Question

What is the coupon rate for a par value bond with ten years until maturity, annual compounding, a current price of $1,280.95, and a yield to maturity of 7%?

Answer 1

Current price=Annual coupon*Present value of annuity factor(7%,10)+1000*Present value of discounting factor(7%,10)

1,280.95 =Annual coupon*7.02358154+1000*0.508349292

Annual coupon=(1,280.95-508.349292)/7.02358154

=$110(Approx)

Coupon rate=Annual coupon/Face value

=110/1000

=11%

NOTE:

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

=Annual coupon[1-(1.07)^-10]/0.07

=Annual coupon*7.02358154

2.Present value of discounting factor=1000/1.07^10

=1000*0.508349292