Formulas
We use the assumptions in Regulation Z, Appendix M1, the method card issuers may use for the “Minimum Payment Warning” on every statement: only the payment you chose each month, no new purchases or fees, the APR stays the same during payoff, no grace period, average daily balance, and all months equal (a daily rate of APR/365 and 365/12 days per month). Payments are credited at the end of the month.
- Monthly rate r = APR ÷ 12 (APR/365 × 365/12 days).
- Interest each month = balance × r, rounded half-up to the cent.
- Payment is worked out from the month's opening balance and that month's interest (as in Appendix M2's sample program). If it is at least the balance plus interest, it pays everything and payoff ends.
- Interest + 1% of balance (min $30): 1% of the balance (at least $5) plus the month's interest, rounded up to the next dollar, at least $30 (example: Comenity Mastercard agreement).
- 2% of balance (min $20): 2% of the balance, rounded to the cent, at least $20 (the sample formula in Appendix M2).
- Custom: your percent of the balance (0.5% to 5%), plus the month's interest if you tick it, at least your dollar minimum, rounded to the cent.
- 3-year payment = balance × r × (1 + r)36 ÷ ((1 + r)36 − 1), rounded to the cent (App. M1(d)). At 0% it is the balance ÷ 36.
- Statement wording: under 2 years it is shown in months; from 2 years it is rounded to the nearest whole year (2 years 6 months to 3 years 5 months reads “3 years”).
- Not within 100 years: we stop counting at 1,200 months. If the first payment doesn't cover the first month's interest, the balance never goes down (negative amortization).
All amounts are whole cents and every rate is an exact fraction (22.36% is 2236/10000), so nothing is lost to floating-point rounding. Our results match the reference calculation to the cent on 441 test cases and a full 228-month schedule. Real statements differ a little: billing cycles are 28 to 31 days, interest compounds daily, payments arrive mid-cycle, and new purchases and fees change the balance.
Fed and prime timeline
| Date | What happened |
|---|---|
| Jan 28 to Jul 29, 2026 | Five FOMC meetings held the federal funds target range at 3.50% to 3.75%. |
| Sept 16, 2026 | FOMC raised the range by 1/4 point to 3.75% to 4.00% (vote 12-0). |
| Sept 17, 2026 | The new range took effect. The prime rate moved from 6.75% to 7.00% (H.15, WSJ, Bank of America, U.S. Bank). |
| Oct 7, 2026 | Fed G.19: average card APR 21.19% on all accounts, 22.36% on accounts charged interest (August 2026 (preliminary), before the hike). |
| Oct 27-28, 2026 | Next FOMC meeting. Not yet decided. |
| Dec 8-9, 2026 | The meeting after that. |
Official Everything above comes from the Federal Reserve or the named banks. We don't forecast the Oct 28 decision.
When a variable APR changes
A variable card APR is a public index plus a fixed margin. Regulation Z lets an issuer raise the APR when “the annual percentage rate varies according to an index that is not under the card issuer's control and is available to the general public” and the increase “is due to an increase in the index” (12 CFR 1026.55(b)(2)). A published prime rate such as the one in the Wall Street Journal qualifies. The issuer can't raise the margin under this exception.
No 45-day notice is needed “when the change is an increase in a variable annual percentage rate in accordance with a credit card or other account agreement that provides for changes in the rate according to operation of an index that is not under the control of the creditor and is available to the general public” (12 CFR 1026.9(c)(2)(v)(C)). Other significant changes, and penalty rates, need 45 days' notice (1026.9(c)(2)(i)(A) and 1026.9(g)).
When your card picks up the change depends on your agreement. One published example (a Comenity Mastercard) uses “the U.S. Prime Rate in the Money Rates section of The Wall Street Journal on the last business day of the calendar month”, and “any APR change will take effect on the first day of the billing period that begins after the Prime Rate changes.” Most cards pick up a prime change within one or two billing cycles. Your cardholder agreement (“How we determine variable rates”) has the exact rule.
Worked examples
Each one is a test in our code and is recomputed by the same engine the calculator uses.
Index + margin (Reg Z official interpretations)
| Index | Margin | APR |
|---|---|---|
| 10% | 7 | 17.00% |
| 10.1% (quarter average) | 7 | 17.10% |
| 10.2% (last day) | 7 | 17.20% |
| 10% | 5 | 15.00% |
| 16% with a 20% maximum | 5 | 20.00% |
A real card agreement, before and after Sept 17
| Margin | APR at prime 6.75% (daily rate) | APR at prime 7.00% |
|---|---|---|
| 21.74 | 28.49% (0.07805%) | 28.74% |
| 14.74 | 21.49% (0.05887%) | 21.74% |
| 22.74 (cash, max 29.99%) | 29.49% (0.08079%) | 29.74% |
Statement wording
| Months | Statement says |
|---|---|
| 23 | 23 months |
| 24 | 2 years |
| 28 | 2 years |
| 29 | 2 years |
| 30 | 3 years |
| 38 | 3 years |
| 41 | 3 years |
| 42 | 4 years |
Interest and minimum payments
| Case | Result |
|---|---|
| $6,000 at 22% vs 22.25%: first month's interest | $110.00 vs $111.25 |
| $6,000 at 28.74%, interest + 1% minimum | Interest $143.70, minimum $204.00 |
| $300 at 28.74%, interest + 1% minimum | Interest $7.19, minimum $30.00 ($30 floor) |
| $6,000 at 28.74%, 2% minimum (2% < 2.395% monthly rate) | Never (balance never goes down) |
| $6,000 at 22.61%, fixed $113.05 (= the interest) | Never (balance never goes down) |
Try them in the calculator. With a 2% minimum and an APR above 24%, the monthly rate is more than 2%, so the balance never shrinks; between about 22% and 23.5% it can take more than 100 years.
Sources
Each link shows the document date or the day we checked it. Reg Z text: Official Interpretations (opens in a new tab).