Learn · Money, in practice
Debt, and the arithmetic of paying it off
The interest rate does most of the work. Everything else is a question about temperament.
Debt is future income committed in advance. The cost of that commitment is the interest rate, and the rate is the number that should drive almost every decision about which debt to clear first.
The arithmetic is not complicated
Wealth Signal calculation
Paying off a debt is a guaranteed return equal to its rate
Clear a balance charging 18% and you have saved yourself 18% a year, certainly, with no market risk. Very few investments offer a guaranteed 18%. This is why high-rate debt is usually addressed before investing — not as a moral point, but as a comparison of returns.
Clear a balance charging 18% and you have saved yourself 18% a year, certainly, with no market risk. Very few investments offer a guaranteed 18%. This is why high-rate debt is usually addressed before investing — not as a moral point, but as a comparison of returns.
That comparison also explains why low-rate debt is treated differently. A loan at 3% is a much weaker case for early repayment, because the guaranteed 3% saved competes with alternatives that may do better.
Two orderings
- Highest rate first. Mathematically optimal. Pays the least interest in total.
- Smallest balance first. Mathematically worse, and it clears individual debts faster, which some people find they can actually sustain.
Interpretation
The optimal plan you abandon is worse than the adequate plan you finish
The arithmetic favours the highest rate without qualification. The evidence on human behaviour is less tidy, and a method that keeps someone engaged can outperform a better method they stop following in month four. Both facts are true and they point different ways.
The arithmetic favours the highest rate without qualification. The evidence on human behaviour is less tidy, and a method that keeps someone engaged can outperform a better method they stop following in month four. Both facts are true and they point different ways.
What the rate does not capture
- Secured against what. A debt secured on your home has a consequence for non-payment that an unsecured one does not, whatever the rates say.
- Whether the rate can change. A fixed rate is a known obligation; a variable one is an unknown that grows when rates rise.
- What it bought. Borrowing against an asset that holds value is a different position from borrowing for consumption that is already gone.
The one that catches people
Minimum payments on revolving credit are structured so that paying only them extends the debt for an extraordinarily long time, because most of each payment services interest rather than reducing the balance.
Interest compounds against you in exactly the way it compounds for you when investing. See compound growth — the mechanism is identical and the direction is reversed.
Education, not advice. These lessons explain how things work. They do not tell you what
to buy, and Wealth Signal does not publish recommendations. Full disclaimer.