How this number is made
A bond paying a fixed coupon is worth the present value of those coupons plus the present value of the face amount, discounted at the yield you require. If the yield equals the coupon, the price equals the face.
- Coupon rate is the bond’s rate on face value, paid here as one annual coupon.
- Yield is the market rate you discount at, not the coupon.
Formula
Price = coupon × (1 − (1+y)^−n) ÷ y + face ÷ (1+y)^n. Coupon = face × coupon rate.
Worked example
With the figures already in the form, price on a coupon date is $1,039.56.
Questions
Why is there no semiannual coupon?
Many US treasuries and corporates pay twice a year. This page compounds and pays once a year so the inputs stay few. A semiannual bond at the same nominal yield will differ slightly.
Does this include accrued interest?
No. The price is a clean price on a coupon date. Between coupon dates a buyer also pays accrued interest.