Machine 1: amortized installment (the good kind)
One formula sets a payment that lands the balance on zero at the last month — $396 on a $20,000/60-month/7% car loan. Interest each month = rate ÷ 12 × current balance, so every extra dollar of principal removes its own future interest. This is the machine the amortization guide dissects, and it's why extra payments punch far above their weight.
Machine 2: revolving compound (the card)
No fixed schedule, daily accrual, and interest capitalizes — unpaid interest earns interest. There's no "term" to shorten; the only variables are your payment and the APR. The escape mechanics live in how card interest works and the payoff calculator.
Machine 3: precomputed/Rule-of-78s (the trap to screen for)
A shrinking minority of auto and personal loans compute total interest up front by schedule; pay early and the "earned" interest barely shrinks (Rule-of-78s front-loads it further — banned for longer terms federally, restricted in many states, but not extinct). Screening question before signing: "Is this simple interest with no prepayment penalty, and are extra payments applied to principal?" Anything but a clean yes is a red flag worth a different lender.
Same APR, different machines, different strategy
- Amortized loan: extras work; target the highest-rate loan first (method guide).
- Card: extras work even harder (compounding avoided), and rate cuts (transfer/consolidation) multiply the effect.
- Precomputed: extras mostly don't work — refinance out to an amortized loan instead (auto refi calculator), which converts the machine itself.
Know the machine, and the right move usually picks itself.