Question

Consider a 30-year bond that pays semi-annual coupons of $500. The face value of the bond is $100, 000. If the annual yield rate is 3%, calculate the following:

a) the annual coupon rate of the bond

b) the price of the bond, one period before the first coupon is paid

c) the price of the bond, immediately after the 15th coupon is paid

d) the price of the bond, 2 months after the 30th coupon is paid

*No financial Calculator*

Answer 1

Say, settlement date of bond is 1/1/2019, so bond will mature on 12/31/2048

a) 6 month coupon rate=500/100000=0.5%

So, annual coupon rate= (1+0.5%)^2-1=1.002%:

b) The price of bond one period before first coupon i.e. at time 0 is $60,661.33. Calculation given below:

c) After 25th coupon is paid price of bond is equal to new bond which will mature in (30-15/2)=22.5 years. Price of this bond is $67482.95.

d) Price immediately after 30th coupon= $90,791.71

2 months accrued interest amount=500*2/6=$166.67

So, clean price after 2 month of 30th coupon=$(90791.71+166.67)=$90958.38