关于解题方法的问题

问题如下：

Given a one-year and a three-year zero coupon bonds price of 95.18 and 83.75 respectively, what should be the price of a two year zero coupon bond using linear interpolation on zero rates (semiannual compounding)?

选项：

A.

95.18

B.

89.47

C.

89.72

D.

83.75

解释：

Step 1: Compute semiannual zero rates for the 1-and 3-year bonds.

1-year bond: FV = 100; N = 2; PMT = 0, PV = -95.18, CPT: I/Y = 2.5008 × 2 = 5.0%

3-year bond: FV = 100; N = 6; PMT = 0, PV = -83.75, CPT: I/Y = 3 × 2 = 6%

Step 2: Use linear interpolation on zero rates for 2-year bond

(6% – 5.%)/2 = 0.5%, zero rates for 2-year bonds = 5% + 0.5% = 5.5%

Step3: Compute 2-year bond price

FV = I00; N = 4; PMT = 0, I/Y = 2.75(5.5/2), CPT: PV = -89.72