Article — Bond Price Calculator
The Bond Price Calculator, with coupons, yield, and duration
Bond price is the present value of every cash flow the bond pays, discounted at the yield investors require today. For a standard coupon bond, P = C × [1 − (1 + y/m)^(−N)] ÷ (y/m) + F ÷ (1 + y/m)^N, where F is face value, C is the per-period coupon, y is annual yield, m is coupons per year, and N = n · m is the total number of periods.
The same formula prices a Treasury note, an investment-grade corporate bond, and a municipal. Differences across issuers show up in the yield, not the math. The U.S. Treasury and the SEC both use this discounted-cash-flow approach in their investor education material.
What is bond price?
A bond is a loan packaged as a security. The issuer (a government or corporation) borrows the face value, pays periodic interest called coupons, and returns the face value at maturity. The bond price is what a buyer pays today for that stream of future payments. It is set in the secondary market and moves with prevailing interest rates, even though the cash flows themselves are fixed.
U.S. Treasury notes and bonds pay semi-annual coupons on a $1,000 face. Corporate bonds usually follow the same convention, though some pay quarterly or monthly. Zero-coupon bonds skip coupons entirely and are sold deeply below par. Whatever the schedule, price is always the discounted sum of cash flows.
The U.S. Treasury bond market is the world's largest, with more than $27 trillion outstanding in 2024 according to TreasuryDirect data. A single basis-point move in 10-year Treasury yields shifts the price of the on-the-run note by about 0.09% — small in percent terms, but enormous in dollar terms across the market.
The bond price formula
Two pieces, discounted to today and added together: the coupon stream and the face value at maturity.
Coupon C = F × c ÷ mPeriods N = n × mPrice P = C × [1 − (1+y/m)^−N] ÷ (y/m) + F ÷ (1+y/m)^NCurrent yield = (F × c) ÷ PWorked example. A 10-year corporate bond pays a 5% annual coupon, semi-annually, on a $1,000 face value. Required yield is 6%. C = 1,000 × 0.05 ÷ 2 = $25. N = 20. y/m = 0.03. Price = 25 × [1 − 1.03^(−20)] ÷ 0.03 + 1,000 ÷ 1.03^20 = $926.40. The bond trades at a discount because its 5% coupon undercuts the 6% market yield.
Coupon rate vs yield to maturity
The coupon rate is fixed at issuance. It is a contractual percentage of face value: a 5% coupon on a $1,000 bond pays $50 a year, every year, regardless of where the price is trading. Yield to maturity, by contrast, is the actual return you earn if you buy at today's price and hold to maturity. It includes both the coupons and any gain or loss versus par.
When yields rise above the coupon rate, the bond's fixed coupons become less attractive than fresh issues, so the price falls until the implied yield matches the market. When yields fall, the bond's coupons look generous, so the price rises. The Federal Reserve publishes daily Treasury yields in the H.15 release that traders use as the risk-free benchmark.
Premium, par, and discount bonds
Three simple cases, set entirely by the relationship between coupon rate and yield:
- Premium — coupon > yield, so price > face. Example: 6% coupon, 4% yield, 10-yr → $1,164.
- Par — coupon = yield, so price = face. Always converges to par at maturity regardless of path.
- Discount — coupon < yield, so price < face. Example: 3% coupon, 5% yield, 10-yr → $844.
- Zero-coupon — no coupons, deep discount, full return from price appreciation.
- Callable — issuer can redeem early at a set price, which caps the upside in a premium scenario.
Duration and bond price sensitivity
Macaulay duration is the weighted average time to receive a bond's cash flows, measured in years. It is also an approximation of price sensitivity: a 7-year-duration bond loses about 7% in price for a 1 percentage point rise in yields, and gains about 7% for a 1-point fall. Longer-maturity bonds have longer duration; higher-coupon bonds have shorter duration because more cash arrives sooner.
Modified duration is the more direct measure of price change. It equals Macaulay duration divided by (1 + y/m). The CFA Institute treats duration as the first-order risk measure for any fixed-income portfolio, with convexity adjusting for the curvature of the price-yield line at large moves.
When you compare two bonds at the same yield, the one with the longer duration carries more interest-rate risk. To dampen the swings without losing yield, mix long-duration and short-duration bonds — the technique is called barbelling and is standard in pension and insurance portfolios.
Clean vs dirty bond price
Bond quotes on screens show the clean price — the price you would pay if the trade settled exactly on a coupon date. When a trade settles between coupon dates, the buyer pays the seller for accrued interest since the last coupon. The all-in figure is the dirty price (also called invoice price).
The formula is straightforward: dirty price = clean price + accrued interest. Accrued interest equals C × (days since last coupon ÷ days in coupon period). The cash that changes hands at settlement is always the dirty price. The calculator on this page returns the theoretical full price on a coupon date, which is identical to the clean price at that moment.
The bond price formula assumes the issuer will make every promised payment. It does not adjust for default risk. A high-yield (junk) bond priced at the same yield as a Treasury is far cheaper because investors require an extra premium for the chance of missed coupons. Always look at the credit rating (S&P, Moody's, or Fitch) alongside the price.
Common bond pricing mistakes
The first error is using an annual yield directly inside a semi-annual formula. Y/m takes care of the period conversion. A 6% annual yield on a semi-annual bond means 3% per period, not 6%. Skip this and prices come out wildly off.
The second is forgetting that the price-yield relationship is convex, not linear. Duration approximates small moves well, but for large yield swings (200+ basis points) the actual price change deviates from duration's estimate. Convexity is the second-order correction, and adds a small positive return because price falls less for a yield rise than it gains for an equal yield fall.
The third is ignoring optionality. Callable bonds and putable bonds embed an option that shifts the cash flows. A callable corporate trading above par will get called near the call date, so its effective duration is much shorter than the stated maturity suggests. Treasury notes and bonds are not callable, which is one reason they remain the cleanest application of the basic formula.