Question

Suppose a​ five-year, $ 1 000 bond with annual coupons has a price of $ 898.03 and a yield to maturity of 6.1 %. What is the​ bond's coupon​ rate?

Answer 1

Current price=Annual coupon*Present value of annuity factor(6.1%,5)+$1000*Present value of discounting factor(6.1%,5)

898.03=Annual coupon*4.200929113+$1000*0.743743324

Annual coupon=(898.03-743.743324)/4.200929113

=$36.73(Approx)

Hence coupon rate=Annual coupon/Face value

=$36.73/$1000

=3.67%(Approx).

NOTE:

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

=Annual coupon[1-(1.061)^-5]/0.061

=Annual coupon*4.200929113

2.Present value of discounting factor=1000/1.061^5

=1000*0.743743324