Ordinary Annuity vs. Annuity Due

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.

You clearly understand when the payments are being made and you can do the correct calculation. I, for one, see nothing wrong with your approach.

I encourage my candidates to draw a timeline for problems such as this. If you do that, it doesn’t matter whether you call it an ordinary annuity or an annuity due.

Thanks for your response. Much appreciated!

My pleasure.