How do you calculate the settlement amount for a forward rate agreement (FRA)?

FRAs (Forward Rate Agreements) are OTC contracts that lock in a future interest rate. The settlement mechanics trip up many candidates because payment occurs at the start of the notional borrowing period, requiring a present value adjustment.

FRA Notation: A x B

An FRA is described as 'A x B' where:

• A = months until settlement
• B = months until the underlying loan matures
• (B - A) = the loan period

So a 3x9 FRA settles in 3 months on a 6-month loan (from month 3 to month 9).

The Setup — Caldwell Corp 3x9 FRA

Caldwell Corp enters a 3x9 FRA to hedge its borrowing cost:

• Notional: $10,000,000
• FRA rate (locked rate): 4.80%
• Reference rate at settlement (actual SOFR): 5.40%
• Loan period: 6 months (180 days)
• Day count: Actual/360

Caldwell is the buyer (long) — they want to lock in 4.80% for borrowing.

Step 1: Calculate the Interest Differential

Since the actual rate (5.40%) exceeds the FRA rate (4.80%), Caldwell benefits — they locked in a lower rate and the market moved against borrowers.

Interest differential = (Reference Rate - FRA Rate) x (Days/360) x Notional

= (0.054 - 0.048) x (180/360) x $10,000,000

= 0.006 x 0.5 x $10,000,000

= $30,000

Step 2: Discount to Settlement Date

Here's the key: settlement occurs at the start of the loan period (month 3), but the interest savings are realized at the end (month 9). To avoid the FRA buyer getting paid too early, we discount the payment back by the loan period:

Settlement Amount = Interest Differential / (1 + Reference Rate x Days/360)

= $30,000 / (1 + 0.054 x 180/360)

= $30,000 / (1 + 0.027)

= $30,000 / 1.027

= $29,211.29

Caldwell receives $29,211.29 at month 3.

Why Discount at the Reference Rate?

The logic: Caldwell receives the settlement today (month 3) and can invest it at the current market rate (5.40%) for 6 months. By month 9, that $29,211.29 grows to $29,211.29 x 1.027 = $30,000 — exactly the interest savings. This makes the settlement fair regardless of when the cash is paid.

If Rates Had Fallen Instead:

If SOFR settled at 4.20% (below the FRA rate):

• Caldwell pays the dealer: (0.048 - 0.042) x 0.5 x $10M = $30,000 undiscounted
• Discounted: $30,000 / (1 + 0.042 x 0.5) = $29,385.00

Caldwell locked in 4.80% but the market rate fell to 4.20% — they're paying for insurance they didn't need.

Exam Tip: The most common mistake is forgetting the discounting step. CFA Level I questions almost always require the present value adjustment. Also note that the buyer profits when rates rise and pays when rates fall.

Practice FRA calculations in our CFA Derivatives question bank.