To solve this, use the duration method for the change in loan value: But first, what data do we have?

• L = €2,000,000
• D = 6 years
• i = 4% (0.04)
• Δi = 0.75% (0.0075)

Now, calculate the change in the loan's value (ΔL) using the duration method:

$$\Delta L = -L D \frac{\Delta i}{1 + i} = -2,000,000 \times 6 \times \frac{0.0075}{1.04} \approx -€86,538$$

So, the change in the loan's value (ΔL) due to the interest rate change is approximately -€86,538.

Things to Remember

• Risk-Adjusted Return on Capital (RAROC) is a risk management framework that helps organizations evaluate the risk-adjusted financial performance of business units or projects.
• The duration method is a technique used to estimate the change in the value of a financial instrument due to a change in interest rates.
• Duration is a measure of the sensitivity of the price of a bond or a financial instrument to a change in interest rates.
• Interest rate risk is the risk that the value of a financial instrument will fluctuate due to changes in interest rates.