Yield to Maturity (Approx)
Estimate a bond's yield to maturity from its price, face value, coupon and years left using the textbook approximation, with a worked discount-bond example.
Results · USD
Approx YTM
- Annual coupon $
- $50.00
- Discount / premium
- $50.00
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Educational estimates · not financial advice · free, no signup
How this was calculated
YTM ≈ [C + (F−P)/n] / [(F+P)/2], where C is annual coupon.
Want more detail? Full formula notes & FAQs ↓
Detailed guide
What it is, how to use it, how to read the numbers, common mistakes, a worked example, formulas, and FAQs.
What this calculator is
Yield to maturity is the annualised return you earn if you buy a bond at today's price and hold it until it matures, collecting every coupon. When a bond sells below face value, you also gain the difference at maturity, so the YTM is higher than the coupon rate; when it sells above, the YTM is lower. The exact YTM requires solving an equation, but a well-known approximation spreads the discount or premium evenly across the remaining years and divides by the average of price and face value. The result is good for quick comparisons with moderate maturities, but it gets less accurate for long maturities or large discounts. It also assumes you reinvest coupons at the same yield and the issuer does not default.
When to use / who it helps
- You want a quick yield for a bond you are considering.
- You are comparing bonds at different prices.
- You are checking a textbook problem.
- You want to see how price changes affect return.
- You do not have a financial calculator for the exact YTM.
How to use
Steps
- Enter the current price.
- Enter the face or par value.
- Enter the annual coupon rate.
- Enter the years to maturity.
- Read the approximate YTM and the annual coupon.
- Use a financial calculator for an exact value if precision matters.
How to interpret results
- YTM above the coupon rate means the bond trades at a discount.
- YTM below the coupon rate means it trades at a premium.
- The approximation understates or overstates the exact value slightly.
- It ignores default risk and reinvestment risk.
- Callable bonds may have a different yield to call.
Common mistakes & gotchas
- Entering the coupon rate as a dollar amount.
- Using years to call instead of years to maturity.
- Ignoring taxes and fees.
- Comparing yields of bonds with different credit quality.
- Treating the approximation as exact.
Worked example
Worked example — $950 price, $1,000 face, 5% coupon, 10 years
- Annual coupon: 5% × 1,000 = $50.
- Discount accretion per year: (1,000 − 950) ÷ 10 = $5.
- Numerator: 50 + 5 = 55. Denominator: (1,000 + 950) ÷ 2 = 975.
- YTM ≈ 55 ÷ 975 = 5.64%. For a $1,050 price the figure would be (50 − 5) ÷ 1,025 = 4.39%.
Result: The approximate yield to maturity is about 5.64%.
To load the form's own demo values, tap Try example above the Calculate button.
How to calculate / formula
YTM ≈ [C + (F−P)/n] / [(F+P)/2], where C is annual coupon.
Frequently asked questions
What is yield to maturity?
The annualised return from holding a bond to maturity at today's price.
Why is YTM higher than the coupon for a discount bond?
You also gain the difference between price and face value.
Is the approximation accurate?
It is reasonable for moderate cases but not exact.
Does YTM include default risk?
No. It assumes all payments are made.
What about callable bonds?
Calculate yield to call as well.
How is this different from current yield?
Current yield ignores the gain or loss at maturity.