How this instrument works
Yield to maturity approximates the annualized return a bond delivers if held until it repays its face value, with every coupon reinvested at that same rate. Solving for the exact figure means iterating a bond-pricing equation until a discount rate makes the present value of every future coupon and the face repayment equal today's price — arithmetic no one does by hand. This instrument uses the standard shortcut instead: a blended annual return, built from the coupon plus the discount or premium spread evenly over the years left, divided by the average of face value and purchase price.
The people who reach for this formula are usually retail investors scanning a bond screener or building a ladder across several maturities, not a corporate treasurer pricing a new issue. They want a fast way to rank several secondary-market bonds against each other without opening a financial calculator. Because the approximation trades precision for speed, treat it as a screening tool rather than a pricing tool — the exact yield-to-maturity solver built into any brokerage platform should confirm any figure that drives a real purchase.
The formula's shape explains its own limits. Spreading the gap between price and face evenly across the remaining years, rather than compounding it, is what makes the arithmetic solvable without algebra — and it is also where the estimate drifts. The farther a bond trades from par, or the longer it has left to run, the more this approximation and the true, compounded yield diverge. The most common misreading is treating this output as the coupon rate printed on the bond; the two only match at the instant a bond trades exactly at face value.
- Enter the Annual coupon payment, $ — the fixed dollar amount the bond pays each year, not the coupon rate as a percentage.
- Enter the Face value, $ — the amount the issuer repays at maturity, typically $1,000 for a corporate or Treasury bond.
- Enter the Current price, $ — what you would pay to buy the bond today on the secondary market, above or below face value.
- Set Years to maturity — how many years remain until the bond repays its face value.
- Read Approximate yield to maturity, % — the annualized return those four figures imply.
Worked example — a $950 bond with a $50 coupon
Take a bond with a $1,000 face value and a $50 annual coupon (a 5% coupon rate), priced at $950 today with 10 years left to maturity. The discount to face is $50, and spreading that over 10 years adds $5 a year to the coupon, for a blended annual return of $55. Dividing by the average of face and price — ($1,000 + $950) / 2 = $975 — and multiplying by 100 gives 55 / 975 × 100 = 5.641%, the exact figure this instrument returns for that sheet.
That 5.641% sits above the 5% coupon rate because the bond is priced below face value: buying at a discount adds a capital-gain component on top of the coupon income, since the issuer still repays the full $1,000 at maturity regardless of the $950 paid today. Price the same bond at a $1,050 premium instead, and the approximate yield falls to about 4.44%, below the coupon — the discount or premium term is doing real work in the arithmetic, not just adjusting a rounding error.
Questions
Why isn't this the same number my brokerage shows as yield to maturity?
This formula is a widely used approximation, not the exact solution. True yield to maturity is the discount rate that makes a bond's future coupons and face repayment, present-valued, equal today's price — found by iterating, which is what brokerage platforms do internally. This shortcut spreads the price gap evenly across the years instead of compounding it, so the two figures sit close for bonds near par and drift apart for bonds priced far from face value or with many years left.
Why is my yield higher than the coupon rate?
Because the bond is priced below its face value. A discount bond returns more than its coupon alone suggests: you collect the coupon every year and also collect the gap between the discounted price you paid and the full face value repaid at maturity. That capital-gain piece is the (F − P) ⁄ n term in the formula, added to the coupon before the total is divided by the average price.
What is the difference between this and current yield?
Current yield is just the annual coupon divided by today's price — it ignores whether the bond sits above or below face value. Yield to maturity folds that gap in and amortizes it over the years remaining, which is why the two only match exactly when a bond trades at par. Current yield understates return on a discount bond and overstates it on a premium bond.
Does this account for reinvesting the coupons?
No. Both this approximation and the exact yield-to-maturity calculation assume every coupon gets reinvested at the same rate as the bond itself, which is rarely how a real account behaves. If coupons sit in cash or go into a lower-yielding fund instead, the return actually realized falls below the figure this instrument reports — a gap bond researchers call reinvestment risk.
Can I use this for a bond that has already been called?
Only if you replace Years to maturity with years to the actual payoff date. A called bond stops paying coupons and returns face value early, so entering the original maturity date overstates how long the discount or premium has left to amortize and skews the yield upward or downward. For a bond callable well before maturity, its yield to call is a separate figure worth checking.
Why does the same price change move yield more for a short bond than a long one?
Because the price gap is divided by years to maturity before it is added to the coupon. For a bond with 2 years left, a $50 discount adds $25 a year to the blended return; for a bond with 20 years left, the same $50 discount adds only $2.50 a year. Short-dated bonds are more sensitive to price in this formula, which mirrors how they behave in practice — any mispricing resolves faster because maturity arrives sooner.
References
- SEC Investor.gov — Bonds or fixed income products
- Federal Reserve — Selected interest rates (H.15 release)
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.