A bond’s coupon rate tells you what it pays, but not what it earns you. That depends on the price you pay. Buy below face value and you collect the coupons plus a gain at maturity; buy above face value and part of every coupon is really a return of your own money. Yield to maturity rolls all of that into one annual rate you can compare across bonds.
How to use the bond yield calculator
- Enter the face value (usually $1,000) and the price you would pay in dollars. Bond quotes are a percentage of par, so a quote of 95.00 means $950 on a $1,000 bond.
- Enter the annual coupon rate and the years to maturity.
- Choose how often coupons are paid — semiannual for most US Treasury and corporate bonds.
- For a callable bond, add the call price and years until the first call to see the yield to call and yield to worst.
Bond yield formulas
Yield to maturity is the periodic rate y that solves:
There is no algebraic solution for y, so the calculator solves it numerically. For a quick sanity check, traders use the shortcut [Annual coupon + (Face − Price) ÷ Years] ÷ [(Face + Price) ÷ 2], which usually lands within a few hundredths of a percent for bonds near par.
Worked example
A 10-year bond with a $1,000 face value and a 5% semiannual coupon trades at $950.
Coupon per period = 1,000 × 5% ÷ 2 = $25; there are 20 periods
Solving 950 = Σ 25 ÷ (1 + y)k + 1,000 ÷ (1 + y)20 gives y = 2.8308% per half-year
YTM = 2.8308% × 2 = 5.662%; current yield = 50 ÷ 950 = 5.263%
The YTM is above the current yield because the $50 discount is earned back when the bond matures at par. The shortcut formula gives 5.641%, close but not exact.
If the same bond instead cost $1,080 and could be called at $1,020 in five years, the YTM would fall to 4.021% and the yield to call to 3.606% — so the yield to worst is 3.606%.
Discount, par and premium bonds
| Price vs. face | Relationship | What it means |
|---|---|---|
| Below face (discount) | Coupon rate < current yield < YTM | Part of the return comes from the price rising to par |
| Equal to face (par) | Coupon rate = current yield = YTM | Return comes only from coupons |
| Above face (premium) | Coupon rate > current yield > YTM | Part of each coupon offsets the price falling to par |
Limits of yield to maturity
YTM assumes every coupon is reinvested at the same yield, which rarely happens exactly. It also assumes the issuer pays in full and on time — a high YTM on a risky bond partly reflects the chance of default. Taxes are ignored: Treasury interest is exempt from state income tax, municipal bond interest is usually exempt from federal tax, and corporate bond interest is fully taxable, so compare after-tax yields when the bonds differ.
For accrued interest, clean and dirty prices and duration on an exact settlement date, use the bond price calculator. For irregular cash flows of any kind, the IRR calculator solves the same kind of equation.
Results are estimates for education and planning, not investment advice. Broker quotes may use different day-count and settlement conventions.
Frequently asked questions
What is yield to maturity?
Yield to maturity is the single annual interest rate that makes the present value of all remaining coupons and the face value equal to the bond's price. It is the bond's internal rate of return if you buy at that price, hold to maturity, receive every payment and reinvest coupons at the same rate.
How is current yield different from YTM?
Current yield is just the annual coupon divided by the price. It ignores the gain or loss you lock in when a discount or premium bond matures at par. For a bond bought below par, YTM is higher than current yield; for a bond bought above par, it is lower.
Why do bond prices fall when yields rise?
A bond's coupons are fixed. When new bonds offer higher rates, an existing bond is only attractive at a lower price, which raises its yield to match the market. The price and yield therefore always move in opposite directions.
What is yield to worst?
For a callable bond, the issuer can repay early at the call price. Yield to worst is the lower of the yield to maturity and the yield to call, the most conservative estimate of what you will earn. Premium callable bonds are the ones most likely to be called.
Why is YTM quoted as a bond-equivalent yield?
US bond markets quote yields as the periodic yield times the number of coupons per year — semiannual yield × 2 for most bonds. The effective annual yield, which compounds the periodic rate, is slightly higher and better for comparing with savings accounts.