Revision as of 21:51, 20 November 2023 by Admin (Created page with "'''Solution: D''' The <math>P V</math> of the liability is <math>\frac{600,000}{1.046^2}=548,387.92</math> and its Macaulay duration is 2 . Then, equating present values: <math display = "block"> \frac{x}{1.046}+\frac{y}{1.046^4}=548,387.92 </math> And equating durations: <math display = "block"> \frac{(x / 1.046)}{548,387.92}(1)+\frac{\left(y / 1.046^4\right)}{548,387.92}(4)=2 </math> Solving the system of equations results in <math>x=382,409</math> {{soacopyright |...")
Exercise
Nov 20'23
Answer
Solution: D
The [math]P V[/math] of the liability is [math]\frac{600,000}{1.046^2}=548,387.92[/math] and its Macaulay duration is 2 . Then, equating present values:
[[math]]
\frac{x}{1.046}+\frac{y}{1.046^4}=548,387.92
[[/math]]
And equating durations:
[[math]]
\frac{(x / 1.046)}{548,387.92}(1)+\frac{\left(y / 1.046^4\right)}{548,387.92}(4)=2
[[/math]]
Solving the system of equations results in [math]x=382,409[/math]
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