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.