Answer: 89.47

## Explanation To find the price of a 2-year zero coupon bond using linear interpolation on zero rates with semiannual compounding: **Step 1: Calculate zero rates from bond prices** For 1-year bond (2 semiannual periods): \[ 95.18 = \frac{100}{(1 + r_1/2)^2} \] \[ (1 + r_1/2)^2 = \frac{100}{95.18} = 1.05064 \] \[ 1 + r_1/2 = \sqrt{1.05064} = 1.025 \] \[ r_1/2 = 0.025 \] \[ r_1 = 5.00\% \] For 3-year bond (6 semiannual periods): \[ 83.75 = \frac{100}{(1 + r_3/2)^6} \] \[ (1 + r_3/2)^6 = \frac{100}{83.75} = 1.19403 \] \[ 1 + r_3/2 = (1.19403)^{1/6} = 1.03 \] \[ r_3/2 = 0.03 \] \[ r_3 = 6.00\% \] **Step 2: Linear interpolation for 2-year rate** \[ r_2 = r_1 + \frac{2 - 1}{3 - 1} \times (r_3 - r_1) \] \[ r_2 = 5.00\% + \frac{1}{2} \times (6.00\% - 5.00\%) \] \[ r_2 = 5.50\% \] **Step 3: Calculate 2-year bond price** \[ \text{Price} = \frac{100}{(1 + 0.055/2)^4} \] \[ = \frac{100}{(1.0275)^4} \] \[ = \frac{100}{1.1154} \] \[ = 89.47 \] Therefore, the correct price is $89.47.

Author: LeetQuiz .