Question

If a bond with annual coupon payments have 12 years to maturity and is selling for $963, with a yield of 7.50%. What must the coupon rate be on this bond 

Answer 1

Current price = Annual coupon*Present value of annuity factor(7.5%,12) + 1000 * Present value of discounting factor(7.5%,12)

963 = Annual coupon * 7.73527827 + 1000 * 0.419854129

Annual coupon = (963-419.854129)/7.73527827 =$70.2167203

Coupon rate = Annual coupon/Face value = 70.2167203/1000 = 7.02%(Approx)

NOTE:

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

= Annual coupon*[1-(1.075)^-12]/0.075

= Annual coupon*7.73527827

2.Present value of discounting factor = 1000/1.075^12

= 1000*0.419854129