FinanceLoans & AmortizationA-Level
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Amortizing Loan Payment (PMT) Calculator

Fixed payment needed to repay a loan over n periods.

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Overview

The Amortizing Loan Payment formula determines the fixed periodic payment required to fully retire a debt over a specified duration at a constant interest rate. It mathematically balances the interest due on the remaining principal with a partial repayment of the principal itself in every installment.

Symbols

Variables

PMT = Payment, PV = Principal (Present Value), r = Rate per Period, n = Number of Payments

Payment
$
Principal (Present Value)
$
Rate per Period
Number of Payments

Apply it well

When To Use

When to use: This formula is applied when calculating monthly payments for fixed-rate installment products like mortgages, car loans, and personal loans. It assumes that interest is calculated on the declining balance and that the interest rate remains unchanged throughout the life of the loan.

Why it matters: It allows borrowers to budget with certainty by knowing the exact amount required to clear a debt by the end of its term. For financial institutions, it structures the recovery of principal while ensuring the time value of money is compensated via interest.

Avoid these traps

Common Mistakes

  • Using APR as r without dividing by payment frequency.
  • Using years for n when payments are monthly.

One free problem

Practice Problem

A homeowner takes out a 30-year mortgage for 300,000 at an annual interest rate of 4.8%. If payments are made monthly, what is the monthly payment (PMT)?

Principal (Present Value)300000 $
Rate per Period0.004
Number of Payments360

Solve for:

Hint: Convert the 4.8% annual rate to a monthly rate by dividing by 12, and the 30-year term to 360 months.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Corporate Finance by Stephen A. Ross, Randolph W. Westerfield, and Jeffrey Jaffe
  2. Fundamentals of Corporate Finance by Richard A. Brealey, Stewart C. Myers, and Franklin Allen
  3. Wikipedia: Amortization (business)
  4. Corporate Finance (Ross, Westerfield, Jaffe)
  5. Principles of Corporate Finance (Brealey, Myers, Allen)
  6. Ross, Westerfield, and Jordan. Fundamentals of Corporate Finance. McGraw-Hill Education.
  7. Amortization (business). Wikipedia. Retrieved from https://en.wikipedia.org/wiki/Amortization_(business)