Unit 3 · Level 1 · Debt, honestly
Compounding, running the other way
Compounding is not on anyone's side. It takes a balance and a rate, and it grows the balance. When the balance is your savings, that feels wonderful. When the balance is what you owe on a card, the exact same maths grows the number every single month. There is a shortcut for how fast, called the rule of 72: divide 72 by the rate and you get the rough number of years until the balance doubles. A card at 22% grows faster than almost anything you could realistically buy with the money.
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What you get asked
Why does an unpaid credit card balance grow faster than most things people own?
Two things stack up. The rate is high, often 18% to 26%, and it is applied every statement rather than once a year.
You owe €2,000 on a card charging 24% a year and you pay nothing for three years. Use the shortcut. Roughly what is the balance then, in euros?
Around €4,000. Seventy two divided by twenty four is three, so three years is one full doubling. You bought nothing new, and you owe twice what you borrowed.
Unpaid interest is added to the balance, so next statement you are charged interest on last month's ___ as well as on what you spent.
That is the difference between simple and compound interest. Once interest joins the debt it stops being interest and becomes principal, indistinguishable from anything you actually bought.
Use the rule of 72: match each borrowing rate to how fast the debt doubles
The rate is not a detail, it is the whole clock. A store card doubles what you owe four and a half times faster than a student loan does.
You hold €3,000 in a savings account paying 5% and you owe €3,000 on a card charging 22%. What does the arithmetic say?
Clearing a 22% debt is a guaranteed 22% return, and no savings account offers that. The usual exception is a small emergency buffer, which buys you the option not to borrow again. That is arithmetic, not advice. 🐜
The rest of this unit
Compounding runs in both directions, and on a credit card it runs at you.