For every $100 in assets, a bank has $30 in interest-rate sensitive assets, and the other $70 in non-interest-rate sensitive assets.The same bank has $60 for every $100 in liabilities in interest-rate sensitive liabilities, the other $40 are in liabilities that are not interest-rate sensitive.If the interest rate on assets decreases from 6 to 5 percent, and the interest rate on liabilities decreases from 4 to 3, percent the impact on the bank's profits per $100 of assets will be:

Question

Quizplus · Accepted Answer

First, calculate the bank's net interest margin (NIM) before and after the interest rate changes.

Before:
NIM = (Interest income - Interest expense) / Total assets 
NIM = [(0.06 * $30) + (0 * $70)] - [(0.04 * $60) + (0 * $40)] / $100 
NIM = $1.80 - $2.40 / $100 
NIM = -$0.60 / $100

After:
NIM = [(0.05 * $30) + (0 * $70)] - [(0.03 * $60) + (0 * $40)] / $100 
NIM = $1.50 - $1.80 / $100 
NIM = -$0.30 / $100

The decrease in NIM is equal to $0.30 per $100 in assets. Therefore, the answer is A) A reduction of $0.30.

For Every $100 in Assets, a Bank Has $30 in Interest-Rate