Enter a bond's price, coupon and time to maturity to find its yield to maturity, and its yield to call if the issuer can redeem it early. Clean price, dirty price and accrued interest are worked out alongside.
Yield to maturity
4.981%
Nominal annual rate, compounded semiannually. Effective annual yield 5.043%.
Discount bond. It costs less than face value, so the yield to maturity is above the coupon rate: the gain at maturity adds to the coupons.
| Clean price 96.250 per 100, the quoted price | $962.50 |
|---|---|
| Accrued interest settles on a coupon date, so no interest has accrued | $0.00 |
| Dirty price what the buyer pays | $962.50 |
| 20 semiannual coupons of $22.50 | $450.00 |
| Face value repaid at maturity | $1,000.00 |
| Received if held to maturity | $1,450.00 |
Yield to maturity is the one annual rate that makes the present value of every remaining coupon, plus the face value at maturity, equal to the price paid. There is no direct formula for it, so the calculator brackets the answer and closes in with Newton steps until the price matches.
Dirty price = Σ C ÷ (1 + y/f)^t + 100 ÷ (1 + y/f)^TC = coupon per period per 100 of face, f = coupons a year, t = periods until each coupon, T = periods until maturity.
Bonds are quoted at a clean price. Between coupon dates the seller has already earned part of the next coupon, the accrued interest, so the buyer pays the dirty price: clean price plus accrued interest. Choose "By dates" to count the days: actual/actual, as U.S. Treasuries do, or 30/360, which MSRB Rule G-33 sets for municipal securities.
For a callable bond the same solve runs to the call date, with the call price in place of face value; the lower of the two yields is the yield to worst.
Example: 10 years left, a 4.5% semiannual coupon, price 96.25. Twenty coupons of 2.25 and the final 100, discounted at 4.981% a year (2.490% per half-year), come back to 96.25.
Prices, yields, bills and payment dates, each with its formula shown.
From a yield to the clean and dirty price, with duration, convexity and a price–yield curve.
A year's coupons divided by the price, compared with yield to maturity.
Discount yield, investment rate and money market yield of a Treasury bill.
Every remaining payment date and amount to maturity, ready to download as CSV.
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Look up a site with WebTraceCheckThe bond costs less than face value, and the gain when it repays at par counts on top of the coupons. Above face value it works the other way round.
Only how the part period up to the next coupon is discounted: the street convention compounds it, the Treasury formula uses simple interest. The yields usually differ in the third decimal place.
Only under its assumptions: you hold to maturity, every payment arrives in full and on time, and each coupon is reinvested at the same yield. Selling early, a default or a call changes the result. It compares bonds; it does not forecast.
The day the bond changes hands, shown on the trade confirmation. It can fall after the trade date, and accrued interest is counted up to it.