Question

Suppose a five-year, $ 1 000 bond with annual coupons has a price of $ 897.41 and a yield to maturity of 6.3 %. What is the bond's coupon rate?

The bond's coupon rate is

nothing %.

(Enter your response as a percent rounded to three decimal places.)

Answer 1

Current price=Annual coupon*Present value of annuity factor(6.3%,5)+$1000*Present value of discounting factor(6.3%,5)

897.41=Annual coupon*4.178207017+$1000*0.736772957

Annual coupon=(897.41-736.772957)/4.178207017

=$38.45(Approx)

Coupon rate=Annual coupon/Face value

=(38.45/1000)

=3.845%(Approx).

NOTE:

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

=Annual coupon[1-(1.063)^-5]/0.063

=Annual coupon*4.178207017

2.

Present value of discounting factor=1000/1.063^5

=1000*0.736772957