Consider the following 3 series of payments:

1. An 11-year increasing annuity with payments of 10, 20, , 110
2. The payments (coupons and maturity value) from an 11-year annual coupon bond with a face amount of 100 and a coupon rate of 10%
3. An 11-year geometric annuity with an initial payment of 10 and an annual growth rate of 27.1%

Each series consists of 11 payments, and in each case the first payment is 10 and the final payment is 110.

Let D^a, D^b, and D^c be the modified durations for annuities a., b., and c., respectively, based on an annual effective interest rate of 10%.

Which of the following correctly describes the relationship among the modified durations for these 3 annuities?

A. D^a > D^b > D^c B. D^a > D^c > D^b C. D^b > D^a > D^c D. D^b > D^c > D^a E. D^c > D^a > D^b