
Explanation:
Since the bond is valued based on the 30/360 day-count convention, there are 11 days between the settlement date (July 20, 2020) and the next coupon date (August 1, 2020).
Each coupon payment is valued at \frac{7\%}{2} \times \`1,000 = \
Dirty Price =
Where:
P = price
C = semiannual coupon
K = number of days until the next coupon payment divided by the number of days in the coupon period, determined as per the relevant day-count convention.
y = periodic required yield
n = number of periods remaining, including the present one
In this case,
n = 4
k =
Dirty Price =
= $34.99 + 34.86 + 34.73 + 1023.21 = `
As of July 20 2018,
Accrued interest = \`35 \times \frac{180 - 11}{180} = \
Clean Price = Dirty Price − Accrued Interest
= $1,127.79 − 32.86 = `
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Q.46 Alphabet has $200 million worth of bonds payable outstanding. The $1,000 par, 7% semiannual coupon bonds will mature on February 1 2022. The coupon dates are February 1 and August 1. They follow the 30/360-day count convention, and the next coupon is due on August 1 2020. Linda Smith bought 1,000 such bonds from Robert Piers on July 20 2020 when the bonds' semiannual yield was 0.75%. The market requires the buyer to compensate the seller for the accrued interest. The clean price of the bond is equal to:
A
$985.25.
B
$1,000.00
C
$1,094.93.
D
$1,090