What does an implied forward rate tell you?

It tells you the break-even interest rate for a future period implied by today's yield curve. If the 1-year spot rate is 4% and the 2-year spot rate is 5%, the market implies a one-year rate one year from now of approximately 6%.

How do forward rates relate to expectations of future interest rates?

Under the pure expectations hypothesis, forward rates equal the market's expectation of future spot rates. In practice, forward rates also embed a liquidity premium, so they tend to be slightly above expected future rates.

What is the difference between a forward rate and a futures rate?

Both estimate future interest rates, but a futures rate is standardized, exchange-traded, and marked to market daily. A forward rate is from OTC instruments or bootstrapped from the yield curve, and has no daily settlement.

Forward Interest Rate Calculator (from Spot Rates)

Calculate the implied forward interest rate between two future periods using today's spot (zero-coupon) rates. Uses the no-arbitrage bootstrap method from the yield curve.

By AbraCalc Editorial Team · Reviewed by AbraCalc Methodology Review · Last reviewed: 2026-06-25

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How to use this tool

Enter spot rate for period 1 (s₁), length of period 1 (t₁), spot rate for period 2 (s₂) and length of period 2 (t₂) in the fields above.
Results update instantly as you type — or click Calculate.
Read your implied forward rate f(t₁,t₂) and the full breakdown beneath it.

⚠ This tool provides general estimates for education only and is not financial, tax or legal advice. Figures may not reflect your situation — verify with a qualified professional.

Formula

The implied forward rate f(T₁, T₂) satisfies the no-arbitrage condition:

(1 + s₂)^T₂ = (1 + s₁)^T₁ × (1 + f)^T₂−T₁

Solving for f: f = [(1 + s₂)^T₂ / (1 + s₁)^T₁]^{1/(T₂−T₁)} − 1

How it works

The implied forward rate is the future interest rate consistent with today's yield curve such that investing for T₁ years at s₁ and then reinvesting for the remaining (T₂ − T₁) years at the forward rate yields the same terminal value as investing at s₂ for T₂ years from the start.

This no-arbitrage relationship assumes annual compounding and is widely used in fixed-income analysis, swap pricing, and yield curve construction (bootstrapping). It does not predict where rates will actually go — it merely states the rate embedded in current market prices.

Worked example

1-year spot = 4%, 2-year spot = 5% — find the 1-year forward rate one year from now

s₁ = 4% = 0.04, T₁ = 1 year; s₂ = 5% = 0.05, T₂ = 2 years
Growth factor ratio: (1.05)² / (1.04)¹ = 1.1025 / 1.04 = 1.060096...
Forward period = 2 − 1 = 1 year, so f = 1.060096^(1/1) − 1 = 0.060096
f ≈ 6.0096%

The 1-year forward rate starting one year from now is approximately 6.0096%, meaning the market implies that 1-year rates will be around 6% in one year's time.

Common mistakes to avoid

Confusing the spot rate at time T1 with the forward rate starting at T1 — spot rates are yields from today to T; forward rates are implied yields for a future period from T1 to T2.
Mixing annually compounded and continuously compounded spot rates in the same formula — use consistent compounding conventions throughout; the no-arbitrage formula changes form for continuous compounding.
Rounding intermediate spot rate values before computing the forward rate, which amplifies errors because the formula raises rates to fractional exponents.

Key terms

What is a spot rate?: A spot rate (zero rate) is the yield on a zero-coupon bond maturing at a specific date. It is the current discount rate for a single cash flow at that maturity.
What is a forward rate?: A forward rate is the interest rate implied by today's spot rates for a future lending or borrowing period. It represents the break-even rate between two investment strategies.
Does the forward rate predict future spot rates?: Not necessarily. Under the pure expectations hypothesis it does, but in practice forward rates also include risk premiums (liquidity premium, term premium). Forward rates are market-implied, not forecasts.
What is bootstrapping the yield curve?: Bootstrapping is the process of deriving a zero-coupon (spot rate) yield curve from the prices of coupon-bearing bonds or swap rates, starting from short maturities and working out to longer ones.

Frequently asked questions

What does an implied forward rate tell you?: It tells you the break-even interest rate for a future period implied by today's yield curve. If the 1-year spot rate is 4% and the 2-year spot rate is 5%, the market implies a one-year rate one year from now of approximately 6%.
How do forward rates relate to expectations of future interest rates?: Under the pure expectations hypothesis, forward rates equal the market's expectation of future spot rates. In practice, forward rates also embed a liquidity premium, so they tend to be slightly above expected future rates.
What is the difference between a forward rate and a futures rate?: Both estimate future interest rates, but a futures rate is standardized, exchange-traded, and marked to market daily. A forward rate is from OTC instruments or bootstrapped from the yield curve, and has no daily settlement.