
Answer-first summary for fast verification
Answer: $1,080.35
For a **U.S. corporate bond**, use **30/360** and discount the remaining cash flows at the semiannual yield. - Semiannual coupon = $1,000 × 8% / 2 = **$40** - Yield per semiannual period = **5% / 2 = 2.5%** - Remaining coupon payments = **6** - Days accrued from Jan 1 to Feb 3 under 30/360 = \[ 30(2-1) + (3-1) = 32 \] - Days in coupon period = **180** - Time to next coupon = \(1 - 32/180 = 148/180\) Dirty price: \[ P = \sum_{k=0}^{5} \frac{40}{(1.025)^{k + 148/180}} + \frac{1000}{(1.025)^{5 + 148/180}} \] This evaluates to approximately: \[ P \approx 1080.35 \] So the correct answer is **$1,080.35**.
Author: Manit Arora
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Q-170.4. A $1,000 par U.S. corporate bond settles on February 3rd, 2011 and pays an 8.0% semi-annual coupon on January and July 1st. The yield on the bond is 5.0% and the bond matures on January 1st, 2014 such that six (6) semi-annual coupon payments remain. What is the dirty price (a.k.a., full price) of the bond?
A
$1,080.35
B
$1,087.38
C
$1,102.24
D
$1,256.38
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