Bond Price Calculator
Calculate a bond's price from its coupon, maturity, and yield, or solve for yield to maturity. See accrued interest, duration, and interest-rate risk.
https://hexacalculator.com/calculators/finance/bonds/bond-price-calculator
Finance
Bonds
Bond Price Calculator
Calculate a bond's price from its coupon, maturity, and yield, or solve for yield to maturity. See accrued interest, duration, and interest-rate risk.
Bond Price Calculator
Add accrued interest and dirty price
Price a bond bought between coupon dates.
Check interest-rate risk
See duration and how the price reacts when yields move.
Compare a tax-free yield
Find the taxable yield that matches a municipal bond.
Show a price range for a yield swing
Estimate the price if the yield rises or falls.
Bond price
The coupon matches the yield, so this bond trades at par (about its face value).
- Coupon payment
- $
- Current yield
- %
- Total coupon income
- $
- Gain or loss at maturity
- $
Was this calculator helpful?
It takes one click and shapes what we fix next.
Add as preferred on GoogleShow the price-yield curve
Plot how the price changes across a range of yields.
Show the price breakdown
Split the price into the value of coupons and the value of the face amount.
Show the cashflow schedule
List every coupon and the final repayment, with present values.
Period | Years | Cashflow ($) | Discount factor | Present value ($) |
|---|---|---|---|---|
| 1 | 0.5 | 0.25 | 1 | 0.25 |
| 2 | 1 | 0.25 | 0.999 | 0.25 |
| 3 | 1.5 | 0.25 | 0.999 | 0.25 |
| 4 | 2 | 0.25 | 0.999 | 0.25 |
| 5 | 2.5 | 0.25 | 0.999 | 0.25 |
| 6 | 3 | 0.25 | 0.998 | 0.25 |
| 7 | 3.5 | 0.25 | 0.998 | 0.25 |
| 8 | 4 | 0.25 | 0.998 | 0.25 |
| 9 | 4.5 | 0.25 | 0.997 | 0.25 |
| 10 | 5 | 0.25 | 0.997 | 0.25 |
| 11 | 5.5 | 0.25 | 0.997 | 0.25 |
| 12 | 6 | 0.25 | 0.996 | 0.25 |
| 13 | 6.5 | 0.25 | 0.996 | 0.25 |
| 14 | 7 | 0.25 | 0.996 | 0.25 |
| 15 | 7.5 | 0.25 | 0.996 | 0.25 |
| 16 | 8 | 0.25 | 0.995 | 0.25 |
| 17 | 8.5 | 0.25 | 0.995 | 0.25 |
| 18 | 9 | 0.25 | 0.995 | 0.25 |
| 19 | 9.5 | 0.25 | 0.994 | 0.25 |
| 20 | 10 | 1,000.25 | 0.994 | 994.27 |
The bond price is the amount one pays today for a series of future payments that consist of regular interest payments and the face value that is paid back at maturity.
This calculator discounts those payments by an inputted rate to show the bond price. If you leave the price blank, it will calculate the fair value of the bond; if you leave the rate blank, it will calculate the yield to maturity from the given price. Additionally, you can add in extra information such as accrued interest, duration and interest risk, after-tax effective yield, and sensitivity ranges.
What is a bond price?
A bond is a loan made to a government or company. In exchange, you receive fixed interest payments called coupons and get back the face value of the bond when it matures. The price of a bond is the present value of all future payments. Because money received later is worth less than money received today, each payment is discounted at the market rate. The sum of the discounted coupons and the discounted face value gives you the bond price.
Here's how to use this calculator:
Enter the par value, annual interest rate, number of years until maturity and frequency of coupon payments. Then enter one of two values. If you enter the interest rate and leave price blank, the tool will calculate fair value; if you enter the price and leave the interest rate blank, it will calculate yield to maturity. The blank field indicates which value the calculation tool is solving for. Optionally enable additional features. Use accrued interest if you purchased a bond between coupon dates; use duration to assess interest rate risk; use effective after-tax yield to evaluate municipal bonds; and use sensitivity range to see results for a series of interest rates.
Understanding of bond pricing formula.
The price is the sum of the current value of the coupons and the present value of the face amount.
Where C is the coupon paid each period, r is the interest rate per period, n is the total number of periods and F is the face value. The coupon per period is the product of the annual coupon rate and the face value divided by the number of payments per year. Consider a bond with a face value of 1,000, a coupon rate of 5 percent paid semiannually, a remaining maturity of 10 years, and a required return of 6 percent. The payment per period is 25, the total number of periods is 20, and the interest rate per period is 3 percent.
The price is below $1,000 because the interest rate is 6 percent higher than the coupon rate of 5 percent, so this bond will trade at a discount. The following table shows each input and its value for this example.
Symbol | Meaning | Example |
|---|---|---|
F | Face or par value | 1,000 |
Coupon rate | Annual coupon as a percent of face | 5 percent |
C | Coupon paid each period | 25 |
n | Number of periods to maturity | 20 |
r | Yield per period | 3 percent |
P | Bond price | 925.61 |
Why bond prices and yields move in opposite directions
Bond coupons are fixed while market interest rates are variable. If interest rates rise the attractiveness of a fixed coupon falls so the price falls until the bond offers the current market rate of interest. If interest rates fall, the price rises. This leverage is a fundamental fact about investing in bonds.
The size of the price swings depends mainly on how much time is left until maturity. A bond that matures in 2 years will react little to interest rate changes, while a 30-year bond can see its price swing wildly. Duration allows us to quantify this sensitivity.
Net price, gross price, accumulated interest
Bonds are rarely bought or sold on the exact coupon date. If a bond is purchased during the period between coupon payments, the buyer must pay the seller the interest that has accrued since the last payment, and this is the accrued interest. A price that does not include the accrued interest is called the net price. The actual amount to be paid, which is the net price plus the accrued interest, is called the gross price.
The accrued interest increases with the number of days since the last interest payment. You can check these values by activating the function for the accrued interest, entering the number of days and selecting the calculation principle to be applied for the number of days.
Duration and interest rate risk
Duration measures the size of a bond's price change for a given level of yield change. Macaulay duration gives the average time in years until capital is returned, weighting each payment by its present value. Modified duration converts this into a price sensitivity. If modified duration is 8, then if yields rise by 1 percentage point, the price will fall by about 8 percent.
The longer the maturity and the lower the coupon, the higher the duration. So long-term zero-coupon bonds have the highest interest rate sensitivity. The Interest Rate Risk function shows both Macaulay's and modified duration and evaluates the bond based on a selected yield change so you can review results before any gain or loss is realized.
Hints for calculating bond prices:
Match the frequency of interest payment to that of the bond in question. As most corporate bonds and US government bonds pay interest semi-annually, a semi-annual setting is common. Enter the yield to maturity as an annual value and the calculator will convert it into yields for each period. For zero coupon bonds, set the coupon rate to zero so that the price equals the discounted face value. Note that the stated yield already accounts for known risks. A significantly higher yield than similar bonds often does not simply mean a bargain but rather a higher credit risk.
Frequently asked questions
How is bond price calculated?
You discount each future payment amount to its present value and add those values together. Each coupon and the final principal are divided by the result of adding one to the yield for each period, then raised to the power of the number of periods until receipt of the payment. The sum of these present values is the bond price.
Why does bond prices fall when interest rates rise?
The coupon rate is fixed during the life of a bond. When interest rates rise, new bonds will have higher interest payments. Therefore, older bonds with lower coupon rates must reduce their price to sell at all. This increases their yield to the new market level. Price and yield move in opposite directions.
What is the difference between bond price and yield?
The price is the amount you pay. The yield to maturity is the annualized return that will be earned if a bond is held until the end of its term and reinvested at this rate. Both are linked, as knowing one value determines the other. This calculator therefore solves for the missing values.
What is the difference between net and gross?
The net price does not include the interest that has accrued since the last interest payment date. The gross price, also called invoice amount, is the net price plus the accrued interest. The actual amount exchanged in a transaction is the gross price.
What can you find out about a bond based on its duration?
Duration indicates the size of the price change when yield changes. The higher the duration, the greater the interest rate risk. By multiplying modified duration by the change in yield, you can get an approximate percentage change in price.
Related calculators
Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.
References
- Investor.gov: Bonds
U.S. SEC overview of how bonds work and what affects their value.
- Investopedia: Bond Valuation
Definition, formula, and worked examples for pricing a bond.
- U.S. Department of the Treasury: Daily Treasury Par Yield Curve Rates
Current Treasury yields to use as a market reference rate.