Gabriele Enterprises has bonds on the market making annual payments, with twelve years to maturity, a par value of $1,000, and selling for $972. At this price, the bonds yield 7.1 percent. What must the coupon rate be on the bonds

6.75%

Explanation:

Current price = Annual coupon*Present value of annuity factor (7.1%,12) + 1000*Present value of discounting factor (7.1%,12)

972 = Annual coupon*7.900528111+$1000*0.439062504

Annual coupon = (972-439.062504) / 7.900528111

=$67.46 (Approx)

Coupon rate = Annual coupon/Face value

= $67.46/1000

= 6.75% (Approx).

NOTE:

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

= Annual coupon [1 - (1.071) ^-12]/0.071

= Annual coupon*7.900528111

2. Present value of discounting factor=1000/1.071^12

= $1000*0.439062504