Remaining Loan Balance
The principal still owed after a given number of payments on an amortizing loan: the present value of the payments that remain.
Remaining Balance (Annual Compounding)
Outstanding loan balance after p payments. The final payment is capped at the amount owed, and the balance stays zero after payoff. At zero interest, balance is max(0, PV − PMT × p).
When to use: Use to find how much you still owe on a loan after some payments.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| B | Remaining Balance | Outstanding loan balance | $ |
| PV | Original Loan | Original loan amount | $ |
| PMT | Payment | Periodic payment amount | $ |
| k | Interest Rate | Annual interest rate | % |
| p | Payments Made | Number of payments already made | integer |
Real-Life Examples
Example 1: Mortgage Balance
A $200,000 mortgage at 6% with annual payments of $19,264.68. Balance after 5 years?
Given
Step-by-Step
For these inputs, Remaining Balance is $159,048.32 under the stated payment, compounding and accounting assumptions.
Example 2: Business Loan
$50,000 loan at 8% with $7,451.47 annual payments. Balance after 3 payments?
Given
Step-by-Step
For these inputs, Remaining Balance is $38,795.15 under the stated payment, compounding and accounting assumptions.
Frequently Asked Questions
Use this formula with the original loan amount (PV), your regular payment (PMT), the interest rate (k), and the number of payments you have made (p). The result is your remaining balance.
Early in a loan, most of each payment goes toward interest because the outstanding balance is large. As you make payments and the balance drops, more of each payment goes to principal, accelerating the balance reduction.
The remaining balance is the principal owed at a point in time. The payoff amount may include accrued interest since the last payment, prepayment penalties, or fees. For a same-day payoff right after a payment, they are typically the same.