🧮 Omni-level explanation
How minimum payments really work (and why extra payments matter)
Credit card debt behaves differently from a normal fixed-payment loan. With a typical loan (like a mortgage),
your payment is fixed and the payoff date is predictable. With a credit card, the “standard” payment is often
the minimum payment set by the issuer — and that minimum is usually a formula, not a fixed amount.
The result is that your payment can shrink over time, which is exactly why balances can linger for years.
1) The minimum payment rule (the model used here)
Many issuers calculate the minimum payment as:
Minimum Payment = max(Percent of Balance, Minimum Floor).
For example, if the percent is 2% and your balance is $4,500, then 2% is $90.
If the floor is $25, the minimum is $90 (because it’s larger).
Later, when the balance drops to $1,000, 2% is $20 — below the $25 floor — so your minimum becomes $25.
This transition (from percentage-based to floor-based) is why the payoff often speeds up a little near the end,
but stays painfully slow for most of the journey.
2) How interest is added each month
Most credit cards quote an APR (annual percentage rate), but interest is applied periodically. A simple monthly model
uses a monthly periodic rate:
r = APR / 12 (expressed as a decimal).
If your APR is 24.99%, then r ≈ 0.2499 / 12 ≈ 0.020825. That means each month, the balance grows by about 2.08%
before your payment is applied.
In each month, the calculator does the same three-step cycle:
- Step A: Add interest: Interest = Balance × r
- Step B: Add any monthly fees you entered (optional)
- Step C: Subtract the payment (minimum rule + extra)
The key insight: if your payment is close to the interest amount, the balance shrinks very slowly.
For example, $4,500 at 24.99% APR has first-month interest of roughly $94. If your minimum payment is around $90,
you’re not even covering full interest in that month — so the balance can stall (or fall by only a few dollars).
That’s why minimum payments can feel like quicksand.
3) Why minimum payments can stretch for years
With a fixed-payment loan, the payment stays constant, so your principal reduction grows over time.
With a minimum-payment credit card rule, the opposite often happens: the payment shrinks as the balance shrinks,
which keeps principal reduction small. Mathematically, this creates a long “tail” — the payoff curve flattens.
Another way to see it is to compare the minimum payment to your monthly interest:
- If Payment < Interest, your balance grows (or doesn’t fall).
- If Payment ≈ Interest, your balance falls slowly (years).
- If Payment > Interest, your balance falls faster (months/short years).
4) The “extra payment effect” is nonlinear
Paying an extra $10–$100 per month doesn’t just reduce your balance by that amount — it can reduce it by far more,
because it changes how much interest you will pay in the future. When you reduce principal early, every future month
of interest is computed on a smaller balance. This is why the “interest saved” number can be surprisingly large.
Think of it like this: the earlier you reduce the balance, the more months you benefit from lower interest.
That’s why a small extra payment often delivers the biggest payoff at the start of your plan.
5) A worked example (so you can sanity-check results)
Suppose you have a $4,500 balance at 24.99% APR, minimum payment = 2% of balance with a $25 floor, and no monthly fees.
Month 1: interest ≈ $4,500 × 0.020825 ≈ $93.71. Minimum payment ≈ 2% × 4,500 = $90. Your balance hardly moves.
Now add an extra $50. Your total payment becomes $140, which clears interest and reduces principal by about $46 in the first month.
That might not sound huge, but month 2 starts with a lower balance, so month 2 interest is lower, so even more of your payment hits principal.
This compounding benefit is why extra payments “snowball” in your favor.
6) What this calculator assumes (and what it doesn’t)
This tool is intentionally simple and transparent for learning and planning. It assumes a constant APR and monthly compounding.
Real cards may calculate daily interest, apply penalty APRs, or use a more complex minimum formula (e.g., interest + 1% principal + fees).
That said, the payoff pattern and the “minimum payment trap” behavior are still very similar, which is why this calculator
is useful for understanding your options and motivating an extra payment strategy.
Want to go even faster? Pair this calculator with a payoff strategy like Debt Snowball (smallest balance first)
or Debt Avalanche (highest APR first), and use the “extra payment” field to simulate what happens when you redirect money
from paid-off cards to the next card.