Can some one help me out with the following question.
“A client plans to send a child to college for four years starting 18 years from now. Having set aside money for tuition, she decides to plan for room and board also. She estimates these costs at $20,000 per year, payable at the beginning of each year, by the time her child goes to college. If she starts next year and makes 17 payments into a savings account paying 5 percent annually, what annual payments must she make”?
Doesn’t the 20,000 per year mean its an auuity due ??
But in the answer, its being considered an ordinary annuity and calculation for PV of four payments of 20,000 per year comes through considering it an ordinary annuity.
Make sure that you’re not confusing the room and board payments (which, if you start counting at the beginning of the first year the child is in university, is an annuity due) with the payments to fund the savings account (which, if you start counting today, is an ordinary annuity).
Sorry for late reply guys, altough I started the post. Anyways, firstly what I understood from the question was that you had to find the PV of the 20,000 annuity and considering it a annuity due as its paid at the beginnning of the year, the PV comes to $74,465.
Secnondly, the PV would become the FV for the 17 annual payements and that would be considered an ordinary annuity as its paid at the end of the year. FV=74,465, N=17, I/Y=5%, PMT=>2,881. But the problem is that the answer shown in the CFA curriculum is $2,744, now I dont’t get that. why is this so.
The CFA curriculum shows the calculation as PV=70,919 in the first instant, because they consiered the 20,000 payment an ordinary annuity. Well how could that be possible, when its being paid at the beginning of the year.