A one-year zero coupon bond with face value $100 sells for $99.46, a two-year zero coupon bond sells for $97.23, and an 3-year zero coupon bond sells for $90.50. Suppose a new coupon paying bond, making annual coupon payments, is issued today with face value $100, maturity of 3 years, and an annual coupon payment of 4.5%.

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

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