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Loan Payment by Frequency & Repayment Total

Estimate a level loan payment, number of installments and repayment total using a stated payment-frequency convention.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Use the result with context

Results are estimates for planning and education. Confirm rates, taxes, fees, and legal requirements with the relevant institution or a qualified professional before making a financial decision.

Formula and method

A 12,000 loan at zero interest over one year with twelve payments per year requires 1,000 per payment and 12,000 in total.

r = annual nominal rate/frequency; n = years × frequency; payment = P × r/(1 − (1 + r)^−n)

Worked example

Enter these known values and leave the other values blank.

Financed principal
12000 USD
Annual nominal interest rate
0 %
Modeled loan term
1:0 yrs / mos
Payment frequency convention
Monthly · 12/year
Modeled number of payments
12
Interest rate per payment period
0 %
Level payment per period
1000 USD
Total modeled loan payments
12000 USD

Assumptions and limitations

  • The model uses a fixed nonnegative nominal rate, equal end-of-period payments and no extra payments, balloon balance, fees or missed payments.
  • At zero interest, principal equals payment times the number of periods. A positive financed balance needs a payment above periodic interest to amortize in finite time.
  • Whole payment counts describe an equal-payment schedule. Fractional terms are continuous mathematical estimates, not exact calendar payoff dates or final partial bills.
  • The calculator retains internal precision. Contractual rounding, daily accrual and irregular dates can change an actual repayment schedule.
  • The frequency presets mean 1, 2, 4, 12, 52.1775 or 365.242 payments per modeled year. The last two are retained average-year conventions, not exact weekly or daily calendar schedules. The annual nominal rate is divided by the selected frequency.
  • Changing frequency changes both periodic interest and the number of modeled payments. This is not an accelerated extra-payment plan.

Common questions

Are weekly and daily choices exact calendar schedules?

No. They use the displayed fixed payments-per-year factors. Use a dated amortization schedule for an exact first or final payment date.

Does the total include fees?

No. It is the level payment multiplied by the modeled number of payments.

References

Bookify explicitly handles zero interest in the payment equation and every retained inverse. Bookify requires positive duration and nonnegative rates, with a payment above periodic interest.

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