Question

Suppose a​ five-year, $1,000 bond with annual coupons has a price of $900.15 and a yield to maturity of 6.2%. What is the​ bond's coupon​ rate?

Answer 1

Current price=Annual coupon*Present value of annuity factor(6.2%,5)+1000*Present value of discounting factor(6.2%,5)

900.15 =Annual coupon*4.18954361+1000*0.740248296

Annual coupon=(900.15-740.248296)/4.18954361

=$38.1668551(Approx)

Coupon rate=Annual coupon/Face value

=38.1668551/1000

=3.82%(Approx)

NOTE:

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

=Annual coupon[1-(1.062)^-5]/0.062

=Annual coupon*4.18954361

2.Present value of discounting factor=1000/1.062^5

=1000*0.740248296