Use the following table to answer the question :

-Assuming that the average duration of its assets is five years,while the average duration of its liabilities is three years,then a 5 percentage point increase in interest rates will cause the net worth of First National to decline by ________ of the total original asset value.
A)5 percent
B)10 percent
C)15 percent
D)25 percent

Question

Use the following table to answer the question :

-Assuming that the average duration of its assets is five years,while the average duration of its liabilities is three years,then a 5 percentage point increase in interest rates will cause the net worth of First National to decline by ________ of the total original asset value.
A)5 percent 
B)10 percent 
C)15 percent 
D)25 percent

Quizplus · Accepted Answer

The net worth decline can be calculated using the formula: ΔNW/NW = -DA * Δy * (A - L/A), where DA is the duration of assets, Δy is the change in yield (interest rates), A is the total assets, and L is the total liabilities. Given DA = 5 years for assets and 3 years for liabilities, and a 5 percentage point (or 0.05) increase in interest rates, the difference in duration (DA - DL) is 2 years. The formula simplifies to a 10% decline in net worth relative to the original asset value, as the change in interest rates affects the longer-duration assets more than the liabilities.

Use the Following Table to Answer the Question