Actuarial FM question:
A one-year zero-coupon bond with face value $100 is trading at $91.4077; a two-year bond with 10% annual coupons and face value $100 is trading at $102.2373; a three-year bond with 10% annual coupons and face value $100 is trading at $100.2487; and a four-year bond with 10% annual coupons and face value $100 is trading at $105.9705.
(i) Calculate the 1, 2, 3, 4−year spot interest rates corresponding to these bond prices.
(ii) Under the spot interest rates found in part (a), the annual effective yield of a four-year, $300 par-value bond with κ% annual coupons is 8.27%. Find κ.