Question

Given a zero-coupon bond (does not make any coupon payment) with a current market price of $550, face value of $1,000 and 13 years to maturity. What is the yield to maturity if the interest on this bond is compounded semiannually?

Answer 1

Given Current Market Price = $ 550

Face value = $ 1000

Years to maturity = 13 Years

We know that Future Value = Present value ( 1+i/2)^2n[ If interest is compounded seemi Anually)

Here i= Rate of interest and n = No.of Years

We also know that Present value of Future Cash inflows is equal to the Market Price of a bond.

$ 1000 = $ 550( 1+i/2)^2*13

$ 1000= $ 550( 1+i/2)^26

$ 1000/$ 550 = ( 1+i/2)^26

1.8182 = ( 1+i/2)^26

( 1.8182)^1/26 = ( 1+i/2)

1.023261 = 1+i/2

1.023261-1 = i/2

0.023261 = i/2

0.04652 = i

Rate of Interest is 4.652%

Hence the YTM of the bond is 4.652%

If you are having any doubt,please post a comment.

Thank you. Please rate it.