Compounded in Arrears

Compounded in Arrears

Compounded in arrears is the standard method for calculating interest on RFR-based floating-rate loans. Each business day's overnight rate is compounded into a running product, and the total interest is determined only at the end of the interest period — hence "in arrears."

The Formula

The effective rate for a period is:

Effective Rate = [ ∏ (1 + rᵢ × dᵢ / basis) − 1 ] × basis / D

Where:

• rᵢ = overnight rate on business day i (decimal)
• dᵢ = calendar days the rate applies (1 for weekdays, 3 for Fridays, holiday-adjusted)
• basis = 360 (USD/EUR) or 365 (GBP)
• D = total calendar days in the interest period

Interest is then: Principal × (Effective Rate + Spread) × D / basis

Weekend and Holiday Treatment

Overnight rates are not published on non-business days. Instead, Friday's rate carries a weight of 3 days (Friday, Saturday, Sunday), and the day before a public holiday carries extra weight for the holiday. This ensures every calendar day in the period accrues interest.

Why It Differs From Simple Average

Compounding produces a slightly higher result than a simple average of daily rates because of the interest-on-interest effect. For a 30-day period at 4.30%, compounding yields approximately 4.313% — roughly 1.3 bps higher than the simple average.

Practical Challenge: Settlement

With rates known only at period end, there is insufficient time to calculate and settle on the same day. The solution is a lookback period — shifting rate observations back by 5 business days so the final rates are known before the period ends.

Comparison with Term Rates

Feature	Compounded in Arrears	Term SOFR / EURIBOR
Rate known	End of period	Start of period
Basis	Daily compounding	Fixed for period
Accuracy	Exact daily rates	Forward-looking estimate
Settlement	Requires lookback	Straightforward

Use the RFR Loan Calculator to model compounded-in-arrears calculations for SOFR, SONIA, and €STR with a full daily ledger.