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Answer: $221.33
**Correct answer: C. $221.33** Dollar duration is the modified duration multiplied by the bond price: \[ \text{Dollar Duration} = D_{mod} \times P \] First convert Macaulay duration to modified duration using the bond-equivalent yield of 10%: \[ D_{mod} = \frac{D_{Mac}}{1+y/2} = \frac{2.916}{1.05} \approx 2.777 \] Now compute the bond price for a 3-year, 2% semiannual coupon bond with 10% bond-equivalent yield: \[ P \approx 79.70 \] Therefore: \[ \text{Dollar Duration} \approx 2.777 \times 79.70 \approx 221.33 \] So the correct answer is **$221.33**.
Author: Manit Arora
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Question-163.3. A three-year bond that pays a 2.0% semi-annual coupon has a bond-equivalent yield of 10.0% (YTM with semi-annual discounting) and a Macaulay duration of 2.916 years. What is the bond’s DOLLAR or VALUE DURATION; i.e., negative of the first derivative of bond price with respect to yield?
A
$23.24
B
$66.48
C
$221.33
D
$232.39
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