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