Respuesta :
The yield to maturity on the 4-year bond is 5.80%
Bond prices are computed using the present value of the bond's future cash flows. The discount rate considered is the yield of the bond. Zero coupon bonds yield zero rates.
3-year zero-coupon government bond price = $85.16
4-year zero-coupon government bond price = $79.81
Zero-coupon bonds yield zero rates. Hence, we will first calculate the yields of the two bonds using the following formula:
[tex]Bond price = {}\displaystyle \frac {F}{(1+r)^t} {}[/tex]
where F is the face value of the bond, r is the yield, and t is the time period.
Let's say R_3 is the yield for a 3-year bond, and R_4 is the yield for the 4-year bond
[tex]85.16 = {}\displaystyle \frac {100}{(1+R_3)^3} {}[/tex]
Solving this equation, we get R_3 = 5.50%
[tex]79.81 = {}\displaystyle \frac {100}{(1+R_4)^4} {}[/tex]
Solving this equation, we get R_4 = 5.80%
So, yield to maturity = 5.80%
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