A $6,000 card balance at 19.99 per cent. The first month's interest is $99.95 no matter what you pay, because interest is charged on the balance before your payment lands.
What the payment decides is everything after that. At $120 a month the balance takes 108.3 months to clear, about nine years, and costs $6,996.20 in interest. At $300 a month it clears in 24.5 months and costs $1,358.14.
Why the curve is so steep
Paying $120 against $99.95 of interest leaves $20.05 coming off the balance. Almost the entire payment is rent on money you have already spent. Because the balance barely moves, next month's interest is barely smaller, and the process repeats.
Raise the payment to $300 and $200.05 comes off the balance in the first month, ten times as much. The balance falls faster, so the interest charge falls faster, so more of each subsequent payment attacks the principal. The effect accelerates.
The middle of the range
The steepest gains come at the bottom of the range, where the payment is closest to the interest charge:
- $120 a month: 108.3 months, $6,996.20 interest
- $200 a month: 41.9 months, $2,385.00 interest
- $250 a month: 30.9 months, $1,724.85 interest
- $300 a month: 24.5 months, $1,358.14 interest
Going from $120 to $200 saves $4,611.20. Going from $250 to $300 saves $366.71. The same $50 or $80 buys far more when the payment is small, because that is where the ratio of interest to principal is worst.
Why minimum payments are structured that way
A minimum payment is usually set as a small percentage of the balance with a floor, which means it falls as the balance falls. Paying exactly the minimum every month is close to the $120 case above: it is designed to clear the debt eventually, and eventually is doing a great deal of work in that sentence.
The practical response is to fix the payment in dollars rather than let it track the balance. Once set, it does not shrink as the balance does, so the surplus over the interest charge grows every month on its own.
Run your own balance and rate through the credit card payoff calculator. If several debts are involved, the debt payoff strategy calculator compares the two common ways to order them.