Forward Rate Calculator — Implied Forward Interest Rate
Given two spot rates for different maturities, this calculator derives the implied forward interest rate for the period between those maturities — the rate that makes a two-step investment equivalent to a single longer-term investment, ensuring no arbitrage.
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years
%
years
Annual rate implied for the period from year 1 to year 2
- 1
Near-term growth factor
(1 + 3% ÷ 100)^1 = 1.03 - 2
Far-term growth factor
(1 + 4% ÷ 100)^2 = 1.0816 - 3
Growth ratio
1.0816 ÷ 1.03 = 1.050097How much more the far-term investment grows relative to the near-term investment. - 4
Forward period
T₂ − T₁ = 2 − 1 = 1 yr - 5
Implied forward rate
(1.050097^(1 ÷ 1) − 1) × 100 = 5.0097
How does this calculator work?
The implied forward rate between year T₁ and year T₂ is f = [(1+r₂)^T₂ / (1+r₁)^T₁]^(1/(T₂−T₁)) − 1. Enter two spot rates and their maturities; the calculator returns the no-arbitrage forward rate for the intervening period.
Formula
How this is calculated
A forward rate is the interest rate implied by the current yield curve for a future period. The core idea is the no-arbitrage condition: investing for T₂ years at the longer spot rate r₂ must give the same terminal value as first investing for T₁ years at r₁ and then rolling over at the forward rate f for the remaining (T₂ − T₁) years. Setting those two paths equal and solving for f gives the formula above.
For example, if the 1-year spot rate is 3% and the 2-year spot rate is 4%, the implied 1-year forward rate one year from now is [(1.04)² / (1.03)¹]^(1/1) − 1 ≈ 5.01%. This tells you the market expects a 5.01% rate to prevail in year 2, assuming no arbitrage and no risk premium.
Forward rates are central to fixed-income analysis: they appear in yield-curve bootstrapping, FRA (Forward Rate Agreement) pricing, and bond relative-value analysis. This calculator assumes continuously-compounded equivalent rates expressed as annual rates — for money-market conventions (simple interest, 360-day basis) the formula differs slightly. Real markets also embed term premiums and credit risk, so the implied forward rate is a theoretical floor, not a guaranteed future rate.
Frequently asked questions
A spot rate is the current interest rate for a loan or investment starting today. A forward rate is the rate implied by the market for a future period — derived from spot rates so that there is no riskless arbitrage between investing in segments versus investing in one long instrument.
Not exactly. Under the Expectations Hypothesis, forward rates equal expected future spot rates. In practice, forward rates also embed a term (liquidity) premium. They are best interpreted as market-implied break-even rates, not direct forecasts.
You need two annual spot rates (as percentages) and their respective maturities in years. The far maturity T₂ must be strictly greater than the near maturity T₁. Spot rates are typically sourced from zero-coupon government bond yields or an OIS curve stripped of credit risk.
Also known as
TG we-Calculate Editorial Team. (2026). Forward Rate Calculator — Implied Forward Interest Rate [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/forward-rate-calculator
TG we-Calculate Editorial Team. "Forward Rate Calculator — Implied Forward Interest Rate." TG we-Calculate. 2026. https://we-calculate.com/calculator/forward-rate-calculator.
TG we-Calculate Editorial Team, "Forward Rate Calculator — Implied Forward Interest Rate," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/forward-rate-calculator
@misc{wecalculate_forward_rate_calculator, title = {Forward Rate Calculator — Implied Forward Interest Rate}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/forward-rate-calculator}}, year = {2026}, note = {TG we-Calculate} }
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