Question

Suppose a​ five-year, $ 1 comma1,000 bond with annual coupons has a price of $ 904.25 and a yield to maturity of 5.9 % What is the​ bond's coupon​ rate?

Answer 1

Current price=Annual coupon*Present value of annuity factor(5.9%,5)+$1000*Present value of discounting factor(5.9%,5)

904.25=Annual coupon*4.223847908+$1000*0.750792973

Annual coupon=(904.25-750.792973)/4.223847908

=36.33(Approx).

Coupon rate=Annual coupon/Face value

=(36.33/1000)

=3.63%(Approx).

NOTE:

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

=Annual coupon[1-(1.059)^-5]/0.059

=Annual coupon*4.223847908

2.Present value of discounting factor=1000/1.059^5

=1000*0.750792973