What Does "Compounded in Arrears" Mean?

When a loan uses SOFR compounded in arrears, the interest rate is not known until the end of the interest period. Each business day during the period, that day's overnight SOFR rate is compounded into the running total. At the end of the period, all of the daily compounding factors are multiplied together to produce the period's effective rate.

This is different from traditional LIBOR-based loans, where the rate was fixed at the start of the period — so the borrower knew their interest charge from day one.

The Compounding Formula

The effective SOFR rate for a period is calculated as:

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

Where:

rᵢ = overnight SOFR rate on day i (as a decimal)
dᵢ = number of calendar days that rate applies (1 for weekdays, 3 for Fridays, holiday-adjusted)
basis = 360 (for USD SOFR, Act/360 convention)
D = total calendar days in the interest period
∏ = product across all business days in the period

The interest charged for the period is then:

Interest = Principal × (Effective Rate + Spread) × D / basis

Why Lookback Is Needed

Under pure "in arrears" compounding, the final rate is only known on the last day of the period — leaving no time for the lender to issue an invoice and the borrower to arrange the payment. To solve this, the lookback period (also called observation lag) shifts rate observations back by a fixed number of business days.

For a 5-business-day lookback, each day's accrual uses the overnight SOFR published 5 business days earlier. This means the rate for the final days of the period is already published — giving both parties time to calculate and settle.

The ARRC recommends a 5-business-day lookback for most syndicated loans.

Lookback Without Shift vs Observation Shift

There are two market conventions for applying the lookback:

Lookback Without Shift (ARRC / Syndicated Loans)

The rate observed is from 5 business days earlier
The day weight (dᵢ) stays tied to the accrual date
Weekend and holiday day weights remain on the actual calendar dates

This is the standard for US syndicated loans per ARRC guidance.

Observation Shift (FRN / Bond Market Standard)

Both the rate and the day weight are taken from 5 business days earlier
The borrower accrues interest as if they were in the observation period, not the accrual period
The annualisation denominator uses the observation period days (not accrual period days)

Both methods are valid — the key is that the loan documentation specifies which convention applies.

Worked Example

Loan: USD 1,000,000
Period: 1 June 2025 – 30 June 2025 (29 calendar days)
Lookback: 5 business days (no shift)
Spread: 2.50%

Suppose overnight SOFR averaged 4.30% across the period. The compounded effective SOFR rate would be approximately 4.31% (slightly higher than simple average due to compounding). With the 2.50% spread:

All-in rate ≈ 6.81%
Interest ≈ USD 1,000,000 × 6.81% × 29/360 ≈ USD 5,486

You can verify this precisely — and see the full daily rate ledger — using our RFR Loan Calculator.

SONIA and €STR: The Same Method

The same compounded-in-arrears approach applies to:

SONIA (Sterling Overnight Index Average) for GBP loans — Act/365 basis
€STR (Euro Short-Term Rate) for EUR loans — Act/360 basis

Our calculator supports all three rates.

Key Takeaways

Compounded SOFR in arrears is the most accurate reflection of overnight rate movements during the period
The lookback period (typically 5 business days) enables timely settlement
Weekend and holiday rates compound into Friday's daily factor
The effective rate differs slightly from a simple average due to the compounding effect
Term SOFR is the "in advance" alternative — rate is set at period start, like LIBOR

Use our free calculator to model your SOFR loan with full daily compounding, customisable lookback, and Excel export.