The following coupon paying bonds are being traded in the market: 4% coupon-paying bond with maturity of 1 year and annual coupons. Its face value is $1000 and its price is $1015:03; 1 4% coupon-paying bond with maturity of 2 years and annual coupons. Its face value is $1000 and its price is $1025:55; 2% coupon-paying bond with maturity of 3 years and annual coupons. Its face value is $1000 and its price is $973:22; 3% coupon-paying bond with maturity of 4 years and annual coupons. Its face value is $1000 and its price is $993:66. Answer the following questions: (a) (10 pts.) What are the continuously compounded spot rates for maturities of 1, 2, 3, and 4 years respectively? (b) (5 pts.) A four-year bond has a face value $1000 and a coupon rate of 5% paid annually. What is the price of this bond if there is no arbitrage? (c) (10 pts.) For the bond from part (b), what are its yield and duration (continuously compounded)?