Question

A five-year par value $10,000 5% bond with quarterly coupons is bought to yield 6% convertible quarterly. Determine the practical dirty and clean values of the bond one month after the eighth coupon payment using the 30/360 rule.

Answer 1

Eight coupon payments mean 2 years have passed

Consider the time when the 8th coupon has just been paid:

Face value = 10000

time = 3 years = 12 quarters

coupon (quarterly) = 5%*10000/4 = 125

Yield = 6%/4 = 1.5% per quarter

P: price of bond

P = (125/1.5%)*(1-1/(1+1.5%)^12)+10000/(1+1.5%)^12 = 9727.312

Dirty price of the bond after 1-month = 9727.312*(1+1.5%)^(1/4) = $9763.586

Accrued interest = (1/4)*125 = $31.25

Clean price of the bond after 1-month = 9763.586-31.25 = $9732.336