Auto-loan amortization, properly derived.

§1.1The amortization formula

For a fixed-rate auto loan with principal P, monthly rate r (= APR / 12), and n monthly payments, the level monthly payment is:

PMT = P · r(1 + r)ⁿ / [(1 + r)ⁿ − 1]

Each monthly payment is constant. What changes month to month is the split between interest and principal: in early months, most of the payment is interest; in late months, most is principal. The mechanics: each month’s interest is the outstanding balance times the monthly rate; whatever is left of the level payment goes to principal.

§1.2Worked example: $25,000 at 7 % over 60 months

P = $25,000, APR = 7 %, monthly rate = 0.583 %, n = 60. PMT = 25,000 × 0.005833 × (1.005833)⁶⁰ / ((1.005833)⁶⁰ − 1) = $495.03/month. Total of payments: $29,701.80. Total interest: $4,701.80.

The first month’s payment splits: interest = 25,000 × 0.005833 = $145.83. Principal = $495.03 − $145.83 = $349.20. Closing balance: $24,650.80.

The last month’s payment (month 60) splits roughly: interest ~$2.86, principal ~$492.17. The same $495 covers different things at the start and end of the loan.

§1.3Front-loaded interest and the early-payoff implication

By month 20 of a 60-month loan, you’ve made 20/60 = 33 % of the scheduled payments by count, but you’ve paid down only about 28 % of the principal. The interest portion is concentrated in the early months because the outstanding balance is high; principal paydown accelerates as the balance falls.

Practical implication: an early payoff (paying off the entire balance in, say, month 30) saves the remaining future interest, which is a much smaller fraction of total interest than 30/60 of the schedule suggests. Of the $4,702 lifetime interest in our example, approximately $3,720 is paid in the first 30 months and only $982 in the last 30. Pay off in month 30 and you save $982, not $2,351. Worth doing if the cash is otherwise idle, less compelling if the cash earns a better return elsewhere.

§1.4Refinancing implications

Refinancing replaces the existing loan with a new loan, typically at a lower APR if your credit has improved or if rates have fallen since origination. Two factors govern whether refinancing is worth it:

1. The interest savings. Equal to the difference between the remaining-interest schedule on the existing loan and the total interest on the new (lower-APR) loan over the new term.
2. The transaction cost. Auto loan refinancing typically has a small transaction cost ($0–$300 in document fees), much less than mortgage refinancing.

Refinancing in months 1–24 of a loan typically produces meaningful interest savings because most of the original loan’s interest is still ahead of you. Refinancing in months 48–60 of a 60-month loan rarely pays off because most of the interest is already paid; the remaining schedule is mostly principal.

§1.5Bi-weekly payments

Some auto-loan servicers offer bi-weekly payment plans: half the monthly payment paid every two weeks. The mechanic produces 26 half-payments per year, which equals 13 monthly payments — one extra annual payment without the borrower noticing. On a 60-month loan, this typically shaves 4–6 months off the schedule and saves a corresponding fraction of interest.

The catch: many servicers charge a setup fee ($150–$400) for the bi-weekly programme. The math you can replicate at no cost: simply divide your monthly payment by 12 and add that amount to each monthly payment as “additional principal.” Same accelerated-payoff effect, no setup fee. Check that your servicer applies extra principal payments to the loan correctly — some apply to future installments rather than to current principal, which doesn’t accelerate payoff at all.

§1.6The Rule of 78s historical artifact

Some older or sub-prime auto loans use the “Rule of 78s” (sum-of-digits) interest computation rather than standard amortisation. Under Rule of 78s, the interest portion of each payment is front-loaded more aggressively than under standard amortisation, which produces a substantial penalty for early payoff (the borrower has “earned” less interest credit than they expected). The CFPB and most state regulators have constrained the use of Rule of 78s on new auto loans, but legacy loans on the books may still use it. If your loan agreement references “Rule of 78s,” “sum of digits,” or similar, the early-payoff math is different and worse than the standard amortisation in this calculator.

§1.7The trade-in-during-loan calculation

If you trade in the vehicle before the loan is paid off, the relevant question is whether the trade-in value exceeds the outstanding balance. The outstanding balance at month m on a fixed-rate amortising loan is:

Balance(m) = P · [(1 + r)ⁿ − (1 + r)^m] / [(1 + r)ⁿ − 1]

For our $25,000 / 7 % / 60-month loan, the month-30 balance is approximately $13,300. If the trade-in value at month 30 is $14,500, you have $1,200 of positive equity. If the trade-in is $11,000, you have $2,300 of negative equity that needs to be either paid in cash or rolled into the next loan. The trade-in equity page covers the rollover mechanics.