Answer: EUR 822.98

The correct price of the 2-year zero-coupon bond is calculated by taking into account the expected future interest rates and the risk premium for duration risk. The formula used in the explanation is a weighted average of the possible future 1-year interest rates, each adjusted for the risk premium, and then discounted back for one year at the current 1-year interest rate. Given: - Current 1-year interest rate = 10.0% - Probability of 1-year interest rate being 12.0% in 1 year = 50% - Probability of 1-year interest rate being 8.0% in 1 year = 50% - Risk premium of duration risk = 50 basis points (bps) each year - Bond's face value = EUR 1,000 The calculation is as follows: \[ \text{Value of the bond} = \left( \frac{50\%}{(1 + 0.12 + 0.005)} + \frac{50\%}{(1 + 0.08 + 0.005)} \right) \times \frac{1}{1.10} \times \text{EUR 1,000} \] Breaking it down: - The first term in the parentheses calculates the present value of the bond if the future interest rate is 12.0%, adjusted for the 50 bps risk premium, which becomes 12.5% (12.0% + 0.5%). - The second term does the same for the 8.0% interest rate, also adjusted for the risk premium, becoming 8.5% (8.0% + 0.5%). The denominator \(1.10\) is the current 1-year interest rate, expressed as a multiplier. After performing the calculations: \[ \text{Value of the bond} = \left( \frac{50\%}{1.125} + \frac{50\%}{1.085} \right) \times 0.9091 \times \text{EUR 1,000} \] \[ \text{Value of the bond} = \left( 0.45 + 0.46 \right) \times 0.9091 \times \text{EUR 1,000} \] \[ \text{Value of the bond} = 0.91 \times 0.9091 \times \text{EUR 1,000} \] \[ \text{Value of the bond} = 0.82727 \times \text{EUR 1,000} \] \[ \text{Value of the bond} = \text{EUR 827.27} \] However, the provided answer in the file content is EUR 822.98, which suggests there might be a rounding or calculation error in the explanation. The correct calculation should yield a value close to EUR 827.27, but due to rounding or a different method of calculation, the provided answer is EUR 822.98.

Author: LeetQuiz Editorial Team