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Financial Planning

Bond Price Calculator

Price a bond from its coupon rate, yield to maturity and term, with Macaulay and modified duration.

Your inputs

Results

Bond price

$925.61

Price as % of par
92.561%
Trades at
Discount
Macaulay duration
7.895 years
Modified duration
7.665 years

✓Exact calculation — rounded only for display

Inputs are never added to links for financial, salary or health calculators.

What this calculator does

A bond’s price is the present value of its future coupons and principal at the market yield. Duration measures how sensitive that price is to changes in yield.

Formula and method

Price = Σ C ÷ (1 + y/f)^k + F ÷ (1 + y/f)^n Macaulay duration = Σ (k/f) × PVₖ ÷ Price; Modified duration = Macaulay ÷ (1 + y/f)

Worked example

Calculated by this tool with its default inputs:

Inputs

  • Face (par) value: 1000 (any currency)
  • Annual coupon rate: 5 %
  • Yield to maturity (annual): 6 %
  • Years to maturity: 10
  • Coupon frequency: Semi-annual

Results

  • Bond price: 925.61
  • Price as % of par: 92.561%
  • Trades at: Discount
  • Macaulay duration: 7.895 years
  • Modified duration: 7.665 years

How to read the results

A modified duration of 7.7 means the price falls roughly 7.7 % if yields rise by one percentage point.

Assumptions and limitations

  • Clean price on a coupon date; accrued interest between coupon dates is not calculated.

Financial results are estimates based on the inputs and assumptions shown. They are not financial advice; confirm figures with your lender, provider or a qualified adviser before making decisions.

Questions

Why do prices fall when yields rise?

Existing fixed coupons become less attractive than new bonds paying the higher yield, so the price adjusts down.

Methodology and verification

Result type
Exact mathematical calculation (rounded only for display)
Formula version
1.0
Automated verification
4 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
Editorial review
Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.

Privacy

Everything you enter is calculated in this browser and is not sent to Numerith or anyone else. Because this calculator can involve personal financial or health details, your inputs are never added to share links or saved to history. Privacy policy