what is the coupon rate for a bond with three years until ma

what is the coupon rate for a bond with three years until maturity a price of 1053.46 and yield to matuity of 6%

Solution

Current price=Annual coupon*Present value of annuity factor(6%,3)+$1000*Present value of discounting factor(6%,3)[here $1000 is the face value of the bond]

1053.46=Annual coupon*2.673011949+$1000*0.839619283

Annual coupon*2.673011949=(1053.46-839.619283)

Annual coupon=213.840717/2.673011949

=$80(Approx).

Coupon rate=Annual coupon/Face value

=(80/1000)

=8%

NOTE:

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

=[1-(1.06)^-3]/0.06

=[1-0.839169283]/0.06

=2.673011949.

2.Present value of discounting factor=$1000/(1.06)^3

=$1000*0.839619283(Approx).