Loan Payment Calculator
Compute the periodic payment for a fully amortising fixed-rate loan from the principal, annual interest rate, term in years, and payment frequency. Returns the constant payment that pays off both principal and interest over the loan term.
Last updated: May 2026
Compare with similar
About this calculator
The formula is the standard amortising-loan payment: PMT = P × (r × (1+r)^n) / ((1+r)^n − 1), where P is the loan principal, r is the periodic interest rate (annual_rate / frequency), and n is the total number of payments (years × frequency). Periodic rate r equals the annual rate divided by payment frequency: for an annual rate of 6.5% and monthly payments (frequency 12), r = 0.065/12 ≈ 0.005417. The frequency input options are 12 (monthly), 26 (bi-weekly), and 52 (weekly). Bi-weekly payments at half the monthly amount (so 26 × half-monthly = 13 monthly equivalents) shorten the loan and save total interest substantially; this is the math behind common 'bi-weekly mortgage hack' advice. Edge cases: if rate is zero, the formula divides 0 by 0; the correct interest-free payment is simply principal / total payments, which the formula does not handle. Very long terms or very low rates can produce floating-point precision issues but for typical mortgage and consumer-loan amounts the formula is robust. The formula assumes fixed rate; for variable-rate loans (ARMs), the payment recalculates when the rate resets, often producing payment shock. It also assumes no fees, no prepayment penalty, and that you pay exactly on schedule — real loans add origination fees, mortgage insurance, escrow for taxes/insurance, and may charge prepayment penalties on early payoff. Use this calculator for back-of-envelope budgeting; for actual loan decisions use the lender's amortisation schedule with all fees included.
How to use
Example 1 — 30-year mortgage at 6.5%, monthly payments. principal $250,000, rate 6.5%, years 30, frequency 12. Step 1: periodic rate r = 6.5/100/12 ≈ 0.0054167. Step 2: total payments n = 30 × 12 = 360. Step 3: (1+r)^n = (1.0054167)^360 ≈ 7.0179. Step 4: numerator = r × 7.0179 = 0.0054167 × 7.0179 ≈ 0.038014. Step 5: denominator = 7.0179 − 1 = 6.0179. Step 6: PMT = 250,000 × 0.038014 / 6.0179 ≈ 250,000 × 0.006317 ≈ $1,579.23. Verify: standard mortgage tables for a $250k 30-year 6.5% loan list the monthly payment at $1,580.17 — within rounding of the result ✓. Over the full term you pay 360 × $1,579 ≈ $568,440, of which ~$318,440 is interest. Example 2 — 5-year auto loan at 8%, weekly payments. principal $30,000, rate 8%, years 5, frequency 52. Step 1: r = 8/100/52 ≈ 0.001538. Step 2: n = 5 × 52 = 260. Step 3: (1+r)^n = (1.001538)^260 ≈ 1.491. Step 4: numerator = 0.001538 × 1.491 ≈ 0.002294. Step 5: denominator = 0.491. Step 6: PMT = 30,000 × 0.002294 / 0.491 ≈ 30,000 × 0.004672 ≈ $140.16/week. Verify: monthly equivalent ≈ $140.16 × 52/12 ≈ $607.36/month; standard amortisation calculators give a monthly payment of about $608 for the same loan — matches within rounding ✓. Weekly payments slightly reduce total interest versus monthly because principal is paid down faster on average.
Frequently asked questions
Why do bi-weekly payments save so much interest?
26 bi-weekly payments per year equal exactly 13 monthly equivalents (since 26 × $X equals 13 × 2$X, where 2$X is what you'd pay per month with the same dollar amount per payment). So a bi-weekly schedule is equivalent to making 13 monthly payments per year instead of 12 — an extra full payment annually that goes entirely to principal reduction. On a 30-year mortgage this typically cuts 4–6 years off the term and saves tens of thousands in interest, depending on rate. The same effect can be achieved with monthly payments by paying 1/12th extra each month or one extra payment per year; you don't need a bi-weekly mortgage product. Some lenders charge fees to set up automatic bi-weekly schedules — these fees can offset the benefit; you can usually achieve the same effect for free by self-managing extra principal payments. Verify with your lender that extra payments go to principal rather than being held as 'overpayment' applied later, which doesn't accelerate payoff.
What's the difference between APR and the interest rate input here?
The 'rate' input is the nominal annual interest rate, which is what's used in the math to compute periodic payments. The Annual Percentage Rate (APR) is the effective annual cost of the loan including most fees (origination, discount points, mortgage insurance, prepaid interest) but excluding some (homeowners insurance, recording fees, third-party closing costs). APR is typically 0.1–0.5 percentage points higher than the nominal rate for mortgages with origination costs. Federal law in the US (Truth in Lending Act) requires lenders to disclose APR alongside the rate to enable apples-to-apples comparison. For this calculator's payment computation, you should use the nominal rate, not the APR — the APR is a disclosure metric, not the rate at which interest accrues. If you want to compare two loan offers with different fees, computing total cost of ownership (down payment + all payments + closing costs minus tax benefit of mortgage interest) is more rigorous than comparing APRs.
How does this differ from interest-only or balloon mortgages?
This calculator computes payments for a fully amortising loan: each payment reduces principal, and the loan is paid off at maturity. Interest-only loans charge only interest for an initial period (often 5–10 years), leaving the full principal due at the end of the interest-only period — payments are lower initially but balloon afterwards. Balloon mortgages similarly have a fixed term during which you make amortising payments based on a longer-term schedule (e.g., 30-year amortisation), then the remaining principal is due as a lump sum at the balloon date (often 5–10 years). Both are riskier than fully amortising loans because they assume you'll refinance, sell, or have lump-sum cash available — a strategy that backfires when rates rise or housing markets decline. The 2008 financial crisis was driven partly by interest-only and option-ARM mortgages whose payments reset upward sharply, causing widespread defaults. This calculator assumes the simple, safe fully amortising structure; for interest-only or balloon products, use specialised calculators that model the payment-shock or balloon-payment risk.
What are the common mistakes when computing loan payments?
The biggest mistake is forgetting to convert the annual rate to a periodic rate — using 6.5 directly instead of 6.5/100/12 gives nonsensical payments. The second is omitting taxes, insurance, mortgage insurance (PMI), HOA fees, and maintenance costs when budgeting; the payment from this formula is principal+interest only (PI), but the total monthly housing cost (PITI + maintenance + HOA) is often 30–60% higher. The third is comparing nominal rates without considering points, origination fees, and other costs that vary across lenders — use APR or a total-cost comparison. People also forget that fixed-rate loan payments don't change over time, but property taxes, insurance, and maintenance do — so PI may stay constant while total housing cost rises with inflation. Adjustable-rate loans (ARMs) re-amortise when rates reset, often producing payment shock — this calculator assumes fixed rate. Finally, prepayment penalties (rare on US residential mortgages now, common in some commercial and consumer loans) can offset the benefit of paying extra principal; check the loan terms before accelerating payoff.
When should I not use this calculator?
Do not use it for variable-rate (ARM) or step-rate loans, where the payment changes when the rate resets — use ARM-specific calculators that model reset risk. It is not appropriate for interest-only or balloon mortgages, which have unique payment structures and risks that simple amortisation doesn't capture. Do not use it for credit-card debt or revolving credit, where the minimum payment is usually a small percentage of the balance and the payoff time depends on payment behaviour, not a fixed term. It is not suitable for total cost of ownership decisions — add property taxes, insurance, PMI, HOA fees, maintenance (1–2% of home value annually), and the opportunity cost of the down payment to compute the real cost of homeownership. The formula returns zero for zero-rate loans (division by zero); for interest-free loans (rare), use principal / total payments directly. For loans with origination fees, discount points, or other upfront costs, compare APR rather than nominal rate. Finally, for actual loan decisions consult a licensed mortgage broker or financial advisor; the calculator is a budgeting tool, not a financial-advice tool.