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Answer: 2.88 years
Compute the present value of each cash flow using continuous discounting: - Year 1: \(4e^{-0.06}\) - Year 2: \(4e^{-0.12}\) - Year 3: \(104e^{-0.18}\) Bond price: \[ P = 4e^{-0.06} + 4e^{-0.12} + 104e^{-0.18} \approx 94.18 \] Macaulay duration under continuous compounding is: \[ D = \frac{\sum t \cdot PV(CF_t)}{P} \] \[ D = \frac{1\cdot 3.767 + 2\cdot 3.547 + 3\cdot 86.868}{94.182} \approx 2.88\text{ years} \] So the correct answer is **C**.
Author: Manit Arora
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Question 161.1. Assume a 3-year, 4.0% annual coupon bond with a face value of $100. The yield is 6.0% per annum with continuous compounding. What is the bond’s duration? (please note: per “annual coupon” the coupon pays once per year. Further, under continuous compounding the modified duration is identical to the Macaulay duration, so “duration” is sufficient only in this special case of continuous discounting.)
A
2.68 years
B
2.78 years
C
2.88 years
D
3.00 years
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