A bank currently has $1.200 million in loans with an average duration of 7.2 years. Currently, the market interest rate is 4%. If the interest rate raises by 0.5%, what is the change in the value of the banks loans in dollar?

To calculate the change in the value of the bank's loans when the interest rate rises, we can use the **duration approximation formula**, which estimates the change in value of a fixed-income instrument due to a change in interest rates:

\[
\Delta V \approx -D \cdot \frac{\Delta r}{1 + r} \cdot V
\]

Where:
- $ V $ = current value of the loans = \$1.200 million
- $ D $ = duration of the loans = 7.2 years
- $ r $ = initial interest rate = 4% or 0.04
- $ \Delta r $ = change in interest rate = 0.5% or 0.005

Now, let's plug in the values to calculate the change in the value of the bank's loans:

\[
\Delta V \approx -7.2 \cdot \frac{0.005}{1 + 0.04} \cdot 1.200
\]

I'll compute that now.The change in the value of the bank's loans is approximately $-\$0.0415$ million, or $-\$41,538$. This means the value of the loans would decrease by about \$41,538 due to the 0.5% increase in interest rates.

Would you like further details or have any questions?

Here are five related questions to expand your understanding:
1. How is bond duration related to interest rate risk?
2. What are the assumptions behind using the duration formula for interest rate changes?
3. How would the loan value change if the duration was longer or shorter?
4. What other factors affect the sensitivity of loan value to interest rate changes?
5. What is the convexity adjustment and how does it refine the duration formula?

**Tip:** Duration is a linear approximation and works best for small interest rate changes. For larger changes, consider using convexity for more accurate results.

A bank currently has $1.200 million in loans with an average duration of 7.2 years. Currently, the market interest rate is 4%. If the interest rate raises by 0.5%, what is the change in the value of the bank's loans in dollar?

Learn how a 0.5% increase in the market interest rate affects a bank's $1.200 million in loans with a 7.2-year duration. This step-by-step solution demonstrates the use of the duration approximation formula to calculate the change in loan value, a key concept in finance.

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