Question

Suppose a five year $1000 bond with annual coupons has a price of $ 902.67 and yield of maturity of 5.9%. What is the 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)

902.67=Annual coupon*4.22384791+1000*0.750792973

Annual coupon=(902.67-750.792973)/4.22384791

=$35.9570302(Approx)

Coupon rate=Annual coupon/Face value

=35.9570302/1000

=3.596%(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*4.22384791

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

=1000*0.750792973