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The Minimum Payment Trap

A card’s minimum payment shrinks as the balance shrinks, so paying only the minimum can stretch a small debt over many years. Set a balance, the APR and the card’s minimum rule, then compare paying the minimum with paying a fixed amount every month.

Banking Lesson 6.3 · about 15 minutes

The balance owed under each plan, with no new charges. Click or tap the chart to read any month; with the chart focused, the left and right arrow keys move one month (Page Up and Page Down move a year).

Minimum only: paid off in
Minimum only: total interest
First minimum payment
Fixed payment: paid off in
Fixed payment: total interest
Interest the fixed plan saves

Debt-free in 36 months

The payment that clears the balance in exactly 36 months, as on the box the CARD Act puts on every statement:

How long the fixed payment takes, from n = −ln(1 − iB/P) ÷ ln(1 + i):

There is no one-cell formula for the minimum plan, because its payment changes every month. A spreadsheet does it a row at a time, just like the table below.

Year by year

The card

$
%

The minimum rule

How the card figures its minimum
%
$

The better plan

$
months

Try an example

From Lesson 6.3. Real cards vary; the statement says which rule yours uses.

Why the minimum is a trap

Each month the card charges interest on the balance, about one-twelfth of the APR:

interest = balance × APR / 12.

(Most issuers figure it daily on the average daily balance, which comes out close.) A common minimum is 1% of the balance plus the month’s interest, or a floor such as $25, whichever is more. Only that 1% actually lowers the debt. As the balance falls, the minimum falls with it, so the debt shrinks more and more slowly. Only the floor finally finishes it off.

A fixed payment works the other way. The payment stays the same while the interest shrinks, so more and more of each payment goes to the balance, the same way a car loan or mortgage is paid off.

The 36-month payment

For a balance B and monthly rate i = APR / 12, the level payment that clears it in n months is

P = B · i / [1 − (1 + i)−n],

which is a spreadsheet’s =PMT. Since the Credit CARD Act of 2009, statements must show how long paying only the minimum would take and what it would cost, and the monthly payment that would clear the balance in 36 months.

How the page figures it

No new charges are made. Interest is the balance times APR / 12, rounded to the cent, and the last payment is whatever is left. A “flat %” minimum is taken on the new balance, after interest. If a minimum would be less than the month’s interest, the balance grows; federal bank examiners have asked card issuers since 2003 to set minimums that pay the balance down, which is why most cards now add the interest to the minimum. The fixed plan pays your fixed amount, or the minimum when the minimum is larger.

Check yourself

  1. A card’s minimum is 1% of the balance plus the month’s interest, or $35, whichever is more. The balance is $3,000 at 24% APR. Find the first minimum and how much of it lowers the balance.
    Answer

    Interest: $3,000 × 0.24 / 12 = $60. Minimum: $30 + $60 = $90, of which only $30 lowers the balance. Paying only the minimum takes 150 months (12 years 6 months) and $4,441.65 of interest; a steady $120 a month takes 36 months and $1,200.37.

  2. A statement shows $4,500 at 22.99% APR. What payment clears it in 36 months, and what is the total interest?
    Answer

    i = 0.2299 / 12, so P = 4,500i / (1 − (1 + i)−36) = $174.17; =PMT(22.99%/12, 36, −4500). Thirty-six payments of $174.17 come to $6,270.12, so the interest is about $1,770.12.

  3. Same $4,500 at 22.99%, paying $150 a month. How long does it take, and what is the interest? Compare with the minimum (1% plus interest, $25 floor).
    Answer

    =NPER(22.99%/12, −150, 4500) = 45.06, so 46 months and $2,258.76 of interest. Paying only the minimum takes 222 months (18 years 6 months) and costs $7,531.18 of interest, more than the $4,500 borrowed.

  4. Load the $5,500 example (a flat 2% minimum at 21.99%). Why does the minimum plan take so long?
    Answer

    The monthly rate is about 1.83%, so a 2% minimum lowers the balance by only about 0.2% of the new balance a month. It takes 861 months, almost 72 years, and $40,289.82 of interest. The steady $125 takes 91 months and $5,799.34.

A bit of history: Charge cards were once a merchant’s convenience for good customers. In 1958 a California bank mailed out tens of thousands of cards that let holders carry a balance from month to month at interest, and the revolving bank credit card was born.

“Owe no man any thing, but to love one another.” — Romans 13:8