PmtCalcEvery result on this site comes from a small set of standard loan formulas applied the way loan servicers apply them. This page lists those formulas, the assumptions behind them, how we test them, and the rules we follow so the numbers stay neutral.
The payment formula
Mortgages, auto loans, personal loans, student loans and most business loans are fully amortizing: the same payment every period, sized so the last payment brings the balance to zero.
Payment = P × r ÷ (1 − (1 + r)−n)
P is the amount borrowed, r is the annual rate divided by the number of payments per year (12 for monthly), and n is the total number of payments. At a 0% rate the payment is simply P ÷ n.
Example: $200,000 at 6% for 30 years gives r = 0.005 and n = 360, so the payment is $1,199.10. The first month’s interest is $200,000 × 0.005 = $1,000.00, so only $199.10 of the first payment reduces the balance. Over 360 payments the interest adds up to $231,677.04. (Run it yourself in the amortization calculator.)
Rounding, the way lenders do it
- The payment is rounded to the cent.
- Each period’s interest is calculated on the current balance and rounded to the cent; the rest of the payment goes to principal.
- The final payment is whatever it takes to bring the balance to exactly $0.00, so it can be a few cents higher or lower than the others. Your lender’s final payment works the same way.
- Totals (total interest, total paid) are the sum of the rounded schedule, not a formula shortcut, so they match the schedule you see line for line.
APR
The annual percentage rate folds upfront finance charges (points, origination and similar lender fees) into a single rate. We find the monthly rate at which the payment repays the loan amount minus those charges, then multiply by 12. Example: the same $200,000 loan with $4,000 in finance charges leaves $196,000 financed, and the $1,199.10 payment over 360 months works out to an APR of 6.189%. This follows the actuarial method in Regulation Z (Truth in Lending); which fees count as finance charges is decided by the lender, so the APR on your Loan Estimate is the official figure.
Other calculations
- Mortgage insurance (PMI): charged when the loan is more than 80% of the price, as an annual percentage of the loan ÷ 12, and shown until the scheduled balance reaches 78% of the original value, when the Homeowners Protection Act requires borrower-paid PMI to end on most conventional loans.
- Extra and biweekly payments: extra amounts go straight to principal in the month they are paid. Biweekly plans are modeled as 26 half-payments a year with interest each two-week period, which assumes your servicer applies each half-payment when it arrives.
- Credit cards: interest is charged monthly at APR ÷ 12 on the carried balance, with no new purchases or fees. The “typical minimum” comparison uses 1% of the balance plus that month’s interest, with a $25 floor.
- Car and equipment leases: payment = depreciation ((capitalized cost − residual) ÷ months) + rent charge ((capitalized cost + residual) × money factor), where money factor = APR ÷ 2400. A 6% rate is a money factor of 0.0025.
- Balloon and interest-only loans: the payment is figured on the longer amortization (or on interest only), and the remaining balance on the schedule at maturity is the balloon.
- Home affordability: works backward from your income to the highest price whose full housing payment (principal, interest, taxes, insurance, PMI) fits both the housing ratio and the total debt-to-income ratio you choose.
- “What this means” summaries: on the mortgage, loan payment, auto loan and credit card payoff calculators, the sentence under the result is assembled from the same computed result (interest per dollar borrowed, the first payment’s interest/principal split, a shorter-term alternative), so it changes with your inputs and never quotes a number the calculator didn’t produce.
- Comparisons (rent vs. buy, refinance, debt consolidation, snowball vs. avalanche, lease vs. loan) run both options on the same inputs and report the difference; nothing is weighted toward either choice.
What the results leave out
A calculator is only as complete as its inputs. Unless a page says otherwise, results assume:
- a fixed rate for the whole term (adjustable-rate resets are not projected);
- interest charged monthly on the balance, not daily, and the first payment one full period after closing;
- payments made on time, with no late fees, skipped payments or new borrowing;
- taxes, insurance and dues that stay at the amounts you enter;
- no income-tax effects (deductions and credits depend on your situation).
Lenders that charge interest daily, or that set a short or long first period, will show slightly different interest and final-payment figures. That is why every page tells you to confirm terms with the lender.
How we test
- Golden values. The shared payment, schedule and APR math that every calculator uses is tested against independent references: published payment figures (for example $1,199.10 for $200,000 at 6% over 30 years), closed-form results worked by hand, and exact 0% cases. Calculators with logic of their own (mortgage insurance, leases, credit cards, balloons, fees, comparisons) have their own tests of the same kind.
- Consistency checks. Schedules must end at exactly zero, principal paid must add up to the amount borrowed, and computed rates (APR, implied lease rates) must reproduce the payment when plugged back in.
- Before every release the full test suite runs and the site build refuses to publish if any page’s default result is missing or broken.
- After every release every page in the sitemap is loaded on the live site and checked for errors.
- Numbers in page examples are produced by running the calculator, not typed by hand.
How pages are reviewed
Each page is reviewed at least once a year, and sooner when a rule it depends on changes: for example, SBA guaranty fees are reset with each federal fiscal year in October. Corrections are made as soon as an error is found. Rates and fees in the default inputs are illustrations, not current market quotes; use the rate you are actually offered.
Neutrality policy
- No lender relationships. PmtCalc is not a lender or broker and is not paid by lenders. We do not rank lenders, link to loan offers or earn referral fees.
- No lead forms. We never ask for your name, email, phone number or credit details.
- Your numbers stay in your browser. Calculations run on your device; inputs are not sent to us or to analytics. “Copy link to these numbers” puts them only in the link you copy. See the privacy policy.
- Ads are kept separate. The site is supported by display ads from Google. Ads are chosen by Google, not by us, and an ad is never an endorsement or a factor in any result.
PmtCalc provides estimates for education and planning only. Results are not an offer of credit, a loan approval, or financial, tax or legal advice. Actual terms depend on the lender and your situation.