Bond Price Calculator: equations, variables, units and worked solution

The bond price calculator calculates Clean price, Dirty price, Accrued interest, Macaulay duration, Modified duration, Current yield, Coupon per period from Face value, Annual coupon rate, Yield to maturity, Years remaining, Fraction of coupon period accrued, Redemption value. It does not hide the arithmetic: the result panel shows the governing formula, canonical-unit conversion, numeric substitution, unrounded evaluation and final rounded answer for every output.

Variables and measurement units

For the Bond Price Calculator, Face value, Annual coupon rate, and Yield to maturity are normalized to USD, %, and % before dirtyPrice-accruedInterest is evaluated. The unrounded value used for dirtyPrice-accruedInterest and Clean price is retained internally; formatting is applied only to the result cards.

Formula model

Bond value is the present value of remaining coupon cash flows plus redemption value, discounted at yield per coupon period; clean price subtracts accrued interest.

Formula-based worked derivation

1. Clean price
   1. Formula: Clean price = dirtyPrice-accruedInterest
   2. Default substitution: Clean price = dirtyPrice-accruedInterest
   3. Unrounded evaluation: 1039.46005349 USD
   4. Displayed answer: 1039.46 USD
2. Dirty price
   1. Formula: Dirty price = sum(cashFlow ÷ (1+yieldPerPeriod)^time)
   2. Default substitution: Dirty price = sum(cashFlow ÷ (1+yieldPerPeriod)^time)
   3. Unrounded evaluation: 1045.71005349 USD
   4. Displayed answer: 1045.71 USD
3. Accrued interest
   1. Formula: Accrued interest = couponPerPeriod × settlementFraction
   2. Default substitution: Accrued interest = couponPerPeriod × (0.25)
   3. Unrounded evaluation: 6.25 USD
   4. Displayed answer: 6.25 USD
4. Macaulay duration
   1. Formula: Macaulay duration = sum(timeYears × presentValue) ÷ dirtyPrice
   2. Default substitution: Macaulay duration = sum(timeYears × presentValue) ÷ dirtyPrice
   3. Unrounded evaluation: 7.91056363086 years
   4. Displayed answer: 7.9106 years
5. Modified duration
   1. Formula: Modified duration = macaulayDuration ÷ (1+yieldPerPeriod)
   2. Default substitution: Modified duration = macaulayDuration ÷ (1+yieldPerPeriod)
   3. Unrounded evaluation: 7.73649254852 years
   4. Displayed answer: 7.7365 years
6. Current yield
   1. Formula: Current yield = annualCoupon ÷ cleanPrice × 100
   2. Default substitution: Current yield = annualCoupon ÷ cleanPrice × 100
   3. Unrounded evaluation: 4.81018965876 %
   4. Displayed answer: 4.8102 %
7. Coupon per period
   1. Formula: Coupon per period = faceValue × couponRate ÷ couponFrequency
   2. Default substitution: Coupon per period = (1000) × (5) ÷ couponFrequency
   3. Unrounded evaluation: 25 USD
   4. Displayed answer: 25 USD

In the Bond Price Calculator, changing Face value, Annual coupon rate, and Yield to maturity rebuilds the numeric substitution for dirtyPrice-accruedInterest. The engine converts selected measurements to USD, %, and %, retains unrounded values, and, when reverse solving is available, inserts the solved variable back into the same equation to verify dirtyPrice-accruedInterest and Clean price with a numerical residual.

Input and output interpretation

Use measured or documented values for Face value, Annual coupon rate, Yield to maturity, Years remaining, Fraction of coupon period accrued, Redemption value. The calculated outputs are Clean price, Dirty price, Accrued interest, Macaulay duration, Modified duration, Current yield, Coupon per period. Check each intermediate line before relying on the final value; an implausible intermediate quantity usually identifies a unit, range or assumption error.

Algorithm and verification

The Bond Price Calculator uses its own `bond-price` JavaScript engine to calculate dirtyPrice-accruedInterest and Clean price from Face value, Annual coupon rate, and Yield to maturity with dirtyPrice-accruedInterest. Calculator-owned boundary and mode tests check that workflow; an external frozen-reference oracle checks the numeric outputs, and physical source mutation testing confirms that a changed `bond-price` engine is rejected.

Visual interpretation

In the Bond Price Calculator, this guidance applies to Face value, Annual coupon rate, and Yield to maturity and the reported dirtyPrice-accruedInterest and Clean price. The `bond-price` workflow evaluates dirtyPrice-accruedInterest in USD, %, and %; Market conventions, day-count bases, call features, taxes, credit risk and settlement rules can change quoted prices. Confirm the security prospectus and broker convention.. Verification context: d6a49a.

Dimensional formula audit

The bond price calculator normalizes faceValue (Face value, USD), couponRate (Annual coupon rate, %), yieldRate (Yield to maturity, %), years (Years remaining, years), settlementFraction (Fraction of coupon period accrued, ratio), redemptionValue (Redemption value, USD) before evaluating the equations. Its reported quantities are Clean price in USD, Dirty price in USD, Accrued interest in USD, Macaulay duration in years, Modified duration in years, Current yield in %, Coupon per period in USD. This separation matters because a numerical value without its measurement dimension can produce a plausible-looking but physically or financially incorrect answer. Conversion factors are applied before substitution, and output conversion occurs only after the canonical result has been calculated at full precision.

• Clean price = dirtyPrice-accruedInterest
• Dirty price = sum(cashFlow ÷ (1+yieldPerPeriod)^time)
• Accrued interest = couponPerPeriod × settlementFraction
• Macaulay duration = sum(timeYears × presentValue) ÷ dirtyPrice
• Modified duration = macaulayDuration ÷ (1+yieldPerPeriod)
• Current yield = annualCoupon ÷ cleanPrice × 100
• Coupon per period = faceValue × couponRate ÷ couponFrequency

Formula sensitivity and boundary verification

To verify the bond price calculator, hold all other inputs fixed and change faceValue within its permitted range. The live substitution line shows exactly where that value enters the equation for Clean price. Repeat the check with couponRate. The result must follow the displayed algebra, remain finite, and retain the stated output unit. At minimum and maximum boundaries, the validator rejects undefined domains, impossible denominators and nonphysical values rather than silently returning a number.

Manual reproduction of the result

For an independent hand check, first convert every selected unit to the canonical units shown in the variable table. Next copy the governing equation, replace each symbol with the canonical value shown in the live derivation, and calculate the intermediate expression without early rounding. Finally round only once to the displayed precision and compare both the numerical value and unit with the calculator card. This process makes the bond price calculator reproducible instead of relying on an unexplained result.

Limitations

Market conventions, day-count bases, call features, taxes, credit risk and settlement rules can change quoted prices. Confirm the security prospectus and broker convention.