Suppose that a bond is trading at a price of $940. This bond has 20 years to maturity and pays coupon interest annually. The market rate of interest for such as bond is 11% p.a. What is the coupon rate for this bond? Pls help me with the formula
Current price=Annual coupon*Present value of annuity factor(11%,20)+$1000*Present value of discounting factor(11%,20)
940=Annual coupon*7.963328117+$1000*0.124033907
Annual coupon=(940-124.033907)/7.963328117
=102.47(Approx)
Coupon rate=Annual coupon/Face value
=102.47/$1000
=10.25%(Approx).
NOTE:
1.Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate
=Annual coupon[1-(1.11)^-20]/0.11
=Annual coupon*7.963328117
2.Present value of discounting factor=1000/1.11^20
=1000*0.124033907
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