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Answer: 4.63
To calculate the Macaulay duration, the following steps are taken: 1. **Approximate Modified Duration (AppxModDur):** \[ \text{AppxModDur} = \frac{(PV_+ - PV_-)}{2 \times \Delta \text{Yield} \times PV_0} = \frac{(100.45 - 99.56)}{2 \times 0.001 \times 100} = 4.45 \] 2. **Macaulay Duration:** The Macaulay duration is derived by multiplying the modified duration by \[ (1 + \text{YTM}) \]: \[ \text{Macaulay Duration} = \text{AppxModDur} \times (1 + 0.04) = 4.45 \times 1.04 = 4.628 \approx 4.63 \] **Option C** is correct because it accurately adjusts the approximate modified duration by the yield-to-maturity to arrive at the Macaulay duration. Options A and B are incorrect due to miscalculations in the adjustment process.
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An analyst collects the following data for a 4% annual-payment bond with a current yield-to-maturity of 4.0%:
Annualized Yield to Maturity | Bond Price 3.9% | 100.45 4.0% | 100.00 4.1% | 99.56
The bond's annualized Macaulay duration is closest to:
A
4.28
B
4.45
C
4.63
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