Revision as of 22:34, 20 November 2023 by Admin (Created page with "'''Solution: A''' For a <math>7.5 \%</math> yield rate, the present value and Macaulay duration of the assets are, respectively, <math>30,000+20,000=50,000</math> and <math>\frac{30,000(28)+20,000(35)}{30,000+20,000}=30.8</math> The present value and Macaulay duration, of the liabilities are, respectively, <math>\frac{50,000(1.075)^y}{(1.075)^y}=50,000</math> and <math>y</math>. Note that the present values of assets and liabilities already match. Since Macaulay durat...")
Exercise
Nov 20'23
Answer
Solution: A
For a [math]7.5 \%[/math] yield rate, the present value and Macaulay duration of the assets are, respectively, [math]30,000+20,000=50,000[/math] and [math]\frac{30,000(28)+20,000(35)}{30,000+20,000}=30.8[/math]
The present value and Macaulay duration, of the liabilities are, respectively, [math]\frac{50,000(1.075)^y}{(1.075)^y}=50,000[/math] and [math]y[/math].
Note that the present values of assets and liabilities already match. Since Macaulay durations must match, [math]y=30.8[/math].
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