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Follow the denominator

Why can the same rate produce different interest?

The balance, number of days and day-count method all affect the calculation. A stated yearly rate alone does not tell you the exact charge on a statement.

Why can the same rate produce different interest?
What you are comparingIn this illustration
Assumed balance and yearly rate$10,000 at 12%
30 days using a 365-day year$98.63 interest
30 days using a 360-day year$100.00 interest
$10,000 × 12% × 30 days ÷ 365 = $98.63

Follow the denominator

The first method is $10,000 × 12% × 30 ÷ 365. The second uses the same balance, annual rate and days, but divides by 360. That difference alone produces $98.63 versus $100.00, with the stated rounding.

To check an actual statement, find the contract’s day-count method, posting dates, relevant balance and rounding rules. These calculations explain a difference; they do not establish which convention your lender may lawfully use.

This is a saved illustration with stated assumptions, not an offer or prediction for your circumstances. The full calculation and original limitations are in the optional archive.

Explore the complete interest fees and debt mathematics guide →
Open the complete calculation, tables and source notesOriginal working documents, complete tables and revision history
About this archive

The explanation above is written for readers. These original working documents preserve the evidence trail, including technical language, dated passages and known corrections. They have not all received independent professional review. Use the marked limits before relying on a particular rule or figure.

DATA & WORKED EXAMPLE

The same 30 days can produce different modeled interest

On the saved $10,000 / 12% / 30-day inputs, end-rounding yields $98.63 with a 365-day denominator and $100.00 with 360. Daily cent posting produces different totals.

Saved research, explicit assumptions and source limits. Full investigation → · All original tables →

E01 — Thirty days of simple accrual

Assumed denominatorCalculation before roundingInterest rounded once at the end
36510000 * 0.12 * 30 / 365 = 98.6301369863$98.63
36010000 * 0.12 * 30 / 360 = 100.0000000000$100.00
366, only as a separately stipulated leap-year branch10000 * 0.12 * 30 / 366 = 98.3606557377$98.36

Rounding changes the result

DenominatorRound only the final period chargeRound each daily amount to cents, then sum 30 daysDifference
365$98.63$3.29 * 30 = $98.70Daily cent posting is $0.07 higher
360$100.00$3.33 * 30 = $99.90Daily cent posting is $0.10 lower

What to keep attached

  • Existing coordinator53check scope supports the arithmetic, not lawful denominator, endpoint, posting or current contract.
  • The2010 generic creditor handout is historical and not a present provider-policy claim.

Source trail

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