The three numbers that decide your payment
Every fixed-rate loan payment — car loan, personal loan, student loan, mortgage — is built from the same three inputs. Lenders dress the offer up with fees and fine print, but the core payment math only needs:
- The principal.
The amount you actually borrow, after any down payment is subtracted. - The monthly interest rate.
The annual rate (APR) divided by 12, then divided by 100. A 6.5% APR becomes a monthly rate of about 0.00542. - The number of payments.
The term in years times 12. A 5-year loan means 60 monthly payments.
The payment must be exactly large enough that, after the last one, the balance hits zero. The amortization formula finds that payment.
The amortization formula
In plain language: you multiply the loan amount by the monthly rate, then divide by a factor that depends on the rate and the term. The longer the term, the smaller that divisor gets — which is why stretching a loan lowers the payment but raises the total interest.
Worked example: $25,000 at 6.5% APR for 5 years
Start with the two conversions, then feed the formula.
Payments: 5 × 12 = 60
Payment: 25,000 × 0.0054167 ÷ (1 − (1.0054167)−60) = $489.15
Total paid: $489.15 × 60 = $29,349.22
Total interest: $29,349.22 − $25,000 = $4,349.22
Answer: the monthly payment is $489.15, and the loan costs $4,349.22 in interest over its life.
Why early payments are mostly interest
Each payment does two jobs. First it pays that month's interest — the remaining balance times the monthly rate. Whatever is left over reduces the balance. In month one of the example above, the interest is $25,000 × 0.0054167 = $135.42, so only $353.73 of the $489.15 touches the principal. By the final month the balance is tiny, so nearly the whole payment is principal.
This is why your first payment and your last payment feel so different even though the amount never changes, and why the total interest depends so heavily on the term: extra months mean extra rounds of interest on a still-large balance.
A quick way to check any lender quote
You don't need the full formula to sanity-check a dealer's or bank's number. Multiply the quoted monthly payment by the number of months, then add any down payment. That total is the lifetime cost of the loan. If the lender's quote doesn't match your multiplication, ask what the difference covers — fees, taxes, or add-ons.
What the formula assumes
The amortization formula describes a plain fixed-rate loan: same rate, same payment, same schedule from start to finish. It does not include property tax or insurance on a mortgage, origination fees, or late penalties. Adjustable-rate loans change the rate mid-stream, so the payment gets recalculated — the formula still applies, just with the new rate and the remaining balance.
What changes when you pay extra
Extra payments go entirely to the principal, skipping the interest line. A smaller balance means less interest next month, which compounds in your favor for the rest of the loan — and the loan ends months or years early. On the $25,000 example, adding $100 a month pays the loan off 11 months sooner and saves $865.44 in interest.
Try it: use the free loan payment calculator for instant results, or the extra loan payment calculator to test what extra payments would save you.