.00 compounded quarterly.
Ouch, this one is nasty. First, clear the TVM worksheet. Hit [2nd] [I/Y]. Make P/Y=1, but arrow down and make C/Y=4. Next, we’re computing the PV of 15,000 per annum, starting at his 66th birthday. If we use the ordinary annuity function, we’re discounting to year 65. That’s fine, as his last payment into his retirement account will end at age 65. 5% nominal rate, compounded quarterly is our given cost of funds. So, N=20, I/Y=5, PMT=15,000, [CPT] PV and you get $185,443.83 as the present value at age 65. Now, clear TVM. We need to factor in the $100 payments that the employer will make. But this is where it gets tricky. The employer will be depositing payments into the account on a monthly basis, not quarterly. This throws our interest assumption out of whack. But the beauty of math is that we can manipulate values to create equivalents in a different time perspective. Hit [2nd] [2], and clear your work in the interest conversion worksheet. Make the nominal rate 5, and change C/Y to 4. Compute the effective yield. You get an effective rate of 5.0945%. Now, leave that value alone and go back and change C/Y to 12, and then compute the nominal rate. You get 4.9793%. This is the nominal rate (annualized for monthly compounding) is effectively the same as a 5% nominal rate with quarterly compounding. Plug that 4.9793 value into the TVM worksheet as I/Y. Hit [2nd] [I/Y], and change P/Y (and C/Y) to 12. Change N to 180, and make PMT 100. Compute the FV and you get $26,682.76. That’s the value of the employer’s contributions up to the person’s 65th birthday. Now, thanks to the additive cash flow principle, subtract this value from $185,443.82. You’re left with $158.761.06. Clear TVM. Make that value the FV. Hit [2nd] [I/Y] and make P/Y=1 and C/Y=4. Now, clear TVM. Make N=15, I/Y=5, and PV=0. Compute PMT. Answer: $7305.16. I don’t think a question like this is realistic on the actual exam.
gdiddy, Nice post mate. If I encounter anything like this - a speedbreaker, I will skip it. S
here’s explanation. when using P/Y and C/Y function, should pay extra attention. its value won’t be cleared by “CLR TVM” or “RESET”, we must enter into “P/Y” then press “2ND+CLR WORK” to clear them, if not it will go to next TVM calculation and cause a wrong answer. That happened times to me. This explanation didn’t use any P/Y and C/Y function to solve the problem. Although it’s hardly meet this kind of tough Q in exam, this still help to deep the understanding of TVM calculation. --------------------------------------------------------------------- The first step is to find the effective annual rate (EAR) that the account offers. With quarterly compounding: The amount the investor needs at retirement is the present value of the $15,000 planned withdrawals. We can find this amount from the following: PMT= -5,000; N = 20; I/Y = 5.0945; FV = 0; CPT¨ PV = 185,444.35. Now we have to account for the series of $100 contributions made by the investor’s employer. These are monthly deposits made to the account and in order to find their future value, we need to convert the EAR found earlier to an effective monthly rate (EMR). We can find the EMR from the relationship: The future value of the employerfs $100 contributions can be found from the following: PV = 0; PMT = -100; N = 180; I/Y = 0.4149; CPT ¨ FV = $26,681.63.This amount reduces the terminal value needed in the account at retirement. The amount the investor is responsible for is $185,444.35 -$26,681.63 = $158,762.72. This must be the future value of the investorfs deposits which we can now find from: PV = 0; FV = -158,762.72; N = 15; I/Y = 5.0945; CPT ¨ PMT = $7,305.25.
I got 7305.15898, after setting the calculations to 5 decimal places. The questions that was given here was not that tough, I came across a question that I consider the most toughest TVM question. I am not trying to scare people around here, but I am sharing something that I came across. Question: A couple plans to pay their child’s college tuition for 4 years starting 18 years from now. The current annual cost of college is C$7,000, and they expect this cost to rise at an annual rate of 5 %. In their planning, they assume that they can earn 6% annually. How much must they put aside each year, starting next year, if they plan to make 17 equal payments? Answer: C$2221.58 each year if they start next year and make 17 equal payments.