How do you calculate the settlement amount on a Forward Rate Agreement (FRA)?

FRA settlement is a classic FRM Part I topic that tests whether you understand present value mechanics in money markets. Here's the breakdown. **What an FRA Does** A Forward Rate Agreement is an OTC contract where two parties agree on an interest rate for a future period. The buyer (long) benefits when rates rise above the agreed rate; the seller benefits when rates fall below it. **Why Settlement Is Discounted** The FRA settles at the **beginning** of the reference period, not the end. Since the interest differential would normally be paid at the end of the period, you must discount it back to the settlement date. This is what distinguishes FRAs from simple rate locks. **Settlement Formula:** $$\text{Settlement} = \frac{N \times (R_{\text{ref}} - R_{\text{FRA}}) \times \frac{d}{360}}{1 + R_{\text{ref}} \times \frac{d}{360}}$$ Where: - N = Notional principal - R_ref = Reference rate at settlement (e.g., SOFR) - R_FRA = Agreed FRA rate - d = Days in the reference period **Worked Example:** You enter a 3×6 FRA (settles in 3 months, covers the period from month 3 to month 6). | Parameter | Value | |---|---| | Notional (N) | $10,000,000 | | FRA rate (R_FRA) | 4.25% | | Reference rate at settlement (R_ref) | 4.80% | | Days in reference period (d) | 91 | **Step 1 — Interest differential:** $10,000,000 × (0.0480 − 0.0425) × (91/360) = $10,000,000 × 0.0055 × 0.25278 = **$13,903** **Step 2 — Discount to settlement date:** Discount factor = 1 + 0.0480 × (91/360) = 1 + 0.01213 = **1.01213** Settlement = $13,903 / 1.01213 = **$13,736** Since you're the buyer and rates rose above the FRA rate, you **receive $13,736** at settlement. **Common Mistakes:** 1. Forgetting to discount — this overstates the settlement by the time-value difference. 2. Using 365 instead of 360 — FRAs use an Actual/360 day count by convention. 3. Confusing the sign — the buyer profits when rates rise, the seller profits when rates fall. For more worked examples on money market instruments, explore our FRM Part I question bank on AcadiFi.