Final answer:
The coupon rate of the bond is calculated at 13.30% by determining the annual coupon payments based on the current yield and market price, and then relating it to the bond's par value. This calculation leads to the correct choice, which is option (a).
Step-by-step explanation:
The question asks for the coupon rate of a bond given a par value, current yield, and market price. To find the coupon rate, you must first determine the dollar amount of the annual coupon payments. The current yield is given by the formula: Current Yield = (Annual Coupon Payment / Market Price) x 100. Since we have a current yield of 6.95% and the bond is quoted at 95.71 (which means the market price is $957.10 for a $1,000 par value bond), we can calculate the annual coupon payment. Using the formula we get: 6.95 = (Annual Coupon Payment / 957.10) x 100. Solving for Annual Coupon Payment gives us approximately $66.52.
Given that the bond pays semiannually, we multiply the annual coupon payment by 2 to find the total coupon value for the year: $66.52 x 2 = $133.04. Now, the coupon rate is found by dividing the annual coupon by the par value and converting it to a percentage: Coupon Rate = (Annual Coupon / Par Value) x 100 = ($133.04 / $1,000) x 100, which results in a coupon rate of 13.30%.