On September 1,2012,an investor purchases a $10,000 par T-bond that matures in 12 years. The coupon rate is 6 percent and the investor buys the bond 70 days after the last coupon payment (110 days before the next). The ask yield is 7 percent. The dirty price of the bond is

Question

Quizplus · Accepted Answer

1. Calculate the accrued interest: 
Day count between last coupon payment and purchase date = 70 
Day count between last coupon payment and next coupon payment = 180 
Accrued interest = (Coupon rate * Par value * Day count between last coupon and purchase date) / Day count between last coupon and next coupon 
Accrued interest = (0.06 * 10000 * 70) / 180 = 23.33

2. Calculate the clean price: 
Clean price = (Coupon payment * ((1 - (1 + r)^(-n)) / r)) + (Par value / (1 + r)^n) 
Where:
Coupon payment = 0.06 * 10000 / 2 = 300
r = 7% / 2 = 0.035
n = 12 years * 2 = 24

Clean price = (300 * ((1 - (1 + 0.035)^(-24)) / 0.035)) + (10000 / (1 + 0.035)^24) = 9313.75

3. Calculate the dirty price:
Dirty price = Clean price + Accrued interest = 9313.75 + 23.33 = 9337.08(rounded off to two decimal places)
Therefore, the answer is C) $9,313.75.

On September 1,2012,an Investor Purchases a $10,000 Par T-Bond That