Question

Given the following annual zero spot rates, starting tomorrow:

Maturity                         1 yr                     2 yr                 3 yr               4 yr                

Annual Rate                  4.5%                  4.9%              5.2%               5.5%

Calculate the prices of 6% coupon (paid annually) bonds at each maturity

Maturity                         1 year                   2 years                   3 years                   4 years

Price:                              

Answer 1

To find out the bond price we have to discount each coupon of a given period by the corresponding spot rate of that period. The calculations are shown below:

Coupon = 6% of 1000 = 60

Price of the bond at 1 year maturity:

(60/ 1.045) + (1000/1.045) = 1014.354

Price of the bond at 2 year maturity:

(60/ 1.045) + (1060/ 1.049^2) = 1020.70

Price of the bond at 3 year maturity:

(60/ 1.045) + (60/ 1.049^2) + (1060/1.052^3) = 1022.397

Price of the bond at 4 year maturity:

(60/ 1.045) + (60/ 1.049^2) + (60/1.052^3) + (1060/ 1.055^4) = 1019.127