Editorial guide
Personal and auto loans look simpler than mortgages — smaller balances, fewer years — but the pricing tricks are subtler, and a one-point rate or a hidden origination fee can cost more than the monthly difference suggests. This guide unpacks the amortisation the calculator uses, how term stretches trade payment relief for interest, and how to read fees so you compare offers on the same basis.
How loan payments are calculated
Like a mortgage, a closed-end installment loan converts a lump sum into equal monthly payments that retire the debt to zero by the last due date. The maths is identical; only the scale changes:
M = P · r · (1+r)n / ((1+r)n − 1)
- P — amount financed. If the dealer quotes $28,000 with $2,000 down, P = $26,000; fees are separate in our default view. Financing fees means P includes them.
- r — monthly rate = APR/12. An 8.5% APR is 0.708% a month — each month you pay 0.708% of the remaining balance as interest.
- n — payments = months. 60 means 60 equal cheques; early termination still owes the remaining balance by definition.
- M — monthly principal & interest. Total interest = M·n − P; total cost = M·n + fees (if fees not financed).
For $25,000 at 8.5% over 60 months: r≈0.007083, (1+r)60≈1.525, M=25,000·0.007083·1.525/0.525≈$513. Month 1 interest is $25,000×r≈$177, principal ≈$336; by month 30 interest is ~$94, principal ~$419 — same M, but the split has inverted. The bar chart visualizes that front-loading: month-one amber (interest) is tall, month-twelve amber is shorter. The donut condenses the whole loan: dark principal you keep as the asset, amber interest you pay for time, grey fees if any.
Three subtleties keep the calculator reconcilable to a Truth in Lending disclosure: (1) monthly compounding with each payment assumed on schedule; (2) interest = starting balance × r, principal = min(balance, M−interest); (3) fees are not amortized into r unless you finance them — the card shows a heuristic effective APR when fees >0, because Reg Z APR would amortize fees into the rate, adding roughly (fees/P)/years to the nominal.
Term comparison: the price of a lower payment
Term is the most common lever dealers pull after price. Longer lowers the cheque today but raises total cost and often the rate itself.
| Term | Rate* | Monthly | Total interest | Total paid (no fees) |
|---|---|---|---|---|
| 36 months | 7.5% | $778 | $2,992 | $27,992 |
| 48 months | 8.0% | $609 | $4,252 | $29,252 |
| 60 months | 8.5% | $513 | $5,769 | $30,769 |
| 72 months | 9.0% | $448 | $7,275 | $32,275 |
| 60 months + $300 upfront fee | 8.5% | $513 | $5,769 + $300 | $31,069 |
*Rate tiers illustrate common lender pricing: longer terms carry +0.5% per year. $25,000 principal, P&I only. Rounded.
Two patterns jump out. First, monthly cost is not linear with term: doubling from 36 to 72 months cuts payment only 42%, because interest accrues for 36 more months. Second, the interest step is steepest at the long end: 60→72 months saves $65/mo but costs $1,506 more — about $23 of interest per dollar of monthly relief, the worst trade in the table. The sweet spot is usually the shortest payment you can afford without sacrificing a 3-month emergency fund.
Fees twist the ranking when terms differ. A $500 origination fee on a 36-month quote is effectively +1.33% APR amortized, but only +0.40% on a 72-month quote, so a longer term can look cheaper by APR even while costing more total dollars. Always compare both the monthly and the total paid rows.
Fees, APR and what the rate really means
Rate shopping fails when fees hide in the fine print. Lenders may quote a low APR but charge an origination fee (1–8% for personal loans), a dealer documentation fee ($100–$800), or require a product such as GAP insurance. The calculator keeps fees outside P so the monthly reflects the note rate, and total cost adds fees on top — transparent for comparison. To see APR truthfully, either finance the fees (increase P) or note the effective APR hint when fees >0.
Simple interest vs precomputed matters less often now, but worth checking: simple interest — the market standard — charges balance×APR/365 each day and lets early or extra payments save interest immediately. Precomputed or Rule of 78s loans pre-assign interest and penalize early payoff; they are largely illegal for >61 months in many states and banned for US federal student and most mortgages, but still appear in some subprime auto paper. Ask “is this simple interest, fully amortizing, no prepayment penalty?” If the answer is not yes, walk.
Practical guardrails when you use the loan page before signing: (1) run the loan amount you actually finance, not the sticker price; (2) slide fees to see APR impact; (3) stress the payment at +2% — if you would need to refinance to afford the payment, the margin is too thin; (4) check the amortisation preview — if you sell the car in year two, the balance column is what you must clear to be free. The cheapest loan is not the lowest monthly; it is the lowest total cost for a payment that leaves breathing room.
Methodology and assumptions
- Product: Fixed-rate, fully amortizing, monthly compounding, level payments. Not interest-only, balloon, or precomputed.
- Scope: P&I plus optional upfront fees. Excludes sales tax, title, registration, insurance, and late fees. Add those from your Loan Estimate or purchase order.
- Formula: M = P·r·(1+r)n/((1+r)n−1), r=APR/12, n=months, P=loan amount. Total interest = Σ interest per month; total paid = M·n + fees. Balance floored at $0, cents rounded.
- Schedule: Month 1 balance = P. Interest = balance×r. Principal = min(balance, M−interest). Balance decremented; loop to 0. Table shows months 1–12 plus final row; full length is actual months (usually n unless extra payments).
- Payoff date: Today plus n calendar months via date arithmetic. For exact maturity, anchor to disbursement plus first-payment lag.
- Fees: Default view: fees are incremental cost, not part of balance. Financed view: add fees to P and set fees input to 0. Heuristic effective APR ≈ nominal + (fees/P)/years×0.9 when fees >0.
- What would shift a disclosure: Daily accrual timing, odd-days interest, state usury fee caps, dealer markup (buy rate vs contract rate), and prepayment penalties all nudge the lender's APR from the note rate shown. Use the note rate here to price the deal, then compare APRs on Loan Estimates.
The fastest way to use this page at the dealership: set amount financed after down payment, try the quoted APR at the salesman's term, add documentation fees, and note the total cost. Then toggle one term shorter to see the real price of stretching.