A client plans to send a child to college for fours 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 $20,00 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?

I find the PV of the college expense ($20,000/yr) with annuity due mood and I got PV=74464, so the PV at the beg of 18th yr= 74464. Then I set FV=74464, N=17, I/Y=5, I got PMT=2882. However, the answer key is PMT=2744. I think the 1-17 payments are ordinary annuity that occur at the end of each year, so the 17th payment occur at the end of 17th yr = at the beg of 18th yr. If the 1-17 payments were annuity due that occur at the beg of each yr, the answer will be 2744. Could you explain why the answer is 2744 instead of 2882? What's wrong with my thinking?