Actual/360, also written Act/360 or A/360, is a day-count convention that measures an interest period using the actual number of elapsed days and divides that count by 360. It converts a stated annual rate into a fraction used to calculate accrued interest. It is not the same as assuming every month has 30 days.
Key Takeaways
- “Actual” describes the numerator: the calculation counts actual elapsed days.
- “360” describes the denominator used to convert those days into a year fraction.
- Actual/360 and 30/360 are different because 30/360 applies formula-based 30-day months.
- With the same principal, stated rate, and actual days, Actual/360 produces more simple interest than Actual/365 Fixed because it uses a smaller denominator.
- The convention affects accrued dollars; it does not by itself define APR, effective yield, compounding, payment dates, or the underlying benchmark.
- The contract, security terms, or market convention must identify the applicable day count.
For simple interest over one period:
$$
I = P r\left(\frac{N}{360}\right)
$$
where:
- (I) is accrued interest;
- (P) is principal or notional amount;
- (r) is the stated annual rate as a decimal; and
- (N) is the actual number of included days.
The day-count fraction is:
$$
DCF_{Act/360} = \frac{N}{360}
$$
This formula assumes a constant principal and rate for the period. Floating-rate loans, derivatives, changing balances, lookback conventions, payment lags, and compounding can require multiple subperiod calculations.
Worked Example: Actual/360 vs. Actual/365
Assume USD 100,000 accrues simple interest at a stated annual rate of 6% for 90 actual days. Ignore fees, compounding, balance changes, and rounding within the period.
Under Actual/360:
$$
I_{360} = 100{,}000(0.06)\left(\frac{90}{360}\right) = 1{,}500.00
$$
Under Actual/365 Fixed:
$$
I_{365} = 100{,}000(0.06)\left(\frac{90}{365}\right) \approx 1{,}479.45
$$
The difference is:
$$
1{,}500.00 - 1{,}479.45 = 20.55
$$
The Actual/360 result is about USD 20.55 higher for this 90-day illustration. That does not mean one product is automatically more expensive or attractive. The stated rate, fees, cash flows, compounding, credit risk, liquidity, and disclosure measure can differ.
Comparison With Other Day-Count Conventions
| Convention | Numerator | Denominator | Important distinction |
|---|
| Actual/360 | Actual elapsed days | 360 | Commonly specified for U.S. dollar money-market and SOFR-based calculations |
| Actual/365 Fixed | Actual elapsed days | 365 | Denominator stays 365, including a leap year |
| Actual/Actual | Actual elapsed days | Actual-year or coupon-period basis | Several defined variants exist; do not infer the formula from the short label |
| 30/360 | Formula-based days using 30-day months | 360 | Does not simply count all actual calendar days |
The table describes broad structures, not every implementation. Start-date inclusion, end-date exclusion, leap-year treatment, business-day adjustments, and coupon schedules can vary by documented convention.
Why Actual/360 Can Produce More Than the Stated Rate Over 365 Days
If a 6% rate is applied as simple interest for all 365 actual days using a 360 denominator:
$$
0.06\left(\frac{365}{360}\right) \approx 6.0833\%
$$
This is a simple annualized accrual illustration, not an APR or effective annual yield. U.S. lending disclosures can require the higher finance charge and APR resulting from applying a 360-based daily factor to actual days. Deposit-account rules and disclosures follow their own requirements.
Where Actual/360 Appears
The convention appears in parts of the U.S. dollar money market, including recommended conventions for SOFR-based loans and instruments. It also appears in some commercial credit agreements, floating-rate notes, derivatives, and deposit calculations when the governing document expressly specifies it.
Do not assume every loan, bond, deposit, or derivative uses Actual/360. U.S. Treasury yield calculations use actual day counts on a 365- or 366-day basis, and other currencies or product types can use different conventions.
How to Evaluate an Actual/360 Calculation
- Confirm that the document explicitly states Actual/360, Act/360, or an equivalent defined term.
- Verify the principal or notional balance for each accrual segment.
- Count included calendar days using the agreement’s start- and end-date rules.
- Identify rate-reset dates, observation periods, spreads, floors, and caps.
- Check whether the rate is simple, compounded, averaged, or weighted across days.
- Distinguish an interest accrual convention from APR, APY, coupon, discount yield, and effective yield.
- Apply payment-date and business-day adjustments separately from the day count.
- Reconcile full-precision interest to the contractual rounding rule.
Risks and Common Mistakes
- Treating Actual/360 as another name for 30/360.
- Dividing by 360 but counting only business days when the contract counts calendar days.
- Assuming a displayed 6% quote means exactly 6% of principal over 365 actual days.
- Comparing rates quoted on different day-count bases without converting the resulting cash flows.
- Ignoring leap days, reset dates, lookbacks, lockouts, or payment delays.
- Applying a general market convention instead of the specific agreement.
- Calling a simple accrual result an effective yield or APR.
- Rounding the daily rate before multiplying by a large balance and many days.
Authoritative Sources
- Daily Interest: Interest accrued by applying a daily rate to an eligible balance.
- Exact Interest: Traditional finance-math label generally associated with actual days and a 365-day basis.
- Ordinary Interest: Traditional label for simple interest using a 360-day denominator.
- Accrued Interest: Interest recognized or accumulated but not yet paid.
- Money Market Yield: Annualized quotation measure used for some short-term instruments.
FAQs
Does Actual/360 assume 30-day months?
No. It counts actual elapsed days in the numerator. A 30/360 convention uses formula-based 30-day months.
Does Actual/360 always charge more than Actual/365?
For the same positive principal, stated rate, and actual day count under simple interest, the 360 denominator produces more interest. Real products can have different rates, fees, and cash-flow terms, so total cost still requires a full comparison.
Is Actual/360 the same as APR?
No. Actual/360 is a day-count convention. APR is an annualized borrowing-cost disclosure whose calculation can include additional rules and charges.
Do all SOFR loans use Actual/360?
No. ARRC recommends Actual/360 for U.S. dollar SOFR conventions, but parties can specify other methods. The executed agreement controls.
This page provides general financial education, not legal, lending, deposit, accounting, tax, investment, or personalized financial advice. Confirm the current contract and applicable disclosure rules for a specific transaction.