Yield to Maturity Calculator

Yield to Maturity (YTM) Formula

Yield to Maturity is the total annualized return you will earn by holding a bond from today until it matures - assuming all coupon payments are reinvested at the same rate.

This page works in annual coupons, compounded annually. That is the convention textbooks and exams use, and it is the one the shortcut formula below is built for. It is not how the US bond market quotes: Treasuries and corporates pay twice a year and are quoted on a semi-annual bond-equivalent basis, which comes out a few basis points lower on the same bond. On a $950 bond with a $50 annual coupon over ten years, this page returns 5.6687% and the semi-annual convention returns 5.662%.
If you want the market convention, or a payment frequency other than annual, use the bond yield to maturity calculator, which takes frequency as an input. Neither figure is wrong. They answer the same question in two different quoting bases, and the difference is worth knowing about before you compare a calculator against a broker screen.

Approximation Formula

The exact yield can only be found by iteration, so most textbooks teach this shortcut instead:

YTM ≈ (Annual Coupon + (Face Value − Price) ÷ Years) ÷ ((Face Value + Price) ÷ 2)

Where:

• Annual Coupon = the fixed interest payment received each year
• Face Value = the amount paid back at maturity (typically $1,000)
• Price = current market price of the bond
• Years = years remaining to maturity

This calculator shows both figures. On the worked example below the approximation comes out at 8.72% and the exact yield at 8.7713%, a gap of about five hundredths of a point. That is close enough for a mental check and not close enough for a trade ticket. The shortcut reads low on discount bonds, high on premium ones, and drifts further the longer the term.

Three Yield Metrics Compared

Coupon Rate = Annual Coupon ÷ Face Value × 100 This is the rate printed on the bond certificate. It never changes.

Current Yield = Annual Coupon ÷ Current Price × 100 This reflects the income return at today’s price. It changes daily as price changes.

Yield to Maturity (YTM) = Includes coupon income + capital gain or loss at maturity. This is the most complete return measure - what you actually earn if you hold to maturity.

The Premium vs Discount Bond Rules

These rules always hold - they are mathematical certainties:

Why? If you buy at a discount ($950 for a $1,000 bond), you receive the coupon PLUS a $50 capital gain at maturity. That gain boosts total return above the coupon rate.

Bond Price Sensitivity to Interest Rates

When interest rates rise, bond prices fall (and vice versa). The relationship is inverse and non-linear:

• Longer maturity bonds fall more than short maturity bonds for the same rate move.
• Lower coupon bonds fall more than high coupon bonds.
• This sensitivity is measured by Duration: a separate metric.

Worked Example

A bond with:

• Market Price: $950
• Face Value: $1,000
• Annual Coupon: $80
• Years to Maturity: 10

Step 1: Current Yield:

Current Yield = $80 ÷ $950 = 8.42%

Step 2: YTM Approximation:

YTM ≈ ($80 + ($1,000 − $950) ÷ 10) ÷ (($1,000 + $950) ÷ 2) YTM ≈ ($80 + $5) ÷ $975 YTM ≈ $85 ÷ $975 = 8.72%

Interpretation: The coupon rate is 8% ($80 ÷ $1,000). Since the bond trades at a discount ($950 < $1,000), YTM (8.72%) > Coupon Rate (8%) - exactly as the rule predicts.

Rate Comparison for This Bond

Pro Tips

• YTM assumes you reinvest all coupons at the same YTM rate: unrealistic in practice. The realized compound yield will differ if rates change.
• When comparing bonds, always compare YTM: not coupon rate or current yield alone.
• U.S. Treasury YTM rates form the risk-free rate used in all other financial valuations.
• A bond’s YTM falling means its price is rising: often a sign the market expects interest rate cuts.