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Remaining Loan Balance After Equal Payments

Estimate outstanding principal after a specified number of scheduled payments on a fixed-rate monthly loan.

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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 repaid over twelve months at zero interest has a balance of 6,000 immediately after six payments.

Bₖ = P × ((1 + r)^n − (1 + r)^k)/((1 + r)^n − 1); at r = 0, Bₖ = P × (1 − k/n)

Worked example

Enter these known values and leave the other values blank.

Original loan principal
12000 USD
Annual nominal interest rate
0 %
Original modeled loan term
1:0 yrs / mos
Elapsed scheduled payment periods
0:6 yrs / mos
Remaining principal after payments
6000 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 annual rate is divided by twelve. The elapsed duration is between zero and the original positive term. A whole number of months means the balance immediately after that payment.
  • This is a forward balance estimate. It does not infer the original term or rate from a balance and does not model extra principal payments.

Common questions

What does zero elapsed time show?

The original principal, before any scheduled payments.

Can I use this after making extra payments?

Not directly. Extra payments change the balance path; this formula assumes only the scheduled level payments.

References

Bookify uses the equivalent remaining-balance identity with an explicit zero-interest branch. Bookify permits the initial balance at zero elapsed periods and requires elapsed time within the positive loan term.

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