Credit cards: the minimum-payment trap.
Revolving credit, no fixed term. The monthly math is deceptively simple — interest portion + principal portion — but minimum payments at 24% APR can trap a $5,000 balance for decades.
You owe $5,000 on a credit card with a 24% APR. You decide to pay the minimum each month — let's say $100. The monthly periodic rate is 24%/12 = 2%. So this month the card charges:
interest = $5,000 × 0.02 = $100
You pay $100. The interest charge was $100. Your balance after this month: $5,000. You did not move it one cent. If you keep paying $100 forever, you will keep owing $5,000 forever — and the bank will collect $1,200 a year, every year, from you. That's the minimum-payment trap, and the math is what this lesson teaches.
Each month, two simple lines.
One credit-card statement on a $5,000 balance at 24% APR with a $200 payment. The interest charged ($100) is computed first, then your payment ($200) is applied. The bottom strip shows your $200 payment split: half went to interest, half to principal.
For one statement period: interest = balance × (r/12), then new balance = balance + interest − payment. The minimum payment is typically 1-3% of balance, often barely covering the interest charge.
Vocabulary you'll see in word problems
- Revolving credit A loan with no fixed term — you can borrow more, pay down, repeat. Credit cards and home-equity lines of credit are the common examples.
- APR (credit card) The annual rate the card charges on unpaid balances. Typical range: 18-29%. Divide by 12 for the monthly periodic rate.
- Minimum payment The smallest payment the card issuer requires each month. Usually 1-3% of balance, plus the interest charged that month. Pays the loan off agonizingly slowly.
- Interest portion The part of your payment that covers the month's interest charge. Computed first; what's left goes to principal.
- Principal portion The part of your payment that actually reduces the balance. Equals payment − interest portion.
$5,000 balance at 24% APR, $200 payment.
"Your credit card balance is $5,000. The card has a 24% APR. This statement period you make a $200 payment. What's your new balance, and how much of your payment went to interest vs. principal?"
Convert APR to a monthly rate.
Credit cards quote APR (annual). For this month's interest charge, you need the monthly rate.
Compute this month's interest charge.
The card charges interest on the current balance, before your payment is applied.
Compute the new balance.
Add the interest charge to the balance, then subtract the payment. Order matters conceptually but not arithmetically.
Split your $200 payment.
Interest portion = the interest charge you just computed. Principal portion = what's left over.
Read the trap.
If you'd paid only $100 (the minimum interest charge), the new balance would be $5,000 + $100 − $100 = $5,000. Same as before. The minimum payment that exactly matches the interest charge keeps the balance frozen forever — which means the bank collects interest from you forever, and you never own the thing you bought.
Three problems. The same two lines, three times.
Balance: $3,000. APR: 18%. Payment this month: $80. What's the new balance?
Continuing from Problem 1: balance is now $2,965, APR still 18%, payment $80 again. What's the new balance after this second statement?
Balance: $1,000. APR: 24%. Payment: $20. What's the new balance after one statement?
Three fast questions before you move on.
Q1. The interest charged on a credit card statement equals...
Q2. New balance after a statement equals...
Q3. If your minimum payment exactly equals this month's interest charge, the balance after the statement...
Why $5,000 at 24% with $100/mo takes 22 years.
The arithmetic that drives the trap: at 24% APR, the monthly periodic rate is 2%. On a $5,000 balance, the first month's interest is $5,000 × 0.02 = $100. If you make a $100 payment, your balance stays at $5,000 forever — you only pay interest, never principal. Pay slightly more, and you slowly chip down. Many cards' minimum payments are designed to be just slightly above the interest charge, so that paying the minimum keeps you in debt for 20+ years even on a relatively small balance.
Next: Student loans — fixed-term amortizing again, but with subsidized vs unsubsidized variants and the "capitalization of accrued interest" wrinkle that the T3 DQ2 preview already hinted at.
Continue to Lesson 05Different angle? Need another rep? These are optional — tap any that look helpful.
Things you should know about your credit card
2024 release. Explains revolving credit, APR, how interest accrues monthly, and the minimum-payment dynamic in plain language.
How Credit Card Interest Is Calculated
Computes daily periodic rate × average daily balance — the actual math behind why the minimum payment barely dents principal at 18-26% APRs.