Question

Suppose that today’s date is April 15. A bond with a 10% coupon paid semiannually every January 15 and July 15 is listed in The Wall Street Journal as selling at an ask price of 1,012.000. If you buy the bond from a dealer today, what price will you pay for it? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Invoice price

Answer 1

Let us take the face value of the bond as $1000 for better calculations.

Quoted price of the bond=Ask price*Face value
Given that ask price=1012
Quoted price of the bond=1012%*$1000=$10120

Accrued interest =Coupon payment*(Month since payment/Months between payments)
Coupon rate=10%.
Given that the coupon is paid semiannually. So, semiannual coupon rate=10%/2=5%
Coupon payment=Face value*Semiannual coupon rate=$1000*5%=$50

Today’s date is April 15, coupon is paid semiannually every January 15 and July 15.
So, last coupon payment was made 3 months back and months between payments (January 15 and July 15) is 6.
Accrued interest =Coupon payment*(Month since payment/Months between payments)
Substituting the values in the equation of accrued interest, we get:
Accrued interest=$50*(3/6)=$25
Price we would pay=Quoted price + Accrued interest=$10120+$25=$10145