Ordinary interest is a traditional finance-mathematics term for simple interest calculated with a 360-day year. The label specifies the denominator but does not always specify how days in the numerator are counted. A modern agreement should use an explicit convention such as Actual/360 or 30/360, which are not the same method.
Key Takeaways
- Ordinary interest generally converts an annual rate to a daily basis using 360.
- The time numerator can use actual elapsed days or approximate 30-day months, depending on the stated method.
- Actual/360 and 30/360 share a 360 denominator but can produce different day counts.
- Ordinary interest is usually simple interest; it does not imply daily compounding.
- From the same positive principal, annual rate, and actual day count, a 360 denominator produces more interest than a 365 denominator.
- Use the contract’s explicit day-count definition for billing, settlement, disclosure, or legal conclusions.
When the calculation uses (N) stated days over a 360-day year:
$$
I_{ordinary} = P r\left(\frac{N}{360}\right)
$$
where:
- (I_{ordinary}) is simple interest;
- (P) is principal;
- (r) is the stated annual rate as a decimal; and
- (N) is the day count produced by the applicable method.
If (N) is the actual number of elapsed calendar days, the calculation resembles Actual/360. If (N) is generated from a 30-day-month formula, it resembles a 30/360 convention. Month-end handling must be defined rather than guessed.
Worked Example: 360 vs. 365 Denominator
Assume USD 250,000 accrues simple interest at 5.4% for 45 actual days. Ignore fees, compounding, rate changes, and rounding within the period.
Using ordinary interest with a 360-day denominator:
$$
I_{360} = 250{,}000(0.054)\left(\frac{45}{360}\right) = 1{,}687.50
$$
Using exact interest with a 365-day denominator:
$$
I_{365} = 250{,}000(0.054)\left(\frac{45}{365}\right) \approx 1{,}664.38
$$
The ordinary-interest result is about USD 23.12 higher:
$$
1{,}687.50 - 1{,}664.38 = 23.12
$$
This isolates the denominator effect. It is not a full comparison of two financial products because a real quote can differ in annual rate, fees, cash-flow timing, compounding, disclosure method, and risk.
Actual/360 vs. 30/360
| Feature | Actual/360 | 30/360 |
|---|
| Day numerator | Actual elapsed days | Formula-based count using 30-day months |
| Year denominator | 360 | 360 |
| Month lengths | Calendar month lengths matter | Month lengths are standardized by a defined rule |
| Month-end dates | Counted as actual calendar dates | Adjusted under the specific 30/360 variant |
| Main use of label | Money-market, floating-rate, and some loan conventions | Many fixed-income and scheduled-payment calculations |
There are multiple 30/360 variants. A broad statement that ordinary interest assumes 12 identical 30-day months can therefore be incomplete: some ordinary-interest exercises use actual days over 360 instead.
Why a 360-Day Basis Changes the Annual Accrual
If a 5.4% rate is applied for 365 actual days with a 360 denominator and no compounding:
$$
0.054\left(\frac{365}{360}\right) = 5.475\%
$$
The dollar interest exceeds 5.4% of principal because 365 daily accruals are each based on one three-hundred-sixtieth of the annual rate. This calculation is not automatically the disclosed APR. U.S. Truth in Lending guidance notes that using a 360-based daily factor over actual days can require disclosures reflecting the higher finance charge and APR.
Where the Term Appears
“Ordinary interest” appears most often in financial-mathematics education and older explanatory material. In market and contract documents, explicit terms such as Actual/360, 30/360, Actual/365 Fixed, and Actual/Actual are more useful because they identify how the year fraction is calculated.
A 360-day basis can appear in loans, money-market instruments, floating-rate securities, and derivatives. That does not mean every product in those categories uses ordinary interest or the same 360-day method.
How to Evaluate an Ordinary-Interest Calculation
- Determine whether “ordinary interest” is actually defined in the source.
- Identify whether the numerator uses actual days or a 30-day-month formula.
- Confirm which start and end dates are included.
- Verify principal and rate changes during the period.
- Separate simple accrual from compounding, payment, and posting rules.
- Check whether the calculation is a contractual amount, accounting accrual, educational estimate, or regulated disclosure.
- Keep full precision until the required rounding stage.
- Replace the broad label with the explicit day-count convention in working papers.
Risks and Common Mistakes
- Assuming ordinary interest always means 30/360.
- Treating Actual/360 and 30/360 as interchangeable.
- Counting business days when the agreement requires calendar days.
- Calling a 360-day convention daily compounding.
- Comparing a 360-based rate with a 365-based rate without comparing dollar cash flows.
- Ignoring month-end rules in a 30/360 calculation.
- Assuming historical textbook terminology controls a modern contract.
- Using a simple-interest result as APR, APY, or effective yield.
Authoritative Sources
- Exact Interest: Traditional simple-interest method generally associated with actual days over 365.
- Actual/360: Explicit convention using actual elapsed days and a 360 denominator.
- Daily Interest: Interest accrued from a daily rate and eligible balance.
- Simple Interest: Interest calculated without adding prior interest to principal.
- Periodic Interest Rate: Rate applicable to one day, month, quarter, or other defined period.
FAQs
Is ordinary interest the same as simple interest?
Ordinary interest is usually a type of simple-interest calculation that uses a 360-day denominator. Simple interest is broader and can use other time conventions.
Is ordinary interest the same as Actual/360?
Not always. If ordinary interest uses actual elapsed days over 360, the arithmetic matches Actual/360. Some uses instead pair the 360 denominator with approximate time or a 30/360 day count.
Does ordinary interest always cost more than exact interest?
For the same positive balance, annual rate, and actual day count, dividing by 360 produces more simple interest than dividing by 365. A real product comparison must also include rates, fees, compounding, timing, and other terms.
Why do financial documents avoid the term ordinary interest?
Explicit labels such as Actual/360 or 30/360 communicate the numerator and denominator more clearly. “Ordinary interest” can leave the day-count numerator ambiguous.
This page provides general financial education, not legal, lending, deposit, accounting, tax, investment, or personalized financial advice. Use the agreement’s defined day-count method for an actual transaction.