Question

Suppose a​ five-year, $ 1000 bond with annual coupons has a price of $ 899.04 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)

899.04=Annual coupon*4.166919048+1000*0.73331718

Annual coupon=(899.04-733.31718)/4.166919048

=$39.77(Approx).

Coupon rate=Annual coupon/Face value

=(39.77/1000)

=3.98%(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*4.166919048

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

=1000*0.73331718