Answer-first summary for fast verification
Answer: $121.60
The bond pays a coupon of \(12\%/2 = 6\) per half-year and is discounted at \(8\%/2 = 4\%\) per half-year. - Accrued interest: \[ AI = 6\times \frac{100}{181} \approx 3.31 \] - There are 15 remaining coupon payments (including the coupon on July 10, 2018), and the time to the next coupon is \(81/181\) of a half-year. - Dirty price: \[ P_{dirty} = \sum_{j=0}^{14} \frac{6}{1.04^{j+81/181}} + \frac{100}{1.04^{14+81/181}} \approx 124.91 \] - Quoted price: \[ P_{quoted} = P_{dirty} - AI \approx 124.91 - 3.31 = 121.60 \] So the nearest quoted price is **$121.60**.
Author: Manit Arora
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Question 719.1. Suppose it is April 20, 2018 and we want to infer the quoted price of a government bond that accrues interest on an actual/actual basis. The bond under consideration is a 12.0% semi-annual coupon bond that matures on July 10th, 2025. The bond has a semi-annual yield of 8.0%; i.e., 8.0% per annum with semi-annual compounding. Because coupons are paid semiannually on government bonds (and the final coupon is at maturity), the most recent coupon date is January 10, 2018, and the next coupon date is July 10, 2018. The (actual) number of days between January 10, 2018, and April 20, 2018, is 100; and the (actual) number of days between January 10, 2018, and July 10, 2018, is 181. What is nearest to the bond's quoted price?
A
$121.60
B
$124.91
C
$127.13
D
$135.57
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