00:01
Assuming that the average duration of first national bank's $100 million assets is five years, while the average duration of its $80 million liabilities is three years, then a five percentage point decrease in interest rates will cause the net worth of first national to increase by blank million dollars.
00:21
So we're given, here's our given information.
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Assets are valued at $100 million.
00:34
Liabilities are valued at 80 million interest rate decreases by 5%.
00:57
So the change in interest rate or change in interest, which is represented by delta i, the little triangle there stands for change, is 5%.
01:11
The original interest rates are not given, so we assume the current interest rate is 5%.
01:17
Deration of assets denoted as d sub -a.
01:28
Equals five years and the duration of liabilities which is denoted as d sub l is three years.
01:48
Now we want to figure out how this affects net worth.
01:52
So we want to look at the change in net worth which equals the duration of assets times the change in interest over one plus the original interest times the asset value minus the duration of liabilities times the change in interest over one plus the original interest times the liabilities value.
02:55
Now using substitution, we get a change in net worth equal...