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Loan Amortization Payment Calculator

Calculates the fixed periodic payment required to fully amortize a loan over a set number of periods.

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Principal Loan Amount

Formula first

Overview

The Loan Amortization Payment formula determines the constant payment amount needed to repay a loan, including both principal and interest, over a specified duration. It is fundamental in personal and corporate finance for structuring loans like mortgages, car loans, and student loans. This formula ensures that by the end of the loan term, the entire principal balance and all accrued interest are paid off.

Symbols

Variables

P = Principal Loan Amount, r = Periodic Interest Rate, n = Total Number of Payments, PMT = Periodic Payment

Principal Loan Amount
$
Periodic Interest Rate
%
Total Number of Payments
payments
PMT
Periodic Payment
$

Apply it well

When To Use

When to use: Use this equation when you need to determine the regular payment amount for a fully amortizing loan, given the principal amount, the periodic interest rate, and the total number of payment periods. It's crucial for budgeting and understanding the financial commitment of a loan.

Why it matters: This formula is vital for financial planning, allowing borrowers to understand their monthly obligations and lenders to structure loan products. It underpins the calculation of mortgage payments, car loan installments, and other forms of debt, enabling individuals and businesses to manage their cash flow effectively and make informed borrowing decisions.

Avoid these traps

Common Mistakes

  • Using an annual interest rate for 'r' when payments are monthly or quarterly, instead of converting it to the periodic rate.
  • Incorrectly calculating 'n' (total number of periods) by not multiplying the loan term by the number of payments per year.
  • Confusing the formula for an ordinary annuity with an annuity due.

One free problem

Practice Problem

A student takes out a loan of $20,000 to be repaid over 5 years with monthly payments. The annual interest rate is 6%, compounded monthly. What is the monthly payment amount?

Principal Loan Amount20000 $
Periodic Interest Rate0.005 %
Total Number of Payments60 payments

Solve for: PMT

Hint: Ensure the interest rate and number of periods are consistent with monthly payments.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Brealey, Richard A., Myers, Stewart C., and Allen, Franklin. Principles of Corporate Finance.
  2. Brigham, Eugene F., and Ehrhardt, Michael C. Financial Management: Theory & Practice.
  3. Wikipedia: Amortization (business)
  4. Brealey, R. A., Myers, S. C., & Allen, F. (2020). Principles of Corporate Finance (13th ed.). McGraw-Hill Education.
  5. Brealey, Myers, and Allen, Principles of Corporate Finance, 13th Edition, McGraw-Hill Education