How to Calculate Yield to Maturity (Approximation and Example)
Short answer. Yield to maturity (YTM) is the single annual return that makes a bond’s cash flows worth today’s price. A quick estimate is (annual coupon + (face value - price) / years) / ((face value + price) / 2). The exact value needs trial and error or a financial calculator.
The formula
YTM ~ (C + (F - P) / n) / ((F + P) / 2)
Step by step
- Collect the bond data. Annual coupon C, face value F, current price P, years to maturity n.
- Spread the gain or loss. (F - P) / n is the yearly pull to par.
- Add the coupon. C + (F - P) / n is the approximate annual income.
- Divide by the average price. Divide by (F + P) / 2 to get the approximate YTM.
- Refine if needed. Exact YTM solves price = sum of discounted cash flows; use a spreadsheet RATE function or calculator.
Worked example
A 5-year bond, $1,000 face, 6% coupon, priced at $950
- C = $60, F - P = 50, so 50 / 5 = $10 per year.
- Approximate YTM = (60 + 10) / ((1,000 + 950) / 2) = 70 / 975 = 7.18%.
- The exact YTM is about 7.2%, close to the estimate.
Common mistakes
- Confusing YTM with current yield (coupon / price).
- Assuming coupons are reinvested at the YTM, which rarely happens.
- Using the formula for bonds that can be called early.
Frequently asked questions
Why is YTM above the coupon rate here?
The bond trades at a discount, so the buyer also earns the gain back to face value.
Is YTM the same as the coupon rate?
Only when the bond is priced at par.
How is YTM different from current yield?
Current yield ignores the gain or loss toward par at maturity.
General education, not personal financial advice. Example figures are illustrative.