Calculate a bond’s yield to maturity (YTM) from its price, coupon, and years to maturity, or solve for the bond price at a target yield.
Yield to Maturity Formula
Yield to maturity (YTM) is the single discount rate that makes the present value of a bond's future coupon payments and its face value equal to its current price. Because the rate sits inside every discounted term, there is no way to isolate it algebraically, so the calculator solves it numerically. The price of a bond at a given yield is:
P = (C/m) * (1 - (1 + y/m)^(-n*m)) / (y/m) + F * (1 + y/m)^(-n*m)
To find YTM the calculator searches for the value of y that reproduces the price you entered. For a quick hand estimate you can use the approximation:
YTM = (C + (F - P) / n) / ((F + P) / 2)
- P = current market price of the bond
- F = face (par) value, the amount repaid at maturity
- C = annual coupon payment in currency (face value times the annual coupon rate)
- y = yield to maturity expressed as an annual decimal
- m = number of coupon payments per year
- n = years to maturity
In the default mode you supply the face value, coupon rate, payment frequency, years to maturity, and the current price, and the calculator returns the exact YTM. Switch the solve-for selector to bond price and it runs the same equation in reverse: you give it a target yield and it returns the price that delivers that yield. The optional yield to call setting repeats the calculation using the call price and the years to the call date instead of the face value and maturity, which tells you the return if the issuer redeems the bond early.
Reading the Price and Yield Relationship
The relationship between a bond's price and its yield is fixed. Where a bond trades relative to par immediately tells you how its yield compares to its coupon rate.
| Bond trades at | Price vs face value | YTM vs coupon rate |
|---|---|---|
| Discount | Price below par | YTM higher than coupon |
| Par | Price equals par | YTM equals coupon |
| Premium | Price above par | YTM lower than coupon |
Payment frequency also changes the result because more frequent compounding raises the effective return. The value you enter for m should match how the bond actually pays.
| Payment schedule | Payments per year (m) |
|---|---|
| Annual | 1 |
| Semi-annual (most US bonds) | 2 |
| Quarterly | 4 |
| Monthly | 12 |
Example Problems
Example 1: Solving for YTM. A bond has a face value of $1,000, a 5% annual coupon paid semi-annually, 10 years to maturity, and currently trades at $950. Using the approximation, the annual coupon is $50 and the amortized discount is ($1,000 - $950) / 10 = $5, so the numerator is $55. The average of face and price is ($1,000 + $950) / 2 = $975. That gives an estimate of $55 / $975 = 5.64%. The exact iterative result the calculator returns is about 5.66%, slightly higher because the bond trades at a discount.
Example 2: Solving for price. A bond has a face value of $1,000, a 6% coupon paid semi-annually, 8 years to maturity, and you want a 5% target yield. With m = 2 the coupon per period is $30, there are 16 periods, and the periodic yield is 0.025. Discounting all 16 coupons and the $1,000 face value gives a price of about $1,065.30. The price is above par because the 6% coupon is more generous than the 5% yield you require.
Frequently Asked Questions
Why does YTM differ from the coupon rate? The coupon rate is fixed against the face value, but YTM is measured against the price you actually pay. If you buy below par you also collect the gain back to face value at maturity, which lifts your yield above the coupon. If you pay a premium, part of that premium is lost at maturity, which pulls your yield below the coupon.
What does YTM assume? YTM assumes you hold the bond until maturity, that every coupon and the final principal are paid on schedule, and that each coupon is reinvested at the same yield. If you sell early or reinvest coupons at a different rate, your realized return will not match the quoted YTM.
When should I look at yield to call instead? Use yield to call for callable bonds, where the issuer can redeem the bond before maturity, usually after rates fall. Enable the yield to call option and enter the call price and years to call. Compare it with YTM and assume the lower of the two as a conservative estimate of your return.
