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Consider a 5-year default-free security with annual coupons and with a face value of $1,000.

(a) What is its coupon rate if it is currently selling at par?
(b) What is its coupon rate if it is currently selling at $1041

User Rolznz
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Final answer:

If the bond is selling at par, the coupon rate is 100%. If the bond is selling above its face value, the coupon rate is still 100%.

Step-by-step explanation:

When a bond is selling at par, it means the bond's price is equal to its face value. In this case, the bond has a face value of $1,000. Since it has a 5-year term and annual coupons, the total annual coupon payment is the coupon rate multiplied by the face value. The total annual coupon payment is $1,000 x coupon rate. But since the bond is selling at par, the annual coupon payment will be equal to the face value, which is $1,000. Therefore, the coupon rate is 100%.

If a bond is selling above its face value, it means the bond's coupon rate is lower than the market interest rate. In this case, the bond is selling at $1,041. However, the bond has a face value of $1,000 and a 5-year term. To calculate the coupon rate, we use the formula: annual coupon payment = face value x coupon rate. Rearranging the formula, we can solve for the coupon rate: coupon rate = annual coupon payment / face value. Since the annual coupon payment is $1,000 and the face value is $1,000, the coupon rate is 100%.

User Niklas Forst
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