Forward Rate Agreement (FRA) Formula: Step-by-Step Payoff Calculation & Hedging Guide (2026)

A Forward Rate Agreement (FRA) is an over-the-counter (OTC) financial derivative contract between two institutions to exchange a fixed interest payment for a floating benchmark interest payment (such as USD SOFR or EURIBOR) on a future settlement date. For commercial borrowers and debt portfolio managers, FRAs are the primary instrument used to hedge against rising interest rates without altering underlying bank loan agreements.

Unlike standard interest rate swaps that involve multiple periodic cash flows over several years, an FRA covers a single future interest rate period and settles in cash on the first day the borrowing period begins. In this technical master guide, we deconstruct FRA notation, master the exact mathematical settlement payoff formula, and walk through a complete $10,000,000 corporate hedging scenario for 2026.

1. Decoding Standard FRA Notation (e.g., 3x9 FRA)

FRAs are quoted in the financial markets using standard "A × B" notation, where both figures represent months from the trade date ($T_0$):

2. The Master FRA Settlement Payoff Formula

Because an FRA settles at the beginning of the borrowing term rather than at the end when interest would normally be paid, the gross interest differential must be discounted back to present value using the prevailing floating settlement rate ($L$):

Payoff = [ (L - R_K) × Notional × (Days / 360) ] / [ 1 + (L × (Days / 360)) ]

Where:

• Payoff: Cash settlement amount paid by the seller to the buyer (or vice versa if negative).

• L: The floating reference benchmark fixing rate on the settlement date (e.g., 6-month CME Term SOFR).

• R_K: The agreed contract fixed FRA rate.

• Notional: The principal dollar amount of the loan being hedged.

• Days: The actual number of days in the loan period (e.g., 180 days for a 6-month term).

3. Worked Corporate Case Study: $10,000,000 3x9 FRA Hedge

Imagine a real estate developer has a $10,000,000 commercial construction loan with a floating rate of 6-month SOFR + 2.00%. The next interest period begins in 3 months and lasts for 6 months (180 days).

Fearing that the Federal Reserve will pause rate cuts or hike rates, the developer buys a 3×9 FRA at a fixed rate of R_K = 4.25% on a $10,000,000 notional amount.

Scenario A: Rates Rise to 5.25% ($L = 0.0525$)

Numerator = (0.0525 - 0.0425) × $10,000,000 × (180 / 360)

Numerator = 0.0100 × $10,000,000 × 0.50 = $50,000

Denominator = 1 + (0.0525 × 0.50) = 1 + 0.02625 = 1.02625

Payoff = $50,000 / 1.02625 = +$48,720.83 (Bank pays Developer)

The bank pays the developer $48,720.83 in upfront cash, which perfectly offsets the higher floating interest payments the developer must make on their commercial bank loan.

Scenario B: Rates Fall to 3.50% ($L = 0.0350$)

Numerator = (0.0350 - 0.0425) × $10,000,000 × 0.50 = -$37,500

Denominator = 1 + (0.0350 × 0.50) = 1.0175

Payoff = -$37,500 / 1.0175 = -$36,855.04 (Developer pays Bank)

The developer pays the bank $36,855.04, but benefits from paying a lower interest rate to their commercial lender. In both cases, the net effective borrowing rate was locked in at exactly 4.25%.

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