Explanation:
Treasury bonds are quoted in 32nds and use an Actual/Actual day count convention.
1. Calculate the quoted price:
Quoted Price = $103-05 = 103 + \frac{5}{32} = 103.15625$
2. Determine the coupon payment:
The bond has a $10%\frac{10%}{2} \times 100 = ` per `$100` face value.
3. Calculate days for accrued interest: Last coupon date: October 25, 2017 Current date: March 28, 2018 Next coupon date: April 25, 2018
Days between Oct 25, 2017 and Apr 25, 2018:
$31 - 25 = 6$ days$30$ days$31$ days$31$ days$28$ days (2018 is not a leap year)$31$ days$256` + 30 + 31 + 31 + 28 + 31 + 25 = 182$ daysDays between Oct 25, 2017 and Mar 28, 2018 (days passed):
$6$ days$30$ days$31$ days$31$ days$28$ days$286` + 30 + 31 + 31 + 28 + 28 = 154$ days4. Calculate the accrued interest:
Accrued Interest = Semi-annual Coupon (Days passed / Total days in period)
Accrued Interest = $5.00 \times \left(\frac{154}{182}\right) = 4.23077$
5. Calculate the cash (dirty) price:
Cash Price = Quoted Price + Accrued Interest
Cash Price = $103.15625 + 4.23077 = 107.38702 \approx `
Ultimate access to all questions.
Q.80 The price of a Treasury bond, which has a coupon of 10% p.a., paid semi-annually on April 25 and October 25, is quoted as 103-05. The last coupon was paid on October 25, 2017. If the current date is March 28, 2018, and the bond will mature on October 25, 2030, the cash price of the bond is closest to:
A
$107.39
B
$111.66
C
$103.46
D
$112.24
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