Question

Suppose a​ five-year,

$ 1 comma 000$1,000

bond with annual coupons has a price of

$ 901.69$901.69

and a yield to maturity of

5.7 %5.7%.

What is the​ bond's coupon​ rate?

Answer 1

Current price=Annual coupon*Present value of annuity factor(5.7%,5)+1000*Present value of discounting factor(5.7%,5)

901.69=Annual coupon*4.24696561+1000*0.75792296

Annual coupon=(901.69-757.92296)/4.24696561

=$33.8517081

Coupon rate=Annual coupon/Face value

=(33.8517081/1000)

=3.385%(Approx)

NOTE:

1.Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate

=Annual coupon[1-(1.057)^-5]/0.057

=Annual coupon*4.24696561

2.Present value of discounting factor=1000/1.057^5

=1000*0.75792296