Question

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

Answer 1

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