Question

Suppose a​ five-year, $1,000 bond with annual coupons has a price of $899.28 and a yield to maturity of 5.8%. What is the​ bond's coupon​ rate?

The​ bond's coupon rate is ____%

Answer 1

Current price=Annual coupon*Present value of annuity factor(5.8%,5)+$1000*Present value of discounting factor(5.8%,5)

899.28=Annual coupon*4.235381758+$1000*0.754347858

Annual coupon=(899.28-754.347858)/4.235381758

=$34.22(Approx).

Coupon rate=Annual coupon/Face value

=$34.22/$1000

=3.42%(Approx).

NOTE:

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

=Annual coupon[1-(1.058)^-5]/0.058

=Annual coupon*4.235381758

2.Present value of discounting factor=1000/1.058^5

=1000*0.754347858