Irish Calculators
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Forward Interest Rate from Spot Rates Calculator

Enter two annual effective spot rates and their maturities to calculate the implied forward rate between them. This is a relationship between supplied rates, not a forecast or a live quote.

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Your numbers

%
Annual effective.
%
Annual effective.
Your figures stay on this device.

How the calculation works

A forward rate is the rate implied for the interval between two maturities when their spot rates describe compatible growth factors. This tool derives that relationship from annual effective inputs, rather than predicting a future market rate.

Forward = exp{[t₂ ln(1+s₂) − t₁ ln(1+s₁)] ÷ (t₂−t₁)} − 1.

  1. Accumulate to each maturity

    Convert each annual effective spot rate into the total growth factor for its own maturity. The time exponent matters when maturities differ.

  2. Isolate the intervening interval

    Divide the longer growth factor by the shorter one. This removes the growth already attributed to the earlier part of the timeline.

  3. Annualise the interval factor

    Raise the remaining factor to the reciprocal of the time between maturities and subtract one. The result is an annual effective forward rate for that interval.

Worked example: Check Annual effective forward rate

Sample inputs demonstrate the method. They are not a forecast or product offer.

The first example supplies 5% spot rates at one and two years. Removing the first year's 1.05 factor from the two-year 1.05-squared factor leaves another 1.05, so the implied annual forward rate is 5%.

Short-maturity spot rate (%)
5
Short maturity (years)
1
Long-maturity spot rate (%)
5
Long maturity (years)
2

Expected result

Annual effective forward rate
5%
Worked example: Check Annual effective forward rate

Sample inputs demonstrate the method. They are not a forecast or product offer.

Short-maturity spot rate (%)
0
Short maturity (years)
1
Long-maturity spot rate (%)
10
Long maturity (years)
2

Expected result

Annual effective forward rate
21%

Understanding your result

A forward rate can differ noticeably from both spot rates because it describes only the additional interval. It is not their arithmetic average or simple percentage-point difference.

The calculation assumes compatible spot-rate inputs. It does not price a particular forward contract, incorporate a bid-offer spread or identify a rate that will actually be available later.

Questions you might have

What does the result include?

Derive the annual effective forward rate between two maturities from compatible annual effective spot rates.

Which limits should I check?

Both spot rates must use annual effective compounding and the same currency and curve.

Choosing the right inputs

Short-maturity spot rate
Use an annual effective spot rate for the shorter maturity. A coupon yield or nominal rate should not be substituted without establishing the correct basis.
Long maturity (years)
The longer maturity must exceed the shorter one. Both durations are measured from the same starting point.
Long-maturity spot rate
Use a spot rate from the same currency and curve as the shorter input; otherwise the two growth factors do not form one comparable term structure.

Common mistakes to avoid

  • Do not enter a market risk premium instead of a spot rate.
  • Do not mix a monthly maturity with a field measured in years.

Assumptions to check

  • Both spot rates must use annual effective compounding and the same currency and curve.
  • All calculations run on your device. Figures are scenarios based on your inputs, not investment recommendations.

Sources and method

Read our calculation and testing approach.