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A one-year zero-coupon bond with a face value of $100 sells for $99.46, a two-year zero-coupon bond sells for $97.23, and a 3-year zero-coupon bond sells for $90.50

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A one-year zero-coupon bond with a face value of $100 sells for $99.46,

a two-year zero-coupon bond sells for $97.23, and a 3-year zero-coupon bond sells for $90.50. Suppose a new coupon paying bond, making annual coupon payments, is issued today with a 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.

 
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