# TVM question

I stumbled on the following yesterday:

"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?

Mistake.

The answer is B, getting PV of 10 years annuity which will be FV that is then used to get simple PV of 4 years.

Exactly Furio. Could you indicate me why we get the simple PV of 4 years instead of 5?

Because it’s the beginning of year 5. Or the end of year 4. So four periods.

draw a timeline out

if a fixed amount of \$10,000 were deposited with 14% rate of interest for 10 years - starting at YR 5

your PV of that cash flow stream = 52161 - at the end of Year 4

so now your PV = 1/1.14^4 * 52161 = 30884

Got it! Thanks guys!

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.