TVM Question

Dear all: Can anyone help me to resolve the questions in CFA book p.212 Q: A client plans to send a child to college for 4 years starting at 18 years from now. Having set aside money for tution, she decide to plan for room and board also. She estimate these costs at 20,000 per year, payable at BEGINNING of each year, by the time her child goes to college. if she start next year and make 17 payments into saving account paying 5% annually, what annual payment must she make? my answer: 1) set calculator to BGN: PM=20,000, i=5%, n=4, PV=? (74,464.9) 2) set calculator to END: FV= 74,464.9, i=5%, n=17, PM=2881.73 (answer) which is different with 2774.5 in the book (which BGN mode not set) I don’t know what’s wrong in my calculation. Can anyone help me

opcfkam, that’s odd. I calculated the same figure as the book, but using BGN mode for your second step as if she began saving today.

^ How do you get that number, i get $2,744.5, unless the original poster made a typo. Also, doing that makes no sense imo as that means that she invests the money today, and stops making contributions for the 17th year. That in turn leaves one year of uncompounded interest. I tend to agree with what opcfkam did for his solutions, i can’t understand why the answer is wrong. Can someone explain? Thanks.

18 years from now is the beginning of the 19th year (on a time line, the 19th year spans between 18 and 19). So at the beginning of the 19th year (or the end of the 18th) the parent has to make the first of the four payments of 20,000 each. That means that at the beginning of the 19 year, the parent has to have into the account an amount equal with (as you put it in BGN mode) 74,464.96. Great! Now, the 17 deposits are made starting 1 year from now (or in other words at the beginning of the second year, or the end of the first year), so the last deposit is made at the end of the 17th year, or the beginning of the 18th year, but this is 1 year before the first 20,000 payment, therefore the account has to have at the end of the 17th year/beginning of the 18th year, 74,464.96/1.05 = 70,919. What amount deposited at the END of the period would after 17 periods be equal with 70,919, at a 5% return? 2,744.5 Conversely, see this as two ordinary annuities: deposit of X amount for 17 years, at the end of the period, period starting today, that would allow for payment of 20,000 at the end of the 18, 19, 20, and 21st year. First calculate the PV of the ordinary annuity of 20,000 payments, that being 70,919. Than, make this the FV of the ordinary annuity for deposits, with I/Y=5, N=17,FV=70,919, PV=0, PMT=-2,744.5.

Many thanks for all answer Sorry for all, I have typo error for the answer, the answer should be $2,744.5 Map1, I understand what you means, many thanks for your help