Bond Duration Calculator
Price a fixed bond and get Macaulay plus modified duration in years.
What it does
Bond prices pivot on timing. Two bonds with the same maturity can react very differently to a rate move when one pays fat coupons early and the other pays nothing until the end. Duration compresses that timing into years: the weighted average moment the cash arrives, and the price sensitivity that follows.
The tool above prices a fixed bond and reports both durations. Enter face, coupon, years, yield, and frequency. It returns price, Macaulay duration, and modified duration. Defaults describe a 5 year 5% semiannual bond at 4%, so the page opens solved at $1,044.91 with 4.50 and 4.41 years.
Read the pair in order. Macaulay 4.50 years says the average dollar arrives well before maturity because coupons pull weight forward. Modified 4.41 years says a 1 point rate rise trims price by about 4.41%. Premium bonds (coupon above yield) price over face and run shorter than their maturity; discount bonds run longer.
The zero coupon case teaches the idea fastest: with no coupons to pull weight forward, Macaulay equals maturity exactly (5.00 years for a 5 year zero). Add coupons and watch duration fall; raise yield and watch it fall again as distant cash discounts harder.
Use the table to feel the pattern across coupons and maturities, then run your bond. The page assumes fixed coupons, no call, and small parallel shifts. Callable, floating, and shaky credit names need option and spread models that duration alone cannot give.
How to use
- Enter face value (often 1000).
- Enter annual coupon percent and years left.
- Enter annual yield percent.
- Pick 1 or 2 payments per year.
- Read price first, then both durations.
- Multiply modified duration by a rate move for a quick price read.
Formula
- Face
- Principal repaid at maturity.
- Coupon
- Annual coupon percent of face.
- Years
- Years to maturity.
- Yield
- Annual yield to maturity in percent.
- Frequency
- Payments per year: 1 or 2.
Cash flows are coupons plus face at maturity, discounted at yield per period. Time weights use years (period / frequency). The page assumes fixed coupons, no call, and a flat yield shift; floating, callable, and credit risky bonds need wider models.
Worked example
Example: 5 year 5% bond at 4% yield
A 5 year bond with face 1000 and 5% coupon pays twice a year. Yield is 4%. Find price and duration.
- Periods = 5 years x 2 = 10. Coupon each = 1000 x 5% / 2 = 25.00.
- Yield each = 4% / 2 = 2%.
- Price = 25 x annuity factor + 1000 / 1.02^10 = $1,044.91.
- Weight each cash flow by time and divide by price: Macaulay = 4.50 years.
- Modified = 4.50 / 1.02 = 4.41 years.
- A 1 point rate rise cuts price by about 4.41%.
Reference table
| Bond | Price | Macaulay | Modified |
|---|---|---|---|
| 5 yr zero | $820.35 | 5.00 years | 4.90 years |
| 5 yr 5% coupon | $1,044.91 | 4.50 years | 4.41 years |
| 10 yr 5% coupon | $1,081.76 | 8.08 years | 7.92 years |
| 10 yr 8% coupon | $1,327.03 | 7.50 years | 7.35 years |
Limits
- Fixed coupons only; no calls or floats.
- Small parallel shifts; large twists differ.
- No credit or liquidity spread modeling.
- Annual compounding convention per period.
Common mistakes
- Reading Macaulay as the price move (use modified).
- Entering yield per period instead of annual.
- Mixing annual coupons with semiannual frequency.
- Pricing a callable bond as option free.
- Extending a 1 point rule to a 3 point shock.
Try it yourself
Quick checks. Answers sit tucked under each question.
10 year 6% semiannual bond at 5% yield?
Price $1,077.95. Macaulay 7.76 years. Modified 7.57 years.
5 year zero coupon bond at 4% yield?
Price $820.35. Macaulay 5.00 years. Modified 4.90 years.
How is the 10 year practice price built?
Periods 20, coupon 30, yield 2.5% per half: price near $1,077.95 and duration near 7.76 years.
Questions
Macaulay versus modified duration?
Macaulay is the cash flow weighted average time to payment, in years. Modified divides it by (1 + yield per period) and measures price sensitivity to rates.
How far does price move when rates shift?
About modified duration in percent. At 4.41 years, a 1 point rise cuts price near 4.41%, and a fall lifts it symmetrically for small moves.
What is the duration of a zero coupon bond?
Yes. A zero coupon bond pays once at maturity, so its Macaulay duration equals its maturity: 5.00 years for the 5 year zero in practice.
Why do coupons and yields shorten duration?
Higher coupons pull cash forward, which shortens duration. Higher yields discount later cash harder, which also shortens it.
Annual or semiannual payments?
Annual uses one period per year; semiannual uses two with half the coupon and half the yield each. The tool handles both; match the bond terms.
What does duration miss?
Duration is a first order guide for small parallel shifts. Large moves, curve twists, calls, and credit events need fuller models.