The correct price of the 2-year zero-coupon bond is calculated by considering the expected future interest rates and incorporating the risk premium for duration risk. The formula for the price of a zero-coupon bond is $P = \frac{FV}{(1 + r)^n}$, where $P$ is the present price, $FV$ is the face value, $r$ is the interest rate, and $n$ is the number of periods until maturity.

Given:

• The face value $FV = EUR 1,000$
• The risk premium for duration risk is 50 basis points (bps) each year, which is 0.005 in decimal form.
• The 1-year interest rate today is 10.0%, which is 0.10 in decimal form.

The expected 1-year interest rate in one year is a weighted average of the two possible rates (12.0% and 8.0%), each with a 50% probability. The expected rate $R$ is calculated as: R = 0.5 \times 0.12 + 0.5 \times 0.08 = 0.05 \text{ (or 5%)}

However, we need to adjust this by adding the risk premium for the second year: R_{adjusted} = R + 0.005 = 0.05 + 0.005 = 0.055 \text{ (or 5.5%)}

The price of the 2-year zero-coupon bond is then: $P = \frac{1000}{(1 + 0.10) \times (1 + 0.055)}$ $P = \frac{1000}{1.10 \times 1.055}$ $P = \frac{1000}{1.1605}$ $P \approx 862.98$

However, the provided answer is EUR 822.98, which suggests that the calculation in the explanation is incorrect. The correct calculation should be: $P = \frac{1000}{(1.10) \times (1.055)}$ $P = \frac{1000}{1.1605}$ $P \approx 862.98$

It seems there is a discrepancy between the provided answer and the calculated price based on the given information. The correct price, based on the formula and the given data, should be approximately EUR 862.98, not EUR 822.98. It's possible that there is a mistake in the provided answer or in the calculation process described in the explanation.