FinanceLoans & AmortizationA-Level
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Remaining Loan Balance Calculator

Balance after k payments on an amortizing loan.

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Remaining Balance

Formula first

Overview

The Remaining Loan Balance formula, also known as the retrospective method, calculates the outstanding principal on a loan after a specific number of payments have been made. It determines the balance by finding the difference between the future value of the original loan amount and the future value of the series of payments made up to that point.

Symbols

Variables

B_k = Remaining Balance, PV = Principal, r = Rate per Period, PMT = Payment, k = Payments Made

Remaining Balance
$
Principal
$
Rate per Period
Payment
$
Payments Made

Apply it well

When To Use

When to use: Use this formula when you need to determine the payoff amount for a fixed-rate amortizing loan at any specific point in its lifecycle. It is applicable in scenarios where the interest rate and payment amount remain constant, such as standard mortgages or auto loans. It assumes payments are made at the end of each period.

Why it matters: Understanding the remaining balance is crucial for financial planning, allowing borrowers to calculate their current equity in an asset. It provides the necessary information for making decisions about refinancing, early loan payoff, or selling property. In accounting, it ensures the accurate reporting of liabilities on a balance sheet.

Avoid these traps

Common Mistakes

  • Using total n instead of k (payments made).
  • Using annual rate when payments are monthly.

One free problem

Practice Problem

A homeowner has a mortgage with an initial loan amount of 200,000. The monthly interest rate is 0.005 and they make monthly payments of 1,200. What is the remaining balance after 5 years (60 months)?

Principal200000 $
Rate per Period0.005
Payment1200 $
Payments Made60

Solve for:

Hint: First calculate (1+r)^k, then find the future value of the principal and subtract the future value of the payments.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Fundamentals of Financial Management by Brigham and Houston
  2. Corporate Finance by Ross, Westerfield, and Jaffe
  3. Wikipedia: Loan amortization
  4. Principles of Corporate Finance by Brealey, Myers, Allen
  5. Wikipedia: Amortization (business)
  6. Brealey, Richard A., Stewart C. Myers, and Franklin Allen. Principles of Corporate Finance. McGraw-Hill Education.