Question

Suppose a​ five-year, $ 1 000 bond with annual coupons has a price of $ 903.06 and a yield to maturity of 6.4%. What is the​ bond's coupon​ rate?

Answer 1

Current price=Annual coupon*Present value of annuity factor(6.4%,5)+1000*Present value of discounting factor(6.4%,5)

903.06=Annual coupon*4.16691905+1000*0.733317181

Annual coupon=(903.06-733.317181)/4.16691905

=$40.7358091(Approx)

Coupon rate=Annual coupon/Face value

=40.7358091/1000

=4.07%(Approx).

NOTE:

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

=Annual coupon[1-(1.064)^-5]/0.064

=Annual coupon*4.16691905

2.Present value of discounting factor=1000/1.064^5

=1000*0.733317181