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 $\displaystyle \frac{-p'(i)}{p(i)}=\frac{1}{i^2}$

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 $\displaystyle 10+5=15$?

Or is the modified duration going to be $\displaystyle \frac{-p'(i)}{p(i)}$ where $\displaystyle p(i)=\frac{d}{i(1+i)^5}$?