# Modified duration of a perpetuity.

• August 12th 2012, 08:25 PM
downthesun01
Modified duration of a perpetuity.
Find the modified duration of perpetuity immediate paying a level payment of d beginning in five years, at an annual effective interest rate of 10%.

Ok. I know that the modified duration of a level payment perpetuity is $\frac{-p'(i)}{p(i)}=\frac{1}{i^2}$

But since this perpetuity starts in five years, I'm a little confused as to what the answer should be.

If the perpetuity started right now, it's modified duration would be 10. Since it's starting in five years, does that make it's modified duration $10+5=15$?

Or is the modified duration going to be $\frac{-p'(i)}{p(i)}$ where $p(i)=\frac{d}{i(1+i)^5}$?
• August 13th 2012, 05:11 PM
Wilmer
Re: Modified duration of a perpetuity.