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Bond Yield to Maturity (YTM) Calculator

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Understanding the bond yield to maturity — concept and principle

Yield to maturity (YTM) is the total annual return you would earn by buying a bond at today's price and holding it until it matures, assuming every coupon is paid on time and reinvested at the same yield. It lets you compare bonds with different prices, coupons and maturities on one scale. This calculator solves for the exact YTM, the current yield and a quick textbook approximation.

Bond yield to maturityPay $950 for a $1,000 bond with a 5% coupon paid twice a year for 6 years: twelve $25 coupons plus $1,000 at maturity. Coupon rate 5%, current yield 50 ÷ 950 = 5.263%, yield to maturity 6.005%.Yield if you hold it to maturityBOND · face $1,000 · 5% coupon · 6 yra $25 coupon every 6 months (12 in all)$25$25$25$25$25$25$25$25$25$25$25$25pay $950now+$50get $1,000at year 6coupon rate5.00%$50 ÷ $1,000current yield5.263%$50 ÷ $950YTM6.005%coupons + $50Buying below face adds the $50 gain to the yield
Coupons plus the $50 pull to face value give a 6.005% yield to maturity.

How it is calculated

With price P, face value F, annual coupon rate c, f coupons a year and N = years × f periods, the coupon per period is C = F × c ÷ f. YTM is the rate y that solves:

There is no closed form, so the calculator searches for the per-period rate by bisection and multiplies it by f.

The principle

YTM is the internal rate of return of the bond. If you pay less than face value, you earn the coupons plus a gain as the price rises to face value at maturity, so YTM is above the coupon rate. Pay more, and the premium is lost by maturity, so YTM is below the coupon rate. The approximation spreads that gain or loss evenly over the years and divides by the average of price and face value.

Worked example

  1. Price $950, face $1,000, coupon 5% paid twice a year, 6 years, so N = 12 and C = 1,000 × 0.05 ÷ 2 = $25.
  2. Solve 950 = Σ 25 ÷ (1 + i)ᵏ + 1,000 ÷ (1 + i)¹²: the per-period rate is i ≈ 3.0024%.
  3. YTM = 2 × 3.0024% ≈ 6.005%.
  4. Current yield = 50 ÷ 950 ≈ 5.263%.
  5. Approximation = (50 + 50 ÷ 6) ÷ 975 ≈ 5.983%, shown rounded as 5.98%.

How to read the result

Here YTM (6.005%) > current yield (5.263%) > coupon (5%), the normal order for a discount bond. The YTM is quoted in the bond-equivalent way, as twice the half-year rate; compounded, it equals about 6.095% a year. Compare YTMs only between bonds of similar credit quality, because a higher yield usually means higher default risk or longer maturity.

Common mistakes

Keep in mind: YTM assumes all payments are made and coupons are reinvested at the same yield. Default, early call or a sale before maturity changes your actual return. This is an estimate, not financial advice.

Frequently asked questions

What does it mean when the price is below face value?

The bond trades at a discount, and its YTM is higher than its coupon rate.

Is YTM the same as the coupon rate?

Only when the bond is priced exactly at face value.

Why does the approximation differ from the exact figure?

It ignores compounding and the timing of payments, so it is usually within a few hundredths of a point for bonds near par.

Sources: Fabozzi, F. J. Bond Markets, Analysis, and Strategies · CFA Institute, Fixed Income curriculum (yield measures)

Checked 8 Nov 2026. Standard financial mathematics (time value of money). Estimates for information only — not financial advice.

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