Question

What is the coupon rate for a bond with 5 years until maturity, a price of $1,075, and a yield to maturity of 6.5%? Interest is paid annually?

1. 7.20%

2. 6.90%

3. 6.50%

4. 8.30%

Answer 1

Current price=Annual coupon*Present value of annuity factor(6.5%,5)+1000*Present value of discounting factor(6.5%,5)

1075=Annual coupon*4.15567944+1000*0.729880837

Annual coupon=(1075-729.880837)/4.15567944

=$83.0475902(Approx)

Coupon rate=Annual coupon/Face value

=83.0475902/1000

=8.30%(Approx)

NOTE:

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

=Annual coupon*[1-(1.065)^-5]/0.065

=Annual coupon*4.15567944

2.Present value of discounting factor=1000/1.065^5

=1000*0.729880837