I'm hoping someone could help me understand this subject better.
Basically I am reading a book and it shows a table
Coupon Rate | 10 yrs | 20 yrs | 30 yrs | 50 yrs 3% | 7.894 | 11.744 | 12.614 | 11.857 6% | 7.030 | 9.988 | 10.952 | 11.200 9% | 6.504 | 9.201 | 10.319 | 10.975 12% | 6.150 | 8.755 | 9.985 | 10.862
It then asks, How can you tell from the table that the modified duration is not an increasing function of maturity?
I don't really understand that. I know that as the coupon rate increases the loan is repaid faster because of the lower modified duration.
But it would seem as maturity increases then so does modified duration. So it would seem like its an increasing function just from looking at it. At least to me.
Can anyone tell me where this information comes from? Like how is it not an increasing function of maturity?