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Answer: $928.70
For a **Treasury bond**, use **actual/actual** timing and discount the remaining cash flows at the semiannual yield. - Coupon payment = $1,000 × 4% / 2 = **$20** - Yield per semiannual period = **6% / 2 = 3%** - Remaining coupons = **10** - Days from Apr 4 to next coupon Jul 1 = **88** days - Days in coupon period Jan 1 to Jul 1 = **181** days - Time to first cash flow = \(88/181\) of a semiannual period Dirty price: \[ P = \sum_{k=0}^{9} \frac{20}{(1.03)^{k + 88/181}} + \frac{1000}{(1.03)^{9 + 88/181}} \] This gives approximately: \[ P \approx 928.70 \] So the correct answer is **$928.70**.
Author: Manit Arora
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Q-170.3. Assume the coupons on a U.S. Treasury bond are paid on January 1st and July 1st. The bond has a par of $1,000 and pays a semiannual coupon of 4.0% with a yield of 6.0%. The bond has a settlement date on April 4th, 2011. The bond matures on January 1st, 2016 such that there are ten (10) remaining semi-annual coupon payments. What is the dirty price (a.k.a., full price) of the bond?
A
$908.89
B
$912.49
C
$928.70
D
$979.17
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