To calculate your loan balance on a standard fixed-rate loan, use the amortization formula B = P × [(1 + r)n − (1 + r)p] ÷ [(1 + r)n − 1], where P is the amount you originally borrowed, r is the monthly interest rate as a decimal, n is the total number of scheduled payments, and p is the number you have already made. All four numbers come straight from your loan paperwork. The worked example below runs through every step.
The Four Numbers You Need From Your Loan Documents
Before touching the formula, pull these figures together:
- The original principal — what you actually borrowed, not the sticker price of the car or house. Your promissory note or closing disclosure lists it.
- The annual interest rate written into the loan agreement. Use the contract rate, not an introductory teaser rate and not the APR, which bundles in fees.
- The total number of payments across the full term, expressed in months. A 30-year mortgage is 360. A five-year auto loan is 60.
- The number of payments you have already made as of the date you want to measure.
Federal law requires lenders to disclose most of this upfront. The Truth in Lending Act directs creditors to disclose the finance charge and the total of payments on every closed-end consumer loan before you sign.1Office of the Law Revision Counsel. 15 USC 1638 – Transactions Other Than Under an Open End Credit Plan Your monthly billing statements then track how many payments you have completed. If any number is unclear, call your servicer before running the math.
The Formula and What Each Piece Does
The standard amortization formula for the balance still owed after p payments is:
B = P × [(1 + r)n − (1 + r)p] ÷ [(1 + r)n − 1]
The variables:
- B is the remaining principal balance.
- P is the original loan principal.
- r is the monthly interest rate (annual rate divided by 12, expressed as a decimal).
- n is the total number of scheduled payments.
- p is the number of payments already made.
The logic is simpler than it looks. (1 + r)n represents the total compounding over the full life of the loan. (1 + r)p captures the compounding that has already occurred through the payments you have made. Subtracting the second from the first isolates the compounding that remains. Dividing by [(1 + r)n − 1] turns that into a proportion of your original principal, and multiplying by P gives you the dollars still owed.
Convert the annual rate to a monthly rate every time. A 6% annual rate becomes 0.06 ÷ 12 = 0.005. Skipping this conversion is the single most common mistake in manual loan calculations and will throw off the result by thousands of dollars.
Worked Example: $25,000 Auto Loan After 24 Payments
Suppose you took out a $25,000 auto loan at 6% annual interest for five years, and you want to know the balance after 24 monthly payments.
The inputs:
- P = $25,000
- Annual rate = 6%, so r = 0.06 ÷ 12 = 0.005
- n = 60
- p = 24
Step 1. Raise the growth factor to the total term. (1 + 0.005)60 = 1.00560 ≈ 1.34885.
Step 2. Raise it to the number of payments made. 1.00524 ≈ 1.12716.
Step 3. Build the numerator. 1.34885 − 1.12716 = 0.22169.
Step 4. Build the denominator. 1.34885 − 1 = 0.34885.
Step 5. Divide. 0.22169 ÷ 0.34885 ≈ 0.63548.
Step 6. Multiply by the original principal. $25,000 × 0.63548 ≈ $15,887.
After two years of payments, roughly $15,887 of the original $25,000 remains. The 24 payments retired only about $9,113 in principal; the rest went to interest. That front-loading of interest is normal for amortized loans.
A spreadsheet handles the exponentiation more cleanly than a handheld calculator. In Excel or Google Sheets, =POWER(1.005,60) returns the growth factor, and the built-in PV function can produce the remaining balance directly. Either way, carry at least five decimal places through the intermediate steps. Rounding too early can shift the final number by hundreds of dollars.
If You’ve Made Extra Payments
The formula assumes you have made exactly the scheduled payment each month with no additional principal. If you have been paying extra, it will overstate your balance, because it does not account for principal you retired ahead of schedule.
Extra principal payments reduce the balance immediately, which means less interest accrues on every month that follows. Making them earlier in the term produces the biggest savings because the eliminated principal no longer compounds for the remaining years. On a 30-year mortgage, even an extra $100 a month in the first few years can shave years off the term and tens of thousands off total interest.
If your extra payments have been irregular, the formula will not give you an accurate balance. You would need to build a month-by-month amortization table that applies each actual payment to the running balance. Loan servicers do this accounting automatically, so checking your statement or requesting a payoff quote is the faster path.
When You Need a Payoff Statement Instead
The formula calculates remaining principal. That is not the same number as what it takes to close out the loan. A payoff amount adds interest that accrues between your last payment and the day the final check clears, plus any outstanding fees or prepayment charges.2Consumer Financial Protection Bureau. What Is a Payoff Amount and Is It the Same as My Current Balance If you are actually paying the loan off, request a formal payoff statement from your servicer rather than relying on your own math.
For home loans, federal law requires your servicer to provide an accurate payoff balance within seven business days of receiving your written request.3Office of the Law Revision Counsel. 15 USC 1639g – Requests for Payoff Amounts of Home Loan The same seven-day standard appears in Regulation Z for all dwelling-secured credit.4Consumer Financial Protection Bureau. 12 CFR Part 1026 Regulation Z – 1026.36 Prohibited Acts or Practices and Certain Requirements for Credit Secured by a Dwelling For auto loans and other non-mortgage installment debt, no equivalent federal timeline exists, but most lenders provide payoff figures within a few business days of a phone or online request.
Every payoff statement includes a “good through” date, typically 10 to 30 days out. After that, accrued interest changes the total and you need a fresh statement. Interest between the last payment and payoff is calculated as a per diem charge — the annual rate divided by 365 (sometimes 360), multiplied by the current balance. On a $200,000 mortgage at 5%, that daily figure runs around $27, so even a few days of timing matters. Any late fees, recording fees for lien releases, or prepayment charges will also appear on the final statement. That itemization is why requesting one before sending funds is always the right move.