TVM Question, please help

Financial Planning - Financial planning in general. (Moderated) 

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Subject Author Date TVM Question, please help Sean-usenet 02-08-2007  Re: TVM Question, please help Tad Borek 02-08-2007  Re: TVM Question, please help Sean-usenet 02-09-2007
Posted by Sean-usenet on February 8, 2007, 4:33 pm Hello Everyone I am a MBA student and my finance teacher and I have a disagreement on the correct answer for the following TVM problem. I have included my answer below it, could someone please confirm if the answer is correct or not? Jim wants to go to Graduate School to get his MBA. He plans to work for 4 years and save for tuition then attend a MBA program full-time for two years. Currently it would cost him $55,000 each year for tuition for the MBA program, however he expects the price of tuition to increase at a rate of 7% each year. He has been offered a special graduate education saving account that earns a nominal annual return of 12%, however interest will compound monthly. Assume that he decides to start saving for his education exactly 48 months (4 years) before the targeted starting date. He plans to make a deposit at the beginning of the first month (at time 0) then at the end of each of the next 48 months (4 years) to finance his graduate education for a total of 49 payments. At the end of the 48 months he should have enough money in his account to finance his education for both years (the tuition for the second year will stay in the account until it is needed at the beginning of the second year). How much will he need to deposit each month in order to finance his graduate education? My answer: Tuition is currently $55,000/year, increasing at 7%/year. In 4 years, tuition will be: 55,000*(1.07)^4 = $72,093.78 In 5 years, tuition will be: 55,000*(1.07)^5 = $77,140.35 The year 5 tuition discounted back 12 months @ 1%/month= $68,458.14 So, at the end of 4 years, we will need $140,551.93 (which is 72,093.78 + 68,458.14) in the savings account to pay for the 2 years of grad school. My professor and I agree 100% up to this point. The student plans to make a deposit right now (at time 0) and at the end of each of the next 48 months. So that is the same thing as a 48 month ordinary annuity with an extra deposit at time 0. That is also the same thing as a 49 month annuity due. So, a 49 month annuity due would need deposits of $2,214.75 at the beginning of each month to end up with the $140,551.93 needed for tuition. Do you all of you also get $2,214.75??? I've asked a few of the finance people in my office they agree with what I have, but my professor says I should be computing a 49 month ordinary annuity. But how can that be right? Since ordinary annuity annuity have payments at the end of each month, we lose out on the deposit at time 0 and we have an extra deposit at the end of month 49, but Jim was supposed to stop depositing at the end of month 48; he is already in school during month 49. Thank so much for any help you can provide, I appreciate it! Sean Posted by Tad Borek on February 8, 2007, 7:38 pm Sean-usenet wrote: > Thank so much for any help you can provide, I appreciate it! I get 2236.85. A simple way to solve it is to treat it as an ordinary annuity of 49 months. The first month nothing happens until the final day when you make your first "deposit." Then, another deposit lands at the end of each month, for the next 48 months. And you immediately see your 140552 at the end of month 49 (which is really just 48 months after your first deposit). This models the deposit pattern you laid out. So you put your calculator in END mode, N=49, PV=0, FV=148552, %I=12, 12 PER/YR, and you get PMT=2236.85. Another, harder way is to treat it as an ordinary annuity of 48 months with an initial deposit (i.e., a non-zero PV). Iterate with N=48, %i=12, FV=140552, 12 PER/YR, "END" mode (for an ordinary annuity) and try to match PV and PMT. You still get 2236.85. Your mistake is equating a 48 month ordinary annuity (with an extra deposit at t=0) with a 49 month annuity due. Those aren't the same. The latter leaves the entire balance invested for an extra month after the end of year four. Play around with the extra 1% you get at the end of the pipe and you'll see what I mean. So your prof sounds right. Keep in mind that he's using the 49 month annuity calculation just as a shortcut to the answer. It's not that the money is invested 49 months, but that the deposit pattern over 48 months (including an initial one) is mathematically equivalent to an ordinary annuity of 49 months. -Tad Posted by Sean-usenet on February 9, 2007, 1:21 pm Hi Tad Yea, $2,236.85 is right, I understand it now. I won't make that mistake again! Thanks for you help! Sean > Sean-usenet wrote: > > Thank so much for any help you can provide, I appreciate it! > > I get 2236.85. > > A simple way to solve it is to treat it as an ordinary annuity of 49 > months. The first month nothing happens until the final day when you > make your first "deposit." Then, another deposit lands at the end of > each month, for the next 48 months. And you immediately see your 140552 > at the end of month 49 (which is really just 48 months after your first > deposit). This models the deposit pattern you laid out. > > So you put your calculator in END mode, N=49, PV=0, FV=148552, %I=12, 12 > PER/YR, and you get PMT=2236.85. > > Another, harder way is to treat it as an ordinary annuity of 48 months > with an initial deposit (i.e., a non-zero PV). Iterate with N=48, %i=12, > FV=140552, 12 PER/YR, "END" mode (for an ordinary annuity) and try to > match PV and PMT. You still get 2236.85. > > Your mistake is equating a 48 month ordinary annuity (with an extra > deposit at t=0) with a 49 month annuity due. Those aren't the same. The > latter leaves the entire balance invested for an extra month after the > end of year four. Play around with the extra 1% you get at the end of > the pipe and you'll see what I mean. > > So your prof sounds right. Keep in mind that he's using the 49 month > annuity calculation just as a shortcut to the answer. It's not that the > money is invested 49 months, but that the deposit pattern over 48 months > (including an initial one) is mathematically equivalent to an ordinary > annuity of 49 months. > > -Tad ======================================= MODERATOR'S COMMENT: Please trim the post to which you are responding. "Trim" means that except for a FEW lines to add context, the previous post is deleted. Similar Threads Posted IRA question January 8, 2007, 5:00 am 529 question January 11, 2007, 4:41 pm S.S. 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