Question

Suppose a​ five-year,

$ 1 comma 000$1,000

bond with annual coupons has a price of

$ 898.22$898.22

and a yield to maturity of

5.7 %5.7%.

What is the​ bond's coupon​ rate?

The​ bond's coupon rate is

nothing​%.

​(Round to three decimal​ places.)

Answer 1

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

898.22=Annual coupon*4.246965615+1000*0.75792296

Annual coupon=(898.22-757.92296)/4.246965615

=$33.03(Approx)

Coupon rate=Annual coupon/Face value

=$33.03/$1000

=3.303%(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*4.246965615

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

=1000*0.75792296