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.
选项：
解释：
1. The six-month rate (semi-annually compounded) is 2 x (100/97－1) = 0.06186 or 6.186%.
2. The one-year rate (semi-annuallycompounded) is 2 × [ (100/93)1/2－1 ] = 0.07390 or 7.390%.
3. 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 7.074%.
4. 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%.
老师你好，请问为什么t=0.5时不能用100/(1+r)^0.5=97来推算0.5年对应的spot rate? 还是不太能分清什么时候是(1+r)^0.5什么时候是（1+r/2）^1，课上何老师讲完还是不太能记得住，麻烦老师讲解一下。谢谢！
