One Formula, Three Questions
Every fixed-rate repayment is governed by the same equation, rearranged depending on what you are missing:
Payment = P × i / (1 − (1 + i)−n)
Solve for the payment when the amount and term are known; for n when the payment is known; for P when you know what you can afford each month. All three are the same relationship read in different directions.
The Term Is the Expensive Variable
$25,000 at 8.5%:
| Term | Monthly payment | Total interest | Total repaid |
|---|---|---|---|
| 12 months | $2,180.49 | $1,166 | $26,166 |
| 24 months | $1,136.39 | $2,273 | $27,273 |
| 36 months | $789.19 | $3,411 | $28,411 |
| 48 months | $616.21 | $4,578 | $29,578 |
| 60 months | $512.91 | $5,775 | $30,775 |
| 84 months | $395.91 | $8,257 | $33,257 |
Extending from 36 to 84 months halves the payment and more than doubles the interest. The payment is what you feel; the interest is what it costs.
Interest Front-Loading
In an amortised loan the payment is constant while its composition shifts. Early payments are mostly interest, because interest is charged on a large balance; later payments are mostly principal. On a 60-month loan at 8.5%, the first payment is about 35% interest and the last is under 1%.
This is why an extra payment early is worth far more than the same payment late, and why selling a car three years into a five-year loan so often leaves negative equity.
Affordability Runs Backwards
Deciding what you can pay each month and solving for the loan amount is more disciplined than choosing a purchase and stretching the term to fit. It also exposes the real trade: at $500 a month and 8.5%, four years buys $20,290 and seven years buys $31,573 — but the seven-year option costs $6,400 more in interest for $11,283 more of car.
Frequently Asked Questions
Why does my balance barely move at first?
Because early payments are mostly interest. On a long loan it can take a third of the term before half of each payment reaches the principal.
Should I take the longest term available?
Only if the cash flow is genuinely needed and there is no prepayment penalty — then you can take the long term for safety and pay it like a short one.
How do extra payments work?
Applied to principal, they reduce the balance immediately and remove every future interest charge that principal would have generated. Instruct the lender explicitly to apply extra to principal, not to the next payment due.