Yield to Maturity (YTM) Calculator
Calculate the exact yield to maturity you earn by holding a bond until it matures. Enter the face value, the price you pay, the coupon, the coupon frequency, and the years remaining. The calculator solves for the precise rate that discounts every coupon and the par repayment back to today’s price, and for callable bonds it also returns yield to call and the conservative yield to worst.
Formula
Worked example
A 1,000 face bond paying a 50 annual coupon, bought for 950 with 5 years left and annual coupons: solving for the rate that discounts the five 50 coupons plus the 1,000 par back to 950 gives an exact YTM of about 6.19%, a touch above the 6.15% textbook approximation. If the same bond were callable at 1,020 in 2 years, the yield to call works out lower, so the yield to worst would be that call figure.
What yield to maturity measures
Yield to maturity is the single annualized rate of return you earn if you buy a bond today and hold it until it matures, collecting every coupon and the face value at the end. It blends two sources of return: the coupon income you receive each period, and any capital gain or loss between the price you pay and the face value repaid at maturity. Because it captures both, YTM is the standard way to compare bonds trading at different prices on an apples-to-apples basis. This calculator also reports the per-payment coupon, the total coupon income to maturity, and the capital gain or loss, so you can see exactly where the yield comes from.
How this calculator finds the exact YTM
The exact yield to maturity is the discount rate that makes the present value of all future coupons plus the face value equal to the bond’s current price. This equation has no closed-form solution, so the calculator solves it by iteration: it splits the annual coupon into the periods you chose, then searches for the per-period rate that prices the bond back to what you pay, and annualizes it by the number of payments per year. This is the same method behind Omnicalculator and DQYDJ, and it matches the YTM you would see on those tools. The textbook approximation is shown alongside as a labeled estimate, and the full cash-flow schedule lists every coupon and the par repayment that the yield is solved against.
Yield to call and yield to worst
Many corporate and municipal bonds are callable, meaning the issuer can redeem them early at a set call price, usually when interest rates fall. For a callable bond, holding to maturity is not guaranteed, so yield to maturity alone can overstate your return. Turn on the callable option and enter the call price and the years to the first call date. The calculator re-solves the same present-value equation, but using the call price as the redemption amount and the call date instead of maturity, to give the yield to call. The yield to worst is simply the lower of the yield to maturity and the yield to call. Prudent investors plan around the yield to worst, because it assumes the least favorable outcome the issuer can force on you.
Why coupon frequency matters
Most real-world bonds pay interest semi-annually, which is why semi-annual is the default here and on the leading calculators. Compounding the same annual coupon more often slightly changes the yield, because cash arrives sooner and is discounted over more, shorter periods. Assuming annual coupons on a bond that actually pays twice a year would push the result off, so set the frequency to match the bond you are pricing: annual, semi-annual, quarterly, monthly, weekly, or daily. You can enter the coupon either as a yearly currency amount or as an annual rate of the face value, whichever you have to hand.
Price, par, and the direction of yield
A bond’s price moves opposite to its yield. When a bond trades below par (a discount), you collect the coupon and also pocket the difference up to face value at maturity, so the YTM sits above the coupon rate. When it trades above par (a premium), the loss back down to face value at maturity drags the YTM below the coupon rate. Only when price equals face value do the coupon rate, current yield, and yield to maturity all line up at the same number.
How price relates to yield
| Bond trades at | Price vs. face | YTM vs. coupon rate | Reading |
|---|---|---|---|
| Discount | Price < face | YTM > coupon | High |
| Par | Price = face | YTM = coupon | Moderate |
| Premium | Price > face | YTM < coupon | Low |
For a fixed coupon, the price you pay determines whether YTM is above, at, or below the coupon rate.
Frequently asked questions
How is the exact yield to maturity calculated?
It is the discount rate that makes the present value of every coupon plus the face value equal the bond’s current price. There is no algebraic formula, so the calculator solves it numerically by searching for the rate that prices the bond exactly, then annualizes it by the coupon frequency.
What is the difference between yield to maturity and yield to call?
Yield to maturity assumes you hold the bond until it matures and receive the face value. Yield to call assumes the issuer redeems the bond early at the call price on the first call date. For callable bonds, the calculator computes both and reports the yield to worst, the lower of the two, which is the conservative return to plan around.
Why does the exact YTM differ from the approximate one?
The approximation spreads the gain or loss evenly over the years and averages price and face value, ignoring the time value of each cash flow. The exact method discounts every coupon at the correct period, so it is more precise. The gap widens for longer maturities and deep discounts or premiums.
What coupon frequency should I choose?
Match it to the bond. Most government and corporate bonds pay semi-annually, which is the default here. If your bond pays annually, quarterly, monthly, weekly, or daily, select that instead, since the frequency affects how the coupon is split and discounted and therefore the yield.