"An investor wants to receive $10,000 annually for ten years with the first payment five years from today. If the investor can earn 14% annual return, the amount that she will have to invest today is:

A. $27,091

B. $30,884

C. $52,161"

I believe the answer is A, since you discount the first PV of 52,161 to 1.14^5 (5 years from now). However they discounted to 1.14^4 and I do not see why. Anyone can help?

The original answer to this question assumes an annuity immediate with PV at t=4 of $52,161. If you wanted to use the PV at t=5, you have to use an annuity due, which produces a PV of $59,463.72. Discounting with 5 years of interest will also produce a final answer of $30,883.

^ this is also right and help to better understand. It’s all about understanding timelines and where will the calculated PV be indexed in. in case of ordinary annuity the PV is indexed at the end of year 4 while for annuity due it will be indexed at the end of year 5.