Question

A bond sells for $1215 in the market and has 12 years until maturity. The bond's...

A bond sells for $1215 in the market and has 12 years until maturity. The bond's YTM = 9.19% and pays its coupons annually. What is the bond's annual coupon rate?

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Answer #1

Current price=annual coupon*Present value of annuity factor(9.19%,12)+$1000*Present value of discounting factor(9.19%,12)

1215=annual coupon*7.092693876+1000*0.348181432

annual coupon=(1215-348.181432)/7.092693876

annual coupon=$122.21(Approx)

Hence coupon rate=annual coupon/Face value

=($122.21/1000)

=12.22%(Approx).

NOTE:

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

=annual coupon[1-(1.0919)^-12]/0.0919

=annual coupon*7.092693876

2.Present value of discounting factor=1000/1.0919^12

=1000*0.348181432

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