Bond Price
Present value of a coupon bond: the sum of discounted periodic coupons plus the discounted face value at maturity. Discount rate is the yield to maturity, applied periodically as y/m.
When to use: Use to price any plain-vanilla coupon bond given face value, coupon rate, yield, term, and coupons-per-year. The closed-form combines an annuity (the coupon stream) with a single-sum present value (the face return).
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| BondPrice | Bond Price | Theoretical (clean) price of the bond | $ |
| F | Face Value | Par value paid at maturity | $ |
| CR | Coupon Rate | Annual coupon rate as a decimal (e.g. 0.05 for 5%) | % |
| y | Yield | Annual yield as a decimal; periodic yield is y/m | % |
| N | Years to Maturity | Years remaining until the bond matures | years |
| m | Coupons per Year | Number of coupons paid per year (e.g. 2 for semi-annual) | integer |
Real-Life Examples
Example 1: Par Bond at Coupon-Equals-Yield
10-year, 5% coupon, semi-annual, $1,000 face. Market yield equals coupon rate at 5%.
Given
Step-by-Step
When yield equals coupon rate, the bond prices at par. Prices above par signal yield below coupon (premium); prices below par signal yield above coupon (discount).
Example 2: Discount Bond at Higher Yield
Same 10-year, 5% coupon, semi-annual, $1,000 face — but the market now demands a 6% yield.
Given
Step-by-Step
A 100bp rise in yield (5%→6%) drops the price ~7.4%, illustrating duration-driven price risk. Selling the bond before maturity locks in this paper loss; holding to maturity recovers par.
Frequently Asked Questions
Because cash flows arrive m times per year, the periodic discount rate (y/m) and number of periods (N×m) reflect the actual timing. This is the standard "nominal annual rate compounded m times per year" convention used across US fixed income.
The formula reduces to P = (F × CR × N) + F — undiscounted coupons plus face. The annuity term is undefined at zero, so the calculator handles that case explicitly.
Clean — assumes pricing on a coupon date with no accrued interest. To get dirty (settlement) price between coupon dates, add accrued interest computed via the accrued-interest formula.
Exactly — bond price IS the sum of an ordinary annuity (the coupons) plus a single-sum present value (the face). Every bond pricing problem decomposes into those two TVM building blocks.