Question

(b) (15 marks) We consider a n-year bond that pays coupon m times per year. You are given that • The bond price at the end of kth year is $5559.433; • The bond price at the end of (k + 2)th year is $5151.2551; • The bond price at the end of (k + 3)th year is $4921.7776; Find the bond price at the end of (k + 1)th year.

Answer 1

Sol: The values provided in the question to calculate the bond price at the end of (k + 1) th year are as follows:

Bond price at the end of k th year = $5559.433

Bond price at the end of (k + 2) th year = $5151.2551

Bond price at the end of (k + 3) th year = $4921.7776

  

Since the bond is paying coupons every year, the price of the bond will decrease by the amount of coupons paid in that year. Coupon paid in any year can be calculated as = Bond price at end of k year - Bond price at end of (k + 1) year

The formula to calculate the bond price at the end of (k + 1) th year is as follows:

Bond price at end of (k + 1) year = Bond price at end of k year - Coupon paid in (k + 1) year

=  Bond price at end of k year - (Bond price at end of (k + 2) year - Bond price at end of (k + 3) year)

= $5559.433 - ($5151.2551 - $4921.7776)

= $5559.433 - $229.4775

= $5329.9555