This is in reference to CFAI pg 343, Fixed Income. Says
Avg life = sigma(1to t) of t x proj principal received at t/ (12 x Tot principal)
So lets assume you plan on paying 1/12 every month, so proj principal/Tot equals 1/12. So then the formula is
Avg life = 1/ (12 x 12) sigma(1 to t) t
Avg life = 1/(12 x 12) x t(t+1)/2
If you are paying 1/12the every month, t=12, so avg life is 0.54 yrs.
How do I make sense of the fact that 12 equal principal payments equals an avg life of 0.54?