Suppose a bank has $500 million in interest rates sensitive assets, with a duration of 5 years, and $600 million of interest rate sensitive liabilities with a duration of 2 years.
a. If interest rates increase from 3% to 4%, what is the percentage change in net worth of the bank? Enter your response as a percent without the percent sign (for example, enter a numerical answer of 0.0525 = 5.25%, as 5.25).
b. Given the information in the previous question, what duration of assets would lead to a duration gap of zero?
c. Given the information in question part a above, what duration of liabilities would lead to a duration gap of zero?