How this is worked out
The payment comes from the standard amortization formula:
M = P · r(1+r)ⁿ ÷ ((1+r)ⁿ − 1)
where P is the amount borrowed, r is the annual rate divided by twelve and n is the number of monthly payments. Each month, interest is charged on the outstanding balance and whatever is left of the payment reduces the principal — which is why the early payments are mostly interest and the split shifts steadily as the balance falls.
An origination fee is added to the total cost of borrowing rather than to the payment, because most lenders deduct it from the amount disbursed. If yours is financed into the loan instead, add it to the amount borrowed and leave the fee field at zero.
The refinance comparison runs the same formula twice — once on the remaining balance at the current rate and term, once at the new rate and term — then adds the switching cost to the new figure. Break-even is the switching cost divided by the monthly saving. The lifetime difference is the number that decides it.
A worked example
- Amount borrowed
- $30,000
- Rate / term
- 7.5% over 5 years
- Monthly payment
- $601.14
- Total interest
- $6,068.31
- Origination fee
- $0
- Total cost of borrowing
- $6,068.31
- Total repaid
- $36,068.31
A lower monthly payment is not a cheaper loan
This is the mechanism behind nearly every bad car loan in America, and it is worth stating plainly: stretching the term lowers the payment and raises the total cost, every single time. A $30,000 loan at 7.5% costs $6,068 in interest over five years and $9,986 over eight. The payment falls from $601 to $417, which is the number the finance office will show you.
Eighty-four and ninety-six month auto loans exist because $417 sounds affordable and $601 does not. What they buy is a longer period during which you owe more than the car is worth — a car depreciates fastest in the first three years while an eight-year loan barely touches the principal in the same period.
Negotiate the price of the car, then the rate, and only then discuss the term. Any conversation that starts with "what monthly payment are you looking for?" is a conversation about the dealer’s margin, not your budget.
APR includes the fee; the interest rate does not
Under the Truth in Lending Act, lenders must disclose an annual percentage rate that folds mandatory fees into a single comparable figure. A 6.9% loan with a 5% origination fee has an APR well above 9%, and the APR is the honest number.
Personal lenders in particular deduct origination fees from the disbursement. Borrow $30,000 with a 5% fee and $28,500 reaches your account while you repay the full $30,000 with interest. If you need $30,000 in hand you must borrow more, which increases the fee, which increases the amount you need to borrow.
Enter the APR in the rate field and leave the fee at zero, or enter the interest rate and the fee separately. Do not do both — you will double-count.
Refinancing: three questions, in order
Does the new rate beat the old one after fees? Do you keep the loan long enough to pass the break-even point? And does the total cost go down, not just the payment? The comparison panel above answers all three, and it flags the case where the payment falls but the loan costs more overall — which is what most refinance offers actually are.
For auto loans specifically, refinancing works best in the first two years, while the balance is large enough for a rate reduction to matter. Credit unions are usually the sharpest option, and a genuine improvement in your credit score since the original purchase is the strongest reason to look.
Watch for prepayment penalties on the existing loan, and for precomputed interest — a small number of subprime auto lenders still use a Rule of 78s structure that front-loads interest so that early payoff saves far less than a simple-interest loan would.
What an extra $100 a month does
On the worked example, an extra $100 a month clears the loan ten months early and saves $1,050 in interest. Every extra dollar goes straight to principal, which stops it accruing interest for the whole remaining term.
Two things to confirm first. That your lender applies extra payments to principal rather than treating them as an advance on next month’s payment — many do the latter by default unless you say otherwise. And that there is no prepayment penalty, which is rare on federally regulated auto loans but not unheard of on personal loans.
Assumptions and sources
- Amortization formula
- Standard annuity formula, applied monthly. Verified in tools/test/finance.mjs against published amortization tables.
- APR disclosure
- Truth in Lending Act (Regulation Z) requires APR disclosure including mandatory finance charges. checked 2026-08
- Origination fee range
- Typically 1–8% of the amount borrowed on personal loans; usually deducted from the disbursement. You enter your own figure.
- Rate
- You enter your own figure. Auto and personal loan rates depend heavily on credit score, term and lender type.