Final answer:
The change in income for the bank when the interest rate increases by 1% is $400,000. This is calculated by subtracting rate-sensitive liabilities from rate-sensitive assets and multiplying the result by the interest rate change. For larger rate changes, the income impact is proportionally higher.
Step-by-step explanation:
To calculate the change in income of a bank when the interest rate increases by 1%, we use the bank's rate-sensitive assets and liabilities. In this case, the assets are $60 million and the liabilities are $20 million. The difference between the rate-sensitive assets and liabilities is $60 million - $20 million = $40 million. This amount represents the exposure to the interest rate change. When the interest rate increases by 1%, this change will result in an additional income of 1% of the $40 million exposure, which equals $400,000.
If we were to look at interest rate increases of 4% and 5%, we would multiply the exposure of $40 million by these percentages to find the resulting change in income. For example, at a 4% increase, the change in income would be $40 million * 0.04 = $1.6 million, and at a 5% increase, it would be $40 million * 0.05 = $2 million. These calculations illustrate the sensitivity of the bank's income to changes in interest rates.