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XYZ bonds mature in 15 years and the yield to maturity is 3%. These bonds are...

XYZ bonds mature in 15 years and the yield to maturity is 3%. These bonds are currently valued at $1120.08. Find the coupon rate.

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Answer #1

Current price=Annual coupon*Present value of annuity factor(3%,15)+1000*Present value of discounting factor(3%,15)

1120.08=Annual coupon*11.9379351+1000*0.641861947

Annual coupon=(1120.08-641.861947)/11.9379351

=$40.058691

Coupon rate=Annual coupon/Face value

=40.058691/1000

=4.01%(Approx)

NOTE:

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

=Annual coupon[1-(1.03)^-15]/0.03

=Annual coupon*11.9379351

2.Present value of discounting factor=1000/1.03^15

=1000*0.641861947

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