The price of a 3-year zero coupon government bond is 85.16.The price of a similar 4-year bond is 79.81.What is the yield to maturity (effective annual yield)on the 4-year bond?

Question

Quizplus · Accepted Answer

To calculate the yield to maturity (YTM) of the 4-year bond, we need to use the formula:

Current price = Face value / (1 + YTM)^n

where n is the number of years to maturity.

For the 3-year bond:

85.16 = Face value / (1 + YTM)^3

Solving for the face value, we get:

Face value = 85.16 x (1 + YTM)^3

For the 4-year bond:

79.81 = Face value / (1 + YTM)^4

Substituting the face value from the previous equation, we get:

79.81 = 85.16 x (1 + YTM)^3 / (1 + YTM)^4

Simplifying the equation:

79.81 = 85.16 / (1 + YTM)

(1 + YTM) = 85.16 / 79.81

(1 + YTM) = 1.0674

YTM = 0.0674

Effective annual yield = (1 + YTM)^4 - 1

= (1.0674)^4 - 1

= 0.058 or 5.8%

Therefore, the answer is C, 5.8%.

The Price of a 3-Year Zero Coupon Government Bond Is