Transparent method
The formula
Worked example
Example inputs
How to interpret the result
A bond's price and its stated coupon move in opposite directions relative to current market yields. When market rates rise above a bond's fixed coupon, the bond has to trade below face value to remain competitive, and when market rates fall below the coupon, the identical bond commands a premium above face value.
Before you rely on it
What to check
Compare the bond's coupon rate against current market yields for similar bonds to understand why a specific bond is pricing at a premium or a discount.
The common error
Where people go wrong with bond price calculator
Expecting a bond to always trade at its face value. Price moves inversely with market yields relative to the fixed coupon, so a bond trading well above or below face value isn't a pricing error: it's the market doing exactly what it's supposed to.
Sensitivity evidence
How yield to maturity changes the estimated bond price
| Yield to maturity | Estimated bond price | Current yield |
|---|---|---|
| 4.0% | $1,082 | 4.6% |
| 5.0% | $1,000 | 5.0% |
| 6.0%worked example | $926 | 5.4% |
| 7.0% | $858 | 5.8% |
| 8.0% | $796 | 6.3% |
Every input, tested
Which input moves the estimated bond price most
| Input | Tested from | To | Estimated bond price at each end | Swing |
|---|---|---|---|---|
| Face value | $900 | $1,100 | $833 to $1,018 | $185 (20%) |
| Annual coupon rate | 4.0% | 6.0% | $851 to $1,000 | $149 (16%) |
| Yield to maturity | 5.0% | 7.0% | $1,000 to $858 | $142 (15%) |
| Years to maturity | 7.0 years | 13.0 years | $944 to $911 | $33 (3.6%) |
| Payments per year | 1 | 3 | $926 to $925 | $1.05 (0.1%) |
Two variables at once
Estimated bond price by yield to maturity and face value
| Yield to maturity \ Face value | $800 | $1,000 | $1,200 |
|---|---|---|---|
| 4.0% | $865 | $1,082 | $1,298 |
| 5.0% | $800 | $1,000 | $1,200 |
| 6.0% | $740 | $926 | $1,111 |
| 7.0% | $686 | $858 | $1,029 |
| 8.0% | $637 | $796 | $955 |
Step by step
The worked example, input by input
| Input | Value used |
|---|---|
| Face value | $1,000 |
| Annual coupon rate | 5.0% |
| Yield to maturity | 6.0% |
| Years to maturity | 10.0 years |
| Payments per year | 2 |
| Estimated bond price | $926 |
| Current yield | 5.4% |
Where the inputs come from
Face value, also called par, is what the bond repays at maturity, usually $1,000. The annual coupon rate is the interest the bond pays as a percent of face value, fixed at issue. Yield to maturity is the return the market currently demands on similar bonds, the discount rate used to price the cash flows. Years to maturity and payments per year set the schedule; most US corporate and Treasury bonds pay twice a year. Take the yield from a bond quote or a comparable bond.
Using the estimated bond price in a real decision
Use it to see how much a bond might drop if rates move, and to compare bonds with different coupons.
When the result stops applying
The formula assumes the bond is held to maturity, pays every coupon on time and that the yield stays constant. It ignores accrued interest, which is part of the price you actually pay between coupon dates, taxes and transaction costs. Callable bonds can be redeemed early, which changes the yield. Credit risk is reflected in the yield, not modeled here.
What to compare it with
Work backward from a market price with the yield to maturity calculator, and see how sensitive the price is on the bond duration and convexity pages. The current yield calculator shows income relative to price, and the zero-coupon bond page covers bonds with no coupons. The callable bond calculator handles bonds that can be redeemed early.
People also ask
Frequently asked questions
Why does a bond's price fall when interest rates rise?
Because new bonds pay higher coupons, so investors will pay less for an older bond with a lower coupon until its yield matches the market.
What does trading at a discount mean?
The bond sells below its face value, which happens when its coupon is lower than the current market yield. At maturity it repays the full face value.
What is accrued interest?
Interest earned since the last coupon payment. A buyer pays it to the seller on top of the quoted price, so the invoice price is higher than the quote.