# Yield to Maturity

> Yield to maturity is the total return of a bond held to maturity. Learn how YTM is calculated, current yield, yield to call and worst, and YTM's assumptions.

Source: https://learn.tradelabsai.com/bonds-credit/yield-to-maturity/  
Track: Bonds, Rates and Credit · Level: Intermediate · Updated: 2026-10-03  
Publisher: TradeLabs AI (https://tradelabsai.com). Education, not financial advice.  
Cite as: TradeLabs Learn, "Yield to Maturity", https://learn.tradelabsai.com/bonds-credit/yield-to-maturity/

Yield to maturity (YTM) is the single most common way to measure a bond's return. It is the annual rate of return an investor would earn by buying a bond at today's price and holding it to maturity, assuming every coupon is paid on time and reinvested at the same rate. YTM lets investors compare bonds with different prices, coupons and maturities on one scale. It is also the discount rate that makes the present value of a bond's cash flows equal to its price.

## The definition

YTM is the rate y that solves:

```
price = Σ (coupon / (1 + y/f)^t) + face / (1 + y/f)^n
```

where f is the number of coupon payments per year and n is the total number of payments. There is no simple closed form; YTM is found by trial and error or with a calculator. See [Time Value of Money](https://learn.tradelabsai.com/math/time-value-of-money/) and the [Bond Price, Duration and DV01 Calculator](https://learn.tradelabsai.com/tools/bond-calculator/).

## Worked example

**Example: Finding a bond's YTM**
A bond has a face value of $1,000, a 5% annual coupon paid twice a year ($25 every six months) and 6 years to maturity. It trades at $950.

- At a yield of 6%, the present value of the cash flows is about $950.2.
- So the YTM is about 6.0%.

The investor earns $50 a year in coupons plus a $50 gain at maturity as the price rises from $950 to par, which together produce a 6% annual return if coupons are reinvested at 6%.

## A quick approximation

```
approximate YTM ≈ [annual coupon + (face - price) / years] / [(face + price) / 2]
```

For the example: [50 + (1,000 minus 950) / 6] / [(1,000 + 950) / 2] = (50 + 8.33) / 975 ≈ 5.98%. Close to the exact answer.

## Related yield measures

| Measure | Formula or meaning | When used |
|---|---|---|
| Coupon rate | Annual coupon / face value | Fixed at issue |
| Current yield | Annual coupon / price | Quick income measure; ignores gains or losses at maturity |
| Yield to maturity | Total return if held to maturity | Standard comparison |
| Yield to call | Return if the bond is called at the first call date | Callable bonds |
| Yield to worst | The lowest of YTM and all yields to call | Conservative measure for callable bonds |

In the example, the current yield is 50 / 950 ≈ 5.26%, below the YTM because it ignores the $50 gain at maturity.

## Premium, par and discount bonds

| Price | Relationship |
|---|---|
| Below par (discount) | YTM > current yield > coupon rate |
| At par | YTM = current yield = coupon rate |
| Above par (premium) | YTM < current yield < coupon rate |

## Assumptions and limitations

- **Held to maturity:** if sold earlier, the return depends on the price at sale.
- **Coupons reinvested at the YTM:** if rates change, actual returns differ. This is reinvestment risk.
- **No default:** for risky bonds, YTM is a promised yield, not an expected one. See [Default Probability and Recovery Rate](https://learn.tradelabsai.com/bonds-credit/default-probability/).
- **Flat discount rate:** YTM uses one rate for all cash flows, while the yield curve has different rates for different maturities. See [Yield Curves](https://learn.tradelabsai.com/bonds-credit/yield-curves/).
- **Taxes and costs are ignored.**

## YTM and price sensitivity

Small changes in YTM move prices. The size of the move depends on the bond's duration. A bond with a duration of 7 loses about 7% of its value for a 1 percentage point rise in yield. See [Duration](https://learn.tradelabsai.com/bonds-credit/duration/).

## Conventions

US Treasuries and many corporate bonds quote YTM on a semiannual "bond equivalent" basis. Some markets use annual compounding. Comparing yields across markets requires the same convention.

## Frequently asked questions

### What is yield to maturity?

The annual return an investor would earn by buying a bond at its current price and holding it to maturity, assuming all payments are made and reinvested at the same rate.

### What is the difference between current yield and yield to maturity?

Current yield is only the annual coupon divided by the price; yield to maturity also includes the gain or loss as the price moves to par at maturity.

### What is yield to worst?

The lowest yield an investor could receive on a callable bond, considering all possible call dates and maturity.

Next, learn how bond prices respond to yield changes in [Duration](https://learn.tradelabsai.com/bonds-credit/duration/).

## Continue learning

- Next lesson: [Duration](https://learn.tradelabsai.com/bonds-credit/duration/)
- Previous lesson: [Credit Ratings](https://learn.tradelabsai.com/bonds-credit/credit-ratings/)
- Related: [Credit Ratings](https://learn.tradelabsai.com/bonds-credit/credit-ratings/): Credit ratings from S&P, Moody's and Fitch grade the risk of default on bonds. Learn the scales, investment grade vs high yield, default rates by rating and limits.
- Related: [How Bonds Work](https://learn.tradelabsai.com/bonds-credit/how-bonds-work/): A bond is a loan that pays interest and returns principal at maturity. Learn coupons, price and yield, why prices fall when rates rise and the main bond risks.
- Related: [Duration](https://learn.tradelabsai.com/bonds-credit/duration/): Duration measures how sensitive a bond's price is to interest rate changes. Learn Macaulay, modified and effective duration, how to calculate them and their uses.
- Related: [Bond Price, Duration and DV01 Calculator](https://learn.tradelabsai.com/tools/bond-calculator/): Free bond calculator. Enter face value, coupon, yield to maturity, years and payment frequency to get the bond price, current yield, duration and DV01.
- Related: [Time Value of Money](https://learn.tradelabsai.com/math/time-value-of-money/): A dollar today is worth more than a dollar tomorrow. Learn present and future value, discounting, annuities and NPV, the maths behind bonds, valuations and options.
- Related: [Yield Curves](https://learn.tradelabsai.com/bonds-credit/yield-curves/): The yield curve plots bond yields across maturities. Learn normal, flat and inverted curves, what drives them and why inversions have signalled recessions.