A six-month zero coupon bond with face value $100 sells for $99.46, a one-year zero coupon bond sells for $97.23, and an 18-month zero coupon bond sells for $90.50. Suppose a new coupon-paying bond, making semi-annual coupon payments, is issued today with face value $100, maturity of 18 months, and a semi-annual coupon payment of 9% (APR).

(a) Calculate the no-arbitrage price of the coupon paying bond today.

(b) Calculate the implied forward rates in this economy.