问题如下：
The cash prices of 6-month and one-year Treasury bills are 97.0 and 93.0. A 1.5-year and two-year Treasury bond with coupons at the rate of 6% per year sell for 98.5 and 97.5. Calculate the six-month, 12-month, 18-month, and 24-month spot rates with semi-annual compounding.
解释：
The six-month rate (semi-annually compounded) is 2(100/97－1) =0.06186 or 6.186%. The one-year rate (semi-annuallycompounded) is 2×[(100/93)1/2－1 ]=0.07390 or 7.390%.
The coupons on the 1.5 year bond have a value of 0.97 × 3 + 0.93 × 3 = 5.7.
The value of the final payment is therefore 98.5 − 5.7 = 92.8. The discount factor for 1.5 years is 92.8/103 = 0.900971. This corresponds to a spot rate (semi-annually compounded) of 7.612%.
The coupons on the two-year bond have a value of
The value of the final payment is therefore 97.5 – 8.4029 = 89.0971. The discount
factor for two years is 89.0971/103 = 0.8650. This corresponds to a spot rate
(semi-annually compounded) of 7.383%.
