The question is:
Grandparents are funding a newborn’s future university tuition costs, estimated at $50,000/year for four years, with the first payment due as a lump sum in 18 years. Assuming a 6% effective annual rate, the required deposit today is closest to?
The solution is:
I don't understand why we are using 17 Years but not 18 years as it was asked in the task?
From the question, it seems to imply that since
"the first payment due as a lump sum in 18 years"
The payment is due on day 1 (the beginning) of the 18th year. Which is why you calculate the PV of the ordinary annuity at year 17. Which is why $173,255.28 is the present value of 4 payments of $50,000 each.
The PV at the end of year 17 can also be calculated as: (50,000/(1+0.06)^1) + (50,000/(1+0.06)^2) + (50,000/(1+0.06)^3) + (50,000/(1+0.06)^4) = $173,255.28
Perhaps that's a bit more intuitive? (Discounting the cash flows by the time period they occur after the end of year 17, for the subsequent 4 years)
Then since $173,255.28 is the PV at year 17, the deposit needed today to ensure that the grandparents have $173,255.28 at the end of year 17 is (173,255.28/(1+0.06)^17) as stated in the solution.
