Loan Payment Formula: Calculate Your Monthly Payment
The exact formula behind every loan payment, a worked example, and the three levers — rate, term, principal — that change what you pay.
Every fixed-rate loan — car, personal, student, mortgage — uses the same payment formula. Once you can read it, you can sanity-check any lender's quote, compare offers on equal footing, and see exactly why a longer term feels cheaper but costs more.
The formula
M = P × [ r(1 + r)^n ] ÷ [ (1 + r)^n − 1 ]
Where:
- M — monthly payment
- P — principal (amount borrowed)
- r — *monthly* interest rate (annual rate ÷ 12, as a decimal)
- n — total number of payments (years × 12)
The two most common errors happen before any math: forgetting to divide the annual rate by 12, and using years instead of months for n.
A worked example
Borrow $25,000 for a car at 7% annual interest over 5 years:
- P = 25,000
- r = 0.07 ÷ 12 = 0.005833
- n = 60
M = 25,000 × [0.005833 × (1.005833)^60] ÷ [(1.005833)^60 − 1] ≈ $495 per month
Total paid: 495 × 60 = $29,700. Total interest: $4,700. That last number is the one worth staring at — the payment feels manageable, but the interest is the true price of borrowing.
The three levers
| Change | Monthly payment | Total interest |
|---|---|---|
| Base: $25k, 7%, 5 yr | $495 | $4,700 |
| Rate drops to 5% | $472 | $3,307 |
| Term extends to 7 yr | $377 | $6,690 |
| Borrow $20k instead | $396 | $3,761 |
Notice the trap in row three: stretching the term cuts the payment by $118/month but adds nearly $2,000 in interest. Lenders lead with the monthly figure because it's the flattering one. Always compare loans on total interest, not payment size. The Loan Calculator shows both, plus the full payoff schedule.
Where each payment goes
A fixed payment doesn't split evenly between interest and principal. Early payments are interest-heavy: in month one of our example, $146 of the $495 is interest (25,000 × 0.005833) and only $349 reduces the balance. By the final year, the ratio flips. This front-loading is why paying extra early in a loan's life saves disproportionately — the mechanics are unpacked in How mortgage amortization actually works, and the same math drives the Mortgage Calculator.
Extra payments: small amounts, outsized effect
Add $50/month to the example loan and it pays off about 6 months early, saving roughly $500 in interest. Extra payments go entirely toward principal, which shrinks the base that every future month's interest is computed on. Two practical notes: confirm your lender applies extras to principal (not next month's payment), and check for prepayment penalties — rare on auto loans, occasional elsewhere.
FAQ
How do I calculate a loan payment by hand? Convert the annual rate to monthly (÷12), count total payments (years×12), then apply M = P[r(1+r)ⁿ]/[(1+r)ⁿ−1]. A spreadsheet's PMT function or the Loan Calculator does the same thing instantly.
What's the difference between APR and interest rate? The interest rate prices the borrowing itself; APR folds in mandatory fees (origination, some closing costs), making it the better number for comparing offers. APR ≥ rate, always.
Does this formula work for mortgages? Yes — a fixed-rate mortgage is the same amortized loan with a longer n. Property tax, insurance, and PMI ride on top of the principal-and-interest payment the formula gives you.
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*Compare any two loan offers side by side with the free Loan Calculator — payment, total interest, and full schedule, no sign-up.*
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