Forward Rate Calculator
Calculate the implied forward interest rate between two future dates from two spot (zero-coupon) rates, with annual, semi-annual or continuous compounding, and see the shape of the yield curve.
How it works
(1 + r₂/m)^(m·t₂) = (1 + r₁/m)^(m·t₁) × (1 + f/m)^(m·(t₂ − t₁)) ⇒ f = m × [((1 + r₂/m)^(m·t₂) ÷ (1 + r₁/m)^(m·t₁))^(1/(m·(t₂ − t₁))) − 1] · continuous: f = (r₂t₂ − r₁t₁) ÷ (t₂ − t₁)
A forward rate is the interest rate for a future period that is locked in by today’s yield curve. By no-arbitrage, investing for t₂ years at the long spot rate must give the same result as investing for t₁ years at the short spot rate and then rolling over at the forward rate. Forward rates are used to price forward rate agreements, swaps and futures, and are often read as the market’s expectation of future rates (plus a term premium). Use zero-coupon (spot) rates, not par yields, for an exact result.
Worked example
With a 2-year spot rate of 4% and a 3-year spot rate of 4.5% (annual compounding), the growth factors are 1.04² = 1.081600 and 1.045³ = 1.141166. The implied 1-year rate starting in 2 years is 1.141166 ÷ 1.0816 − 1 = 5.507%.
Sources: Wikipedia — Forward rate · Investopedia — Forward Rate
Frequently asked questions
What is the difference between a spot rate and a forward rate?
A spot rate is the yield for borrowing or lending from today to a future date. A forward rate is the yield agreed today for a period that starts in the future.
Why is the forward rate higher than both spot rates here?
When the curve slopes upward the extra yield of the long rate must be earned in the later period alone, so the forward rate sits above the long spot rate. On an inverted curve it sits below.
Does the forward rate predict future interest rates?
Only roughly. Under the expectations hypothesis it would, but in practice forward rates include a term premium, so they tend to overstate future short rates.
Which compounding should I choose?
Match the convention of your spot rates: annual for many zero curves, semi-annual for US Treasury bond-equivalent yields, continuous for derivatives pricing models.
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Educational estimate, not investment, trading or tax advice. Brokers, issuers and data providers use their own conventions, fees and figures — confirm with your broker, the issuer’s documents or a licensed adviser before acting.