Amortization Calculator

How the Amortization Calculator works

Use this calculator when you want to see how a fixed principal-and-interest payment reduces a balance over time or how extra principal could change payoff timing in the app's month-offset model. Use Loan Payment for the simpler payment-only estimate, Payment when solving either payment amount or payoff time, APR when selected fees need a cash-flow-rate estimate, Mortgage Payment when taxes, insurance, PMI, or escrow matter, and lender or servicer documents for real payoff statements, payment allocation, legal disclosures, product terms, or jurisdiction-specific questions.

The app rounds the payment count with termYears * 12 + termMonths and converts the entered annual rate with annualRate / 100 / 12. The scheduled payment is PMT = P * m / (1 - (1 + m)^-n), where P is loan amount, m is monthly rate, and n is payment count; at 0 percent, PMT = P / n. The schedule helper starts with the loan balance, computes monthly interest as balance * m, sets scheduled principal to max(0, PMT - interest), adds extraMonthlyPay every month, adds extraYearlyPay on every 12th payoff month, adds extraOneTimePay when the 1-based payoff month equals extraOneTimeMonth, caps principal at the remaining balance, and repeats until the balance is effectively zero or the 12000-month safety cap is reached. Interest saved is the no-extra schedule's total interest minus the selected schedule's total interest.

Amortization Calculator formula

This formula page covers the app's Amortization Calculator: a fixed-rate monthly schedule summary with optional extra principal assumptions. It solves the scheduled monthly payment, then simulates month-by-month interest, principal reduction, extra monthly, yearly, and one-time principal payments, first-month and first-year splits, payoff months, total payments, total interest, and interest saved. It does not create lender disclosures, payoff statements, servicer instructions, APR calculations, escrow estimates, mortgage insurance estimates, tax answers, or personalised borrowing advice.

Step by step

1. Read loan amount, term years, term months, annual rate, extra monthly payment, extra yearly payment, extra one-time payment, and one-time payment month from the calculator inputs.
2. Convert term years and term months into the rounded payment count with N = round(12Y + M). A zero-month term is not a meaningful planning input.
3. Convert the annual interest-rate percent into the app's fixed monthly rate assumption with m = R / 100 / 12.
4. Solve the scheduled monthly payment with PMT = P times m divided by 1 minus (1 + m) raised to negative N. If the rate is 0, divide loan amount by N instead.
5. Build the no-extra comparison schedule first. It uses the same monthly payment and rate, but no extra monthly, yearly, or one-time principal.
6. Build the selected schedule one month at a time. Monthly interest equals the previous balance times the monthly rate.
7. Scheduled principal equals monthly payment minus current-month interest, floored at 0 by the schedule helper.
8. Extra principal equals the extra monthly amount, plus the extra yearly amount on every 12th payoff month, plus the one-time amount when the current 1-based month equals the selected one-time payment month.
9. Principal paid is scheduled principal plus extra principal, capped at the remaining balance so the final month can be smaller than the scheduled payment plus extras.
10. Track first-month interest, first-month principal, and first-month ending balance from month 1.
11. Track first-year interest and first-year principal by adding the first 12 simulated months.
12. Stop when the balance is effectively paid off, or at the 12000-month safety cap.
13. Calculate payoff years as payoff months divided by 12, total payments as the simulated interest plus principal paid, total interest as summed interest, and interest saved as no-extra total interest minus selected-schedule total interest.
14. Use CFPB, Regulation Z, lender disclosures, servicer materials, or local regulator sources before turning this generic schedule math into APR, Truth in Lending, payoff statement, prepayment-penalty, escrow, tax, insurance, mortgage-insurance, product, legal, or jurisdiction-specific claims.

Worked example

Default examples: no extra payments and extra principal

The default amortization fixture uses a $200,000 loan amount, a 6 percent annual rate, a 15-year term, and no extra payments. The extra-payment fixture keeps the same loan but adds $100 monthly, $1,000 every 12th month, and a $5,000 one-time extra payment in month 24.

1. For the no-extra schedule, convert 6 percent to 0.06 and divide by 12 to get a monthly rate of 0.005.
2. Convert 15 years and 0 months into 180 monthly payments.
3. Apply the scheduled payment formula with P = $200,000, m = 0.005, and N = 180.
4. The calculator reports a scheduled monthly payment of $1,687.71.
5. Month 1 interest is $200,000 times 0.005, or $1,000.00.
6. Month 1 scheduled principal is $1,687.71 minus $1,000.00, or $687.71, leaving a $199,312.29 ending balance.
7. Across the first 12 months, the no-extra fixture reports $11,769.23 of interest and $8,483.33 of principal.
8. The no-extra schedule reports 180 payoff months, $303,788.46 of total payments, and $103,788.46 of total interest.
9. For the extra-payment fixture, month 1 adds the $100 extra monthly payment, so first-month principal rises to $787.71 and the ending balance falls to $199,212.29.
10. The extra yearly payment is added at months 12, 24, 36, and so on; the one-time $5,000 extra principal is added in month 24.
11. With those extras, the fixture reports 149 payoff months, or 12.42 years after display rounding.
12. The extra-payment schedule reports $282,879.98 of total payments and $82,879.98 of total interest.
13. Interest saved is $103,788.46 minus $82,879.98, reported as $20,908.48.

The schedule shows how earlier principal reduction can reduce future interest under a fixed-rate model. It is still a mechanical estimate from entered assumptions, not a lender payoff quote or instruction for how a servicer will apply extra payments.

Assumptions and what this calculator ignores

Geographic scope: works globally. The math is currency-agnostic, so enter amounts in your own currency; local taxes, fees, and product rules are not included.

• The calculator models one fixed-rate monthly principal-and-interest schedule. It does not model variable rates, daily accrual, custom compounding, interest-only periods, negative amortization, balloon payments, skipped payments, refinancing, payment holidays, late fees, taxes, insurance, escrow, mortgage insurance, lender credits, or product-specific contract rules.
• Extra monthly payments are modeled as principal additions every month, extra yearly payments are modeled on every 12th payoff month, and the one-time payment is modeled by 1-based payoff month rather than calendar date. Real lenders and servicers may apply payments first to fees, past-due amounts, current interest, escrow, or future-payment credits before principal.
• Scoped independent comparator checks pass 4 of 4 scoped no-extra fixtures for overlapping fixed-rate schedule outputs. Extra-payment validation is limited because external schedule tools often model extra payments by calendar date while this app uses month offsets. CFPB mortgage amortization and principal-and-interest materials are needed for mortgage payment-split context; CFPB prepayment, servicer, and student-loan materials plus lender documents are needed for extra-payment application claims; CFPB APR guidance and Regulation Z sections 1026.18 and 1026.22 are needed for legal APR, finance-charge, total-of-payments, payment-schedule, or Truth in Lending claims. Results are educational estimates, not financial, tax, legal, lending, mortgage, student-loan, credit, regulatory, consumer-rights, or personalised advice.

What this formula does not include

• The calculator assumes one fixed annual rate divided into monthly periods. It does not model variable rates, teaser rates, daily accrual, custom compounding, rate resets, negative amortization, interest-only periods, balloon payments, or payment holidays.
• A zero-month term is not a meaningful amortization input. The formula page documents the intended monthly schedule model, not every invalid-input edge case.
• Extra monthly payments are modeled as principal additions every month. Extra yearly payments are modeled as principal additions at the end of every 12th payoff month. The one-time extra payment is modeled by 1-based payoff month, not by calendar date.
• Scoped independent comparator checks currently pass 4 of 4 scoped fixtures for fixed-rate schedules without extra payments. Extra-payment comparator validation is limited because the independent comparator schedules extra payments by calendar month and year while this app uses month offsets.
• Real lenders and servicers can apply payments first to fees, past-due interest, current interest, escrow, or future-payment credits before reducing principal. Extra-payment application claims need lender, servicer, CFPB, or local regulator source checks.
• The monthly payment is principal and interest math only. It does not include taxes, homeowners insurance, mortgage insurance, escrow, HOA dues, closing costs, origination fees, credit insurance, late fees, or prepayment penalties.
• The entered interest rate is not automatically an APR. APR, finance charge, amount financed, payment schedule, total of payments, Truth in Lending, and jurisdiction-specific disclosure claims need CFPB, Regulation Z, lender, or local regulatory source checks.
• The app returns a schedule summary, not a full lender amortization table, payoff statement, contractual due date calendar, servicing ledger, credit decision, refinancing recommendation, or product quote.
• Payoff months stop when the balance is effectively zero or at the 12000-month safety cap. Extremely long schedules indicate inputs that should be reviewed before treating the output as useful.
• The result is an educational estimate from the entered assumptions, not financial, tax, legal, lending, credit, mortgage, consumer-rights, regulatory, or personalised advice.

Common mistakes to avoid

• Reading monthly payment as a full mortgage payment. This calculator models principal and interest only; taxes, homeowners insurance, PMI, HOA dues, escrow, and lender fees need separate sources or calculators.
• Assuming every extra payment immediately reduces principal in the same way. The app treats extras as principal additions in its schedule, but real payment allocation and paid-ahead rules depend on lender, servicer, loan type, and jurisdiction.
• Using a zero-month term, legal APR question, lender payoff amount, payoff statement, disclosure schedule, student-loan repayment-plan rule, or borrowing recommendation as if this calculator produced an official answer.

Key terms

Scheduled principal

The part of the regular monthly payment left after current-month interest. It is the normal balance reduction before optional extra principal is added.

Extra principal

The app's modeled additional principal from monthly, yearly, or one-time extra-payment inputs. The app applies it by payoff month and caps it to the remaining balance in the payoff month.

Interest saved

The no-extra schedule's total interest minus the selected schedule's interest. It isolates the modeled effect of extra principal before lender, servicer, fee, tax, escrow, or product rules.

Frequently asked questions

Methodology, sources, and disclaimer

This calculator is an original month-by-month amortization simulation layering simultaneous extra monthly, yearly, and one-time principal payments onto the fixed-rate schedule and reporting interest saved against the baseline, validated by deterministic fixtures. It is not copied from a single source.

Fixtures pin the first-month and first-year interest-principal splits and the extra-payment savings math on the $200,000 default. The result remains an educational estimate, not a servicer amortization statement or a payoff instruction.

Formula version 2026.05.22-generic-amortization-extra-payments. The version marks the calculation logic and validation fixture set used for this estimate.

• CFPB mortgage amortization and principal-and-interest materials should be used when copy explains mortgage principal, interest allocation, fixed-rate amortization, or total monthly mortgage-payment boundaries.
• CFPB prepayment penalty, mortgage-servicer extra-payment, student-loan extra-payment, and lender or servicer materials should be used when copy discusses extra-payment application, principal-only payments, paid-ahead status, payoff timing, or prepayment penalties.
• CFPB APR versus interest-rate guidance and Regulation Z sections 1026.18 and 1026.22 should be used when copy discusses APR, payment schedules, total of payments, finance charges, disclosures, or legal lending terminology.
• Lender disclosures and relevant local regulator sources should be used before copy makes product-specific, jurisdiction-specific, variable-rate, escrow, tax, insurance, mortgage insurance, negative-amortization, payoff statement, or consumer-credit legal claims.

Results are educational estimates, not advice. Read the full disclaimer.

Related reading

• Monthly loan payments explained
• How Calcs.finance validates calculator formulas

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