Bootstrapped Zero Rate Calculator

Work out bootstrapped zero rate instantly with clear inputs, formula shown and shareable results.

About Bootstrapped Zero Rate Calculator

Bootstrapping builds a zero-coupon curve one maturity at a time. Discount the known earlier coupons at rates already solved, and whatever price remains must be explained by the final cash flow — which pins down the next zero rate.

Formula

Bootstrap step

P = C/(1+z₁) + (100+C)/(1+z₂)² → solve z₂

P: Bond price
C: Coupon
z1: 1-year zero
z2: 2-year zero

Worked example

With the default values below, Bootstrapped Zero Rate Calculator returns Bootstrapped 2-Year Zero Rate of 5.0252%. Change any input above and every figure here is recalculated in your browser.

Inputs used

Known 1-Year Zero Rateaccepts 0–100 %: 4 %
2-Year Bond Coupon Rateaccepts 0–100 %: 5 %
2-Year Bond Price Per 100minimum 0: 100

Results

Bootstrapped 2-Year Zero Rate: 5.0252%
Present Value Of First Coupon: $4.8077
2-Year Discount Factor: 0.906593
Implied 1-Year Rate One Year Out: 6.0606%

Step by step

1Values used
2Bootstrap step
3Bootstrapped 2-Year Zero Rate= 5.0252
4Present Value Of First Coupon= 4.8077
52-Year Discount Factor= 0.906593
6Implied 1-Year Rate One Year Out= 6.0606

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why not use the bond's yield to maturity?

YTM assumes every cash flow is discounted at one rate. Zero rates discount each date properly and are what pricing models need.

What if the bond trades at par?

Then the par yield and the coupon coincide, and the 2-year zero sits slightly above the coupon on an upward-sloping curve.