Question

Suppose a​ five-year,

$1,000

bond with annual coupons has a price of

$902.91

and a yield to maturity of

6.4%.

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(6.4%,5)+1000*Present value of discounting factor(6.4%,5)

902.91=Annual coupon*4.16691905+1000*0.733317181

Annual coupon=(902.91-733.317181)/4.16691905

=$40.6998113

Coupon rate=Annual coupon/Face value

=40.6998113/1000

=4.07%(Approx)

NOTE:

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

=Annual coupon[1-(1.064)^-5]/0.064

=Annual coupon*4.16691905

2.Present value of discounting factor=1000/1.064^5

=1000*0.733317181