Amortization Calculator

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What is Amortization?

Amortization describes how a loan balance is repaid through a series of payments. Each payment first covers interest for the period; the rest reduces principal. With a positive fixed rate and equal payments, the interest part usually falls as the outstanding balance falls. The total payment can stay level while its composition changes.

This calculator estimates a regular principal-and-interest payment and simulates repayment with an optional extra amount each payment period. It supports several payment frequencies. Its compounding-frequency selector is currently not used by the calculation, however: the annual rate is divided by payments per year. That limitation matters when comparing a quote whose compounding convention differs from the payment schedule.

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How to Use This Calculator

  1. Enter the loan principal and its currency. This is the balance being financed, rather than the sum of all future repayments.
  2. Enter the annual interest rate as a percentage, such as 6 for six percent. Choose the payment frequency; this determines both the periodic rate and the number of periods.
  3. Enter the amortization term and choose years or months. The calculator converts the selected duration to the corresponding number of payment periods.
  4. Enter an optional extra payment per payment period. Keep it in the same currency as the principal; currency dropdowns do not perform exchange-rate conversions.
  5. Calculate and read the original periodic payment and total paid. For a lender comparison, verify the actual interest convention, payment dates and fees separately. Changing only the compounding selector does not change this implementation’s result.
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Formula Used

Periodic rate r = annual percentage rate / (100×payments per year). Number of payments n = years×payments per year. Base payment = P×r/[1−(1+r)^(−n)]; at zero interest, base payment = P/n.
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Variables Explained

InputMeaning in this calculator
Loan amount, PStarting principal. The model assumes the full amount is outstanding at the start.
Interest rateAnnual percentage divided by payment frequency in this simplified model; it is not automatically an all-in APR including fees.
Payment frequency1, 2, 4, 12, 26, 52 or 365 payments per year for yearly through daily options.
Amortization termPlanned repayment duration. A twelve-month term with monthly payments produces twelve base periods.
Extra paymentAdditional principal-and-interest payment amount included each period in the repayment simulation.
Compounding frequencyA visible selector that is not currently used in the controller. This tool does not model an independent compounding schedule.
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Worked Example

For a loan of 10,000 at 6% annual interest over one year with monthly payments, r = 0.06/12 = 0.005 and n = 12. Substitution gives a base monthly payment of approximately 860.66. The first month’s interest is 10,000 × 0.005 = 50. About 810.66 of the first payment reduces principal, leaving about 9,189.34 before the next interest calculation.

Without extra payments, the model gives approximately 10,327.97 paid in total and 327.97 of interest. Intermediate figures are calculated at greater precision than the displayed payment. Adding 100 each month makes the planned payment about 960.66; repayment finishes sooner, with a smaller final payment when the outstanding principal is less than the normal principal contribution. The tool adjusts that last payment rather than charging a full payment after the balance is cleared.

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Why Use This Calculator?

The original periodic payment is the amount calculated for the chosen original term. It does not fall just because you add an extra payment. Extra payments instead affect the simulated time to repay and the total interest. The model assumes the extra amount is made regularly and can be applied without restrictions; the actual loan contract may handle prepayments differently.

There is a further implementation limit: the simulation stops after about 1,001 payment periods. A long daily or weekly schedule can exceed this cap, so its totals may be incomplete. The page is best treated as a simplified estimate, particularly for schedules requiring many periods. It does not add taxes, insurance, origination fees, late charges or rate changes. Compare a real financing offer using the lender’s written repayment schedule and disclosed costs, not just the regular payment figure.

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Common Mistakes

    • Do not assume the compounding dropdown changes the result; the current model derives interest solely from payment frequency.
    • Do not confuse biweekly with twice monthly. This implementation uses 26 biweekly payments per year.
    • Do not assume every displayed monetary total covers a long daily schedule beyond the simulation cap.
    • Do not enter negative extra payments or a zero-length term. Those do not describe the ordinary repayment model explained here.
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Frequently Asked Questions

Why does selecting continuous compounding not change my payment?

The controller receives the compounding choice but does not use it in the interest expression. It divides the annual rate by the number of payments per year. For loans with a different stated convention, the result may differ from the lender’s calculation even with the same nominal annual rate.

Does extra payment reduce the original payment amount?

No. The base payment is computed first from principal, rate and term. The extra amount is added to that base amount during simulation. It can reduce the outstanding balance faster, but the original payment displayed is still the original formula result.

Why might a real repayment schedule differ by a few units?

Lenders may round each payment, calculate interest using actual dates or impose different first-period rules. This model uses equal periods and retains internal precision until totals are displayed. Those differences are separate from larger discrepancies caused by fees or a different interest convention.

What happens at zero interest?

The payment is principal divided by the number of periods. For 12,000 over twelve monthly periods, that is 1,000 per payment before any extra amount. There is no interest component in this case, so each payment directly reduces the remaining principal.

Are taxes and insurance included?

No. The inputs model loan principal, interest and extra payments. Housing-related charges or other insurance and fees need a separate budget. A payment small enough for this calculation is not automatically the complete recurring cost of holding the loan or owning the financed asset.

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Sources & References

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