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Spot Rate From Yield Curve Calculator

Work out spot rate from yield curve instantly with clear inputs, formula shown and shareable results.

About Spot Rate From Yield Curve Calculator

Traded points on a yield curve are sparse, so intermediate maturities are read off by interpolation. Linear interpolation between the 2-year and 10-year spot rates gives the zero rate and discount factor for any maturity in between.

Formula

Linear interpolation

z(t) = z₂ + (z₁₀ - z₂) × (t - 2)/8

t
Target maturity
z2
2-year rate
z10
10-year rate

Worked example

With the default values below, Spot Rate From Yield Curve Calculator returns Interpolated Spot Rate of 4.2000%. Change any input above and every figure here is recalculated in your browser.

Inputs used

2-Year Spot Rateaccepts 0–100 %
3.9 %
10-Year Spot Rateaccepts 0–100 %
4.7 %
Target Maturity In Yearsaccepts 2–10
5

Results

Interpolated Spot Rate
4.2000%
Curve Slope
10.00
Discount Factor At That Maturity
0.814069
Present Value Of 100 At Maturity
$81.4069

Step by step

  1. 1Values used
  2. 2Linear interpolation
  3. 3Interpolated Spot Rate= 4.2000
  4. 4Curve Slope= 10.00
  5. 5Discount Factor At That Maturity= 0.814069
  6. 6Present Value Of 100 At Maturity= 81.4069

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

Is linear interpolation good enough?

For pricing and quick valuation, yes. Trading desks prefer cubic-spline or monotone-convex fits that keep forward rates smooth.

Why report the discount factor too?

Because that is what you actually multiply cash flows by — the rate alone still needs converting.

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