PV of annuity problem

Q:an investor will receive an annuity of $4000 a year for ten years. The first payment is to be received five years from today. At a 9% dusciybt rate, this annuity’s worty today is closest to.

A:$16684 B:$18186 C: $25671

Answer: B

So I calculated PV of this annuity at five years from now, $25670.63. But why should I use N=4 instead of N=5 when discount it to today based on five years from now PV?

Thank you!

draw a timeline first for all of these problems.

from year 5 onwards for 10 years he receives 40K per year.

When you calculate the PV of that series- your PV is at year 4 - isn’t it? (One year earlier).

oh shoot thats right! thanks a lot man! sorry if its a dumb question

First payment beginning of year five = annuity due

You 1. either put your calculator in BGN mode and then discount by 5 years, or 2. you keep your calculator in END mode and “simulate” the first payment as of year end 4. By doing so, you only need to discount back by 4 years.

In any case a timeline is extremely helpfull when solving this kind of problems.