# Price On A Coupon Date

A sequence of equal cash flows at regular intervals is called an Annuity
The coupon payments on a bond are an example of an annuity.
You can calculate the price of a bond on a coupon date by:
1) Using the PV function.
2) Using any of the functions or methods for Between Coupon Dates.

### Annual Coupons

Compounded annually. What is the price of an 8 year bond with a par value of \$1,000 and a 10% coupon paid annually?
Lets assume that the interest rate (or discount rate) is 4%.
The price of a bond on a coupon date can be calculated in Excel using the PV function. This bond is selling at a premium because the interest rate is less than the coupon rate.

### Semi-Annual Coupons

Compounded semi-annually.
What is the price of an 10 year bond with a par value of \$1,000 and a 10% coupon paid semi-annually?
Lets assume that the interest rate (or discount rate) is 12%.
1) Calculate the number of coupon payments - The coupon is paid semi-annually so there will be 2 coupon payments a year, making 20 coupon payments in total
2) Calculate the value of each coupon payment. The coupon rate will be 10/2 = 5% of the bond par value, so (1000 * 0.05) = \$50.
3) Calculate the semi annual interest rate. The semi-annual interest rate will be 12/2 = 6%. The price of a bond on a coupon date can be calculated in Excel by using the PV function. This bond is selling at a discount because the interest rate is greater than the coupon rate.

### M Coupons A Year

where m represents the frequency of the coupon payments.
where C is the annual coupon amount
If quarterly then m=4. If monthly then m=12 