Why the Minimum Payment Shrinks as Fast as the Balance

A fixed loan payment and a credit card minimum look like the same kind of thing. They are opposites. A loan payment is a constant, so every month it retires more principal than the last. A card minimum is a percentage of what you still owe, so every month it asks for less.

That single difference is the whole subject. Below, one balance is run through the calculator on this site with figures chosen to work through — 5,000 at an APR of 22%, a minimum of 2% of the statement with a floor of 25. No part of that is a claim about any real card; card terms vary by issuer and yours are on your own statement.

The first payment already tells you the ending

An APR of 22% is a monthly rate of 1.8333%. On 5,000 that is 91.67 of interest posted before anything is paid. The statement balance becomes 5,091.67, and 2% of that is a minimum of 101.83.

Subtract the interest and what is left to touch the debt is 10.17. That is 9.98% of the payment. The other 90% buys one month of the balance sitting still.

Another way to hold that first month: 91.67 across roughly thirty days is 3.06 a day. That is the rent on the balance, charged whether or not a payment arrives, and it is the number the minimum is mostly covering.

Pay it and the balance goes from 5,000 to 4,989.83. Next month the interest is smaller, so the minimum is smaller too, and the share that reaches the debt is the same 9.98% it was before.

That last sentence is the trap. Progress does not accelerate, because the payment falls at exactly the rate the balance does.

A percentage minimum is a decay rate, not a payment

Write one month as arithmetic. The balance grows by the monthly rate, then loses the minimum percentage of the result:

At 22% and 2% that multiplier is 0.997967. The balance falls by 0.2033% a month, forever, with no reference to how large it is. A geometric decay has a half-life, and this one is 341 months.

Four points of APR between the last two rows nearly double the half-life. The minimum percentage is fighting the monthly rate directly, and what survives that fight is a small difference between two similar numbers — which is why it moves so violently.

What it adds up to

Run the full schedule and the 5,000 balance clears in 817 months, which is 68 years and one month. Total interest is 35,957.75, and total paid is 40,957.75 — 8.19 times what was borrowed.

The figure worth carrying is not the 68 years. It is that the tail is paid at a trickle by construction: by the time the balance is small, the minimum is small too, and it stays that way until the floor takes over.

Freeze the first minimum and nothing else

Here is the comparison that isolates the rule from the money. Take the same first payment, 101.83, and simply keep paying that number every month instead of whatever the statement asks.

Month one is identical in both columns. Nothing was tightened, no extra was found, and the difference is 690 months and 28,040.52.

The reason is that a held payment turns a shrinking percentage into a fixed amount, which makes the principal share grow every month instead of standing still. It is the ordinary loan structure, recovered by refusing to let the payment fall.

Where a percentage minimum stops working at all

There is a rate above which the minimum cannot reduce the balance at any size. The payment is p of the statement, the interest is i of the balance, so the payment stops covering the interest when p(1 + i) is no longer greater than i. Rearranged, the balance stops falling when the monthly rate reaches p / (1 - p).

Above the threshold the arithmetic does not merely stall, it reverses: the multiplier (1 + i)(1 - p) rises above one and the balance grows every month while the payments are being made on time. The calculator returns that case as a stated result rather than a number, because there is no month at which it clears.

Two practical notes sit under that table. The first is that being below the threshold guarantees almost nothing: at 22% the 2% minimum is comfortably under 24.49% and still takes 817 months.

The second is a boundary in the tool rather than in the arithmetic. The calculator walks a schedule 1,200 months long and then stops, reporting that the balance does not clear. On this balance that report begins at 22.86% APR, well below the 24.49% at which the balance genuinely stops falling. Between those two figures the debt is shrinking, just not inside a century.

The floor is what ends it, and it bends the clock

A percentage of a balance never reaches zero. What ends the schedule is the dollar floor underneath it, and the floor starts binding once the percentage falls below it — at a balance of 1,250, which is the floor divided by the percentage.

Below that point the payment stops shrinking, so the ordinary loan arithmetic takes over and the last stretch runs quickly. Which produces a result that looks wrong and is not:

Five times the balance takes 11.2 times as long. A debt that starts above the crossover spends years in the slow phase before it ever reaches the part where the floor helps, and everything above 1,250 in that table is being paid at 0.2033% a month.

What it costs to pick a date instead of a percentage

The other way to use the tool is backwards: decide when the balance should be gone and read off what that costs. These are the fixed payments that clear 5,000 at 22% in a chosen number of months.

Set that last row against the minimum. 138.09 a month is 36.26 more than the first minimum of 101.83, and it turns 68 years into five while cutting the interest from 35,957.75 to 3,285.67.

The curve through those rows is steep at the short end and flat at the long one. Going from 60 months to 48 costs 19.44 more a month; going from 24 to 12 costs 208.58 more. Buying the first few years back is cheap, and buying the last one is not.

The interest is not front-loaded here, and that is the problem

On an ordinary amortising loan the early payments are mostly interest and the late ones are mostly principal, which is why paying extra early is worth so much more than paying extra late.

A percentage minimum has no such shape. Run the 817-month schedule and the first ten years account for 9,769.58 of interest — only 27.2% of the 35,957.75 total. The remaining three quarters are spread across the decades that follow.

That is not a mercy. It means there is no stretch of the schedule where the debt starts behaving itself, because the ratio of interest to principal is fixed at the same 9.98% split that showed up in month one. A loan gets easier as it goes. This does not.

None of this settles which debt to clear first when there is more than one card. That is a separate question with its own arithmetic, and the debt payoff calculator runs the two standard orders against the same monthly pool so the difference between them is a number rather than an argument.

What this model is not

The schedule here posts interest once a month at APR divided by twelve. Card issuers generally use a daily periodic rate against an average daily balance, so a real statement will differ in the cents and sometimes in the dollars.

Minimum-payment structures also vary. Percentage-plus-floor is one common shape, not a standard, and some issuers add the month's interest and fees on top of the percentage. The two inputs on the tool exist so you can copy the rule off your own statement rather than accept the one used here.

And everything above is general information about arithmetic rather than financial advice. It describes what a given rule does to a given balance. It cannot know your accounts, your rates, or which debt is worth clearing first.

Common mistakes reading a payoff schedule

• Treating the minimum as a plan. It is the smallest payment that keeps the account current, and on a percentage rule it is calibrated to the balance rather than to any date.
• Assuming progress speeds up. Under a percentage minimum the share of each payment that reaches the balance is constant, so the hundredth month looks like the first.
• Comparing balances by size alone. The floor crossover means a balance twice as large can take far more than twice as long.
• Reading "does not clear" as "grows". A schedule can be reported as not clearing simply because it runs past the horizon the tool walks.
• Expecting the loan-shaped relief. On an amortising loan the interest is front-loaded and the schedule eases; under a percentage minimum the split stays where it started, so it never does.