Bond Calculator — Present Value & Yield
Bond Calculator
Price, Yield & Accrued Interest for Fixed-Rate Bonds
For bonds priced exactly on a coupon payment date. Choose the unknown value, then supply the remaining four to solve for it.
Bond Parameters
For bonds trading between coupon dates. Returns the dirty (invoice) price, clean (quoted) price, and accrued interest owed to the seller.
Bond & Trade Details
Understanding Bond Pricing
A bond is a promise: lend money today, and receive scheduled interest payments plus your principal back at a fixed future date. But a bond's price almost never equals its face value once it starts trading — it rises and falls with prevailing interest rates, time remaining, and the coupon it carries. These calculators translate that relationship into two practical tools: solving for any single unknown among a bond's core terms, and pricing a bond precisely on the date it actually changes hands.
Price Moves Opposite to Yield
When market yields rise above a bond's fixed coupon rate, its price falls below face value (a discount) to compensate new buyers. When yields fall below the coupon, the price rises above face value (a premium). A bond priced exactly at face value has a yield equal to its coupon rate.
Five Variables, One Equation
Price, face value, yield, coupon, and time to maturity are all linked by a single discounted cash flow equation. Know any four, and the fifth is fully determined — which is exactly what the first calculator above solves for.
Clean vs. Dirty Price
Bonds rarely trade exactly on a coupon date. The clean price is what gets quoted publicly; the dirty price is what the buyer actually pays, since it folds in the interest the seller has already earned but not yet received.
Day-Count Conventions Matter
The market doesn't count days the same way everywhere. Corporate bonds typically use 30/360, while U.S. Treasuries use Actual/Actual. The convention changes the accrued interest slightly — usually by fractions of a cent per $100 of face value, but it matters for settlement accuracy.
The Bond Pricing Formula
A bond's price is the present value of every future coupon payment plus the present value of the face value repaid at maturity, all discounted at the periodic market yield.
Where P is price, C is the coupon paid each period, r is the yield per period, N is the number of periods to maturity, and F is the face value.
Worked Example
- Face Value: $100
- Coupon: 5% annually
- Yield Required: 6%
- Time to Maturity: 3 years
- Price: $97.33 (a discount, since yield > coupon)
Accrued Interest & Settlement Pricing
Bond interest accrues continuously between coupon dates, but payments are only made on the coupon date itself. If you buy a bond three days after the last coupon, you owe the seller three days of interest — even though you haven't received a payment yet. That amount is the accrued interest, and it's added to the clean price to arrive at the dirty price you actually pay at settlement.
- 30/360 (Bond Basis): Assumes every month has 30 days and every year has 360 — the standard for most U.S. corporate and municipal bonds.
- Actual/360: Counts real calendar days elapsed, but still divides by a 360-day year. Common for money-market instruments.
- Actual/365: Counts real calendar days elapsed against a fixed 365-day year, used by some non-U.S. government bonds.
- Actual/Actual: Uses the true number of days in both the accrual period and the year — the convention used for U.S. Treasury securities.
Key Takeaways
- Bond prices and yields move in opposite directions: rising rates push existing bond prices down, and falling rates push them up.
- The current yield differs from yield to maturity: the yield used in these calculators reflects the return required over the life of the bond, not simply the coupon divided by today's price.
- The dirty price is what actually settles: published bond quotes almost always show the clean price, so remember to add accrued interest when comparing to what you'll actually pay.
- These tools price fixed-rate bonds only: they do not account for call provisions, credit risk, embedded options, or liquidity premiums that can move real-world market prices.
Frequently Asked Questions
- In the Bond Price Calculator tab, choose which value you want to solve for: price, face value, yield, time to maturity, or annual coupon.
- Fill in the remaining four known values and select the coupon payment frequency.
- Click Calculate to see the result.
- For a trade settling between coupon dates, switch to the Clean & Dirty Price Calculator tab and enter the bond's face value, yield, coupon, maturity date, and settlement date to get the clean price, dirty price, and accrued interest.
A bond's price is the present value of its future cash flows: every coupon payment plus the face value repaid at maturity, each discounted back to today using the required market yield. Because a dollar received in the future is worth less than a dollar today, each future payment is divided by (1 + yield per period) raised to the number of periods away it occurs, and all of those discounted amounts are summed to arrive at the bond's price.
Present value is what a future payment is worth in today's dollars once you account for the time value of money. For a bond, this means every coupon payment and the final face-value repayment are each discounted back to the present using the yield the market currently requires, and their sum is the bond's fair price today.
If a bond's coupon rate is below the yield the market currently requires, investors will only pay less than face value for it — it trades at a discount. If the coupon rate is above the required yield, investors will pay more than face value for the extra income — it trades at a premium. When the coupon rate equals the required yield, the bond trades at par (exactly face value).
To solve for a bond's price you need its face value, annual coupon rate, required yield (market interest rate), years to maturity, and coupon payment frequency (annual, semi-annual, quarterly, or monthly). Any one of price, face value, yield, maturity, or coupon can be solved for if the other four are known.