Loan Amortization Calculator
Calculate the periodic payment on an amortizing loan given the principal, annual interest rate, term in years, and payment frequency. Use it for any fully-amortizing fixed-rate loan — mortgage, auto, student, personal — where each payment is the same and the balance reaches zero at the end.
Last updated: May 2026
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About this calculator
The formula is the standard amortizing-loan equation: PMT = P × [r(1+r)^n] / [(1+r)^n − 1], where P is the principal (loan amount), r is the periodic interest rate (annual rate ÷ payment frequency, so for monthly it's annual ÷ 12), and n is the total number of payments (term years × payment frequency). The result is the fixed payment that, applied consistently for n periods, drives the loan balance to exactly zero. Each payment splits between interest (computed on the remaining balance at the start of the period) and principal (everything left after interest); early in the loan the interest share is large because the balance is large, and late in the loan the principal share dominates because the balance has shrunk. This shifting split is what "amortization" means and is the same math whether payments are weekly, bi-weekly, monthly, or quarterly. Higher payment frequency means each individual payment is smaller but you pay slightly less total interest because more frequent payments mean the balance falls a bit faster. Edge cases: a rate of 0% breaks the formula (division by zero); for an interest-free loan, payment is simply P ÷ n. Very short terms (1–2 years) make the payment nearly equal to principal divided by periods because interest has little time to accumulate; very long terms (25+ years for mortgages) push total interest paid above the original principal at typical consumer rates. The formula assumes constant rate, constant payment, and no extra principal payments — real loans with extra payments or rate resets need a more sophisticated amortization schedule.
How to use
Example 1 — 30-year mortgage, monthly payments. Loan principal $400,000, annual rate 6.5%, term 30 years, monthly payment frequency (12). Enter 400000 for Principal, 6.5 for Annual Interest Rate, 30 for Term, and 12 for Payment Frequency. Result: approximately $2,528 per month. Verify: r = 0.065/12 ≈ 0.005417, n = 360; (1.005417)^360 ≈ 7.0145; 400000 × (0.005417 × 7.0145) / (7.0145 − 1) ≈ 400000 × 0.0380 / 6.0145 ≈ $2,528. ✓ Over the life of the loan you pay 2528 × 360 = $910,080 total, including $510,080 in interest — more than the original principal in interest cost. Example 2 — 5-year auto loan, biweekly payments. Loan principal $32,000, annual rate 7.5%, term 5 years, biweekly payment frequency (26). Enter 32000, 7.5, 5, and 26. Result: approximately $295 per biweekly payment. Verify: r = 0.075/26 ≈ 0.002885, n = 130; (1.002885)^130 ≈ 1.4530; 32000 × (0.002885 × 1.4530) / (1.4530 − 1) ≈ 32000 × 0.004191 / 0.4530 ≈ $296. ✓ At biweekly frequency you make 26 payments per year (equivalent to ~$641 monthly), slightly less total interest than equivalent monthly payments would, and you pay off about 2 weeks faster.
Frequently asked questions
What is the difference between amortization and simple interest?
Amortizing loans calculate interest on the declining balance each period; as you pay down principal, the interest portion of each payment shrinks and the principal portion grows, with the total payment held constant. Simple interest loans calculate interest only on the original principal for the full term — so a 5-year simple-interest loan at 10% on $10,000 always charges 10% × $10,000 = $1,000 per year regardless of how much you've already paid. Most modern consumer loans (mortgages, auto, student, personal) use amortizing interest; simple interest mainly survives in short-term consumer loans and in some textbook examples. The amortizing structure is fairer to the borrower in nearly all cases because interest naturally declines with the loan balance; simple interest can produce situations where the borrower has paid significant amounts but still owes the full principal.
How do extra payments affect the loan?
Extra principal payments reduce the loan balance, which in turn reduces all future interest calculations because interest is computed on the remaining balance each period. The compounding effect over time is substantial. On a 30-year $400,000 mortgage at 6.5%, adding just $200 to every monthly payment shortens the loan by about 8 years and saves roughly $200,000 in total interest. Even one extra full payment per year (made via biweekly payment plans or a lump-sum once annually) shortens a 30-year mortgage by 4–6 years. Always confirm with your lender that extra payments are applied to principal (not advancing your next monthly payment due date), and check for prepayment penalties — most modern consumer loans do not charge them, but some older or commercial loans do. Mathematically, extra principal payments earn a guaranteed risk-free return equal to your loan's interest rate, which beats almost any other safe investment.
Why do biweekly payments save interest?
Biweekly payments save interest in two complementary ways. First, you make 26 biweekly payments per year (52 weeks ÷ 2), which equals one extra monthly payment per year compared to a standard 12-monthly-payments schedule — that extra annual payment goes entirely to principal and accelerates payoff by years. Second, the shorter compounding interval (14 days vs. 30 days between payments) means principal reductions happen faster, so each subsequent interest calculation is on a slightly lower balance. The savings are real but modest from the second effect alone (typically a few percent); the much larger effect comes from the extra-payment-per-year mechanism. Most banks that offer "biweekly payment plans" achieve the savings by collecting half a payment every two weeks and applying the equivalent of one full monthly payment to the loan each month, with the extra accumulated half applied to principal annually. Some charge a fee for this service — you can replicate it for free by manually paying an extra 1/12th of your monthly payment each month.
What are the most common mistakes people make with amortizing loans?
The biggest is focusing only on the monthly payment instead of the total cost of borrowing — a longer-term loan with "lower monthly" often costs much more in total interest. The second is confusing nominal interest rate with APR; APR includes fees and is the better comparison. The third is not shopping multiple lenders — rates can vary by 1–3 percentage points between lenders for the same borrower, and savings on a typical mortgage or auto loan from comparison-shopping easily reach $1,000–$10,000. The fourth is rolling existing debt (trade-in car loan, credit-card balance) into a new loan, silently extending repayment and inflating interest. The fifth is missing prepayment penalties on older loans — most modern loans don't have them but some commercial or older consumer loans still do. Finally, people often forget that an amortizing loan's early payments are mostly interest; if you're planning to move or refinance within a few years, you'll have built very little equity, and points or other upfront costs may not pay off.
When should I not use this calculator?
Skip it for variable-rate loans (ARMs, most HELOCs, many private student loans) — the formula assumes a fixed rate, so the payment estimate breaks down when the rate changes. It is the wrong tool for interest-only loans, balloon-payment loans, and reverse mortgages, all of which have very different payment structures. Do not use it for credit cards, which compute a sliding minimum payment as a percentage of the balance — use a dedicated credit-card payoff calculator. It also assumes no fees or insurance are included in the payment; for full PITI on a mortgage (with property tax and insurance), use a dedicated mortgage payment calculator. For loans with irregular payment schedules (skipped payments, deferment periods, graduated repayment), the standard amortization math doesn't directly apply. And for income-driven repayment student loans, federal forgiveness programs change the math entirely — use the federal Student Aid loan simulator instead.