I’ve always felt a little uncomfortable with spotting the difference with these. I got the correct answer to the following question, but just did it a different way. My question is, does that matter? I swithed the calculated to BGN mode and calculated PV of 4x $20K payments for 4 years. Then, switched back to END mode, and calculated the PV of $71,542 over 10 periods to get $33,138. I suppose the difference is the PV at the time the first $20K payment is made, but it seems to me that it would be the correct method since she will need to pay $20K school fees on day one (i.e., the beginning of the period) in 10 years time, right? Comments? Thoughts? Thanks for the help.
It will cost $20,000 a year for four years when an 8-year old child is ready for college. How much should be invested today if the child will make the first of four annual withdrawals 10-years from today? The expected rate of return is 8%.
A) $66,243. B) $33,138. C)__$30,683.
First, find the present value of the college costs as of the end of year 9. (Remember that the PV of an ordinary annuity is as of time = 0. If the first payment is in year 10, then the present value of the annuity is indexed to the end of year 9). N = 4; I/Y = 8; PMT = 20,000; CPT → PV = $66,242.54. Second, find the present value of this single sum: N = 9; I/Y = 8; FV = 66,242.54; PMT = 0; CPT → PV = 33,137.76.