Question

A one year zero coupon bond has an effective annual rate of 7.5%. A three year zero coupon bond has an effective annual rate of 10.5%. If a 3 year coupon-bearing bond that pays coupons of 14.5% annually has a yield of 10.1%, what is the effective annual rate of a two year zero coupon bond?

Answer 1

Calculation of effective annual rate of a two year zero coupon bond:

Assume face value = $100

(14.5/1.101) + (14.5/1.101^2) + (114.5/1.101^3) = (14.5/1.075) + (14.5/(1+r)^2) + (114.5/1.105^3)

(14.5/(1+r)^2) = 110.922914 - 98.3514253

(14.5/(1+r)^2) = 12.5714887

(1+r)^2 = 14.5/12.5714887

(1+r)^2 =1.15340357

1+r = 1.15340357 ^(1/2)

1+r = 1.07396628

r = 1.07396628 - 1

r = 0.07396628 or 7.396628% or 7.40%

Effective annual rate of a two year zero coupon bond = 7.40% (Rounded to two decimal places)