# Math

# If a bond has a face value of $1000 and a coupon rate of 4.25%, calculate the annual coupon payments. The annual coupon payment for a bond with face value$1000 and a coupon rate of 4.25% is $42.50. ## Expert Answers A coupon payment is the amount of interest which a bond issuer pays to a bondholder from the issue date until it matures . The annual coupon payment 'C', is given by the mathematical expression: C=\frac{c\times F}{n} where 'c' is the coupon rate, 'F' is the Face value of the bond, and 'n' is the Number of coupon payments per year. The coupon rate 'c' is the periodic rate of interest paid by bond issuers to the bond holders and is calculated on the bond's face value. The face value 'F' is the value that the bondholders will receive when their bond fully matures, unless it is defaulted. So, if you know the face value of the bond and its coupon rate, you can calculate the annual coupon payment using the above expression. From the question, it is clear that the bond has a face value of$1000 and a coupon rate of 4.25%.

So here,

F= 1000 and c= 4.25% = 0.0425

Here n =1 , because payment is made annually.

So, substituting these values in the above mathematical formula we get,

C = \frac{0.0425 \times 1000}{1}

= 42.5

The annual coupon payment is $42.50. This means that the bond issuer should pay$42.50 after a year to the bond holder.

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