Bond Yield to Maturity Calculator Formula

Understand the math behind the bond yield to maturity calculator. Each variable explained with a worked example.

Use the Bond Yield to Maturity Calculator

Formulas Used

Approximate YTM

approx_ytm = current_price > 0 ? ((coupon_payment + (face_value - current_price) / years_to_maturity) / ((face_value + current_price) / 2)) * 100 : 0

Annual Coupon Payment

annual_coupon = coupon_payment

Current Yield

current_yield = current_price > 0 ? coupon_payment / current_price * 100 : 0

Total Coupon Income

total_income = coupon_payment * years_to_maturity

Variables

VariableDescriptionDefault
face_valueFace (Par) Value(USD)1000
current_priceCurrent Market Price(USD)950
coupon_rateAnnual Coupon Rate(%)5
years_to_maturityYears to Maturity(years)10
coupon_paymentDerived value= face_value * coupon_rate / 100calculated

How It Works

Bond Yield to Maturity

YTM is the total return expected on a bond held to maturity, accounting for coupon payments and any price discount or premium.

Approximate YTM Formula

YTM = [C + (F - P) / n] / [(F + P) / 2]

Where:

  • C = Annual coupon payment
  • F = Face value
  • P = Current market price
  • n = Years to maturity

    • Premium vs Discount

  • Discount bond (price < par): YTM > coupon rate
  • Par bond (price = par): YTM = coupon rate
  • Premium bond (price > par): YTM < coupon rate

    • Worked Example

    $1,000 face value bond, $950 current price, 5% coupon, 10 years to maturity.

    face_value = 1000current_price = 950coupon_rate = 5years_to_maturity = 10
    1. 01Annual coupon = $1,000 x 5% = $50
    2. 02Price gain = ($1,000 - $950) / 10 = $5/year
    3. 03Average price = ($1,000 + $950) / 2 = $975
    4. 04Approx YTM = ($50 + $5) / $975 = 5.64%

    Frequently Asked Questions

    What is yield to maturity?

    YTM is the total annualized return you would earn if you buy the bond at its current price and hold it until maturity, reinvesting all coupon payments at the same rate. It is the most comprehensive bond yield measure.

    Why is approximate YTM used?

    The exact YTM requires solving a complex polynomial equation iteratively. The approximation formula gives results within 0.1-0.3% of the exact value and is much simpler to calculate.

    How does YTM differ from current yield?

    Current yield = annual coupon / current price. It ignores the gain or loss at maturity. YTM includes both the coupon income AND the price change, giving a more complete picture.

    Ready to run the numbers?

    Open Bond Yield to Maturity Calculator