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Answer: USD 96.93
## Explanation **B is correct.** The clean price is calculated as the dirty price minus accrued interest. ### Step 1: Calculate the number of days from last coupon to settlement date - Total coupon period (T): 184 days - Days from settlement to next coupon: 37 days - Days from last coupon to settlement (t): 184 - 37 = 147 days ### Step 2: Calculate the semi-annual coupon payment - Face value: USD 100 - Annual coupon rate: 3% - Semi-annual coupon payment (c): (100 × 3%) / 2 = USD 1.5 ### Step 3: Calculate accrued interest Using the formula: $i_a = c \frac{t}{T}$ - $i_a = 1.5 × \frac{147}{184} = USD\ 1.1984$ ### Step 4: Calculate clean price - Dirty price: USD 98.13 - Clean price = Dirty price - Accrued interest - Clean price = 98.13 - 1.1984 = USD 96.9316 ≈ USD 96.93 The clean price represents the quoted price of the bond excluding accrued interest, which is what option B correctly provides.
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A bond portfolio manager purchased a US Treasury bond with a settlement date of September 25. The previous coupon payment was made on May 1, and the next coupon payment will be made on November 1. The manager applies the actual/actual day count convention and determines that there are 184 days in the coupon period, and 37 days between the settlement date and the next coupon payment date. Additional information about the bond is provided below:
What is the clean (quoted) price of the bond on the settlement date of September 25?
A
USD 95.73
B
USD 96.93
C
USD 97.83
D
USD 99.33
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