Bond Price Calculator
Calculate the fair price of a fixed-rate bond from its coupon rate, yield to maturity, face value, and time to maturity.
Example: A $1,000 face-value bond with a 5% annual coupon, 10 years to maturity, priced at a 6% market yield, is worth $926 today — below face value because its coupon rate is lower than the market's required return. Its Macaulay duration is about 7.7 years, meaning a 1 percentage-point rise in yields would cut its price by roughly 7.7%.
Price = Σ [Coupon / (1+y)ᵗ] + [Face Value / (1+y)ⁿ], the standard present-value bond pricing formula.
How bond price is calculated
This calculator discounts every coupon payment, plus the face value repaid at maturity, back to today at the market yield — the sum of those discounted cash flows is the bond's price. Duration is the present-value-weighted average time until you receive those cash flows, a useful measure of how sensitive the bond's price is to interest rate changes: longer duration means more sensitivity. Yield to maturity is solved independently from the resulting price as a consistency check, and should closely match the market yield you entered.
Duration tells you the first-order effect of a yield change on price, but the real relationship between yield and price is curved, not straight — convexity captures that curvature, meaning duration alone slightly understates gains when yields fall and overstates losses when yields rise. The market yield you enter here should be one appropriate for the bond's credit risk — see the Risk-Free Rate calculator for a government-bond baseline, and the Sharpe Ratio calculator for judging whether a bond's extra yield over that baseline is adequately compensating you for its additional risk.
Frequently asked questions
- Why does the bond price differ from the face value?
- When the market yield is above the bond's coupon rate, the bond trades at a discount (price below face value) — investors need a lower price to make up for the below-market coupon. When the yield is below the coupon rate, it trades at a premium. The two are only equal when the coupon rate exactly matches the market yield.
- What is duration?
- Macaulay duration is the weighted average time (in years) until you receive the bond's cash flows, weighted by how much of the bond's present value each payment represents. It's always less than the years to maturity for a coupon-paying bond, and exactly equal to it for a zero-coupon bond.
- Why show yield to maturity if I already entered the market yield?
- Yield to maturity here is solved independently from the calculated price, not just echoed back — it's a way of confirming the pricing math is internally consistent, since the two should always agree almost exactly.
- Does this assume annual coupon payments?
- Yes — this calculator assumes one coupon payment per year, paid at the end of each year.
- Can I use this in my own app?
- Yes — every calculator on Stupidly Clever has a matching REST API and MCP tool that runs the same underlying logic.
- What is convexity in bond pricing?
- Convexity measures how duration itself changes as yields move. A bond with higher convexity gains more in price when yields fall and loses less when yields rise than duration alone predicts — which is why convexity is a desirable property for bond holders.
- What is the difference between clean price and dirty price?
- The dirty (full) price is what you actually pay — it includes accrued interest since the last coupon payment. The clean price strips out accrued interest and is the price typically quoted in the market. This calculator outputs the theoretical fair value (clean price basis).