Question

Suppose a​ five-year,

$ 1 comma 000$1,000

bond with annual coupons has a price of

$ 903.43$903.43

and a yield to maturity of

5.6 %5.6%.

What is the​ bond's coupon​ rate?

Answer 1

Current price=Annual coupon*Present value of annuity factor(5.6%,5)+$1000*Present value of discounting factor(5.6%,5)

903.43=Annual coupon*4.25859976+$1000*0.761518413

Annual coupon=(903.43-761.518413)/4.25859976

=33.32(Approx).

Hence coupon rate=Annual coupon/Face value

=33.32/$1000

=3.33%(Approx).

NOTE:

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

=Annual coupon[1-(1.056)^-5]/0.056

=Annual coupon*4.25859976

2.Present value of discounting factor=$1000/1.056^5

=$1000*0.761518413