Remaining Loan Balance Formula and Calculator

The remaining loan balance formula calculates how much principal is still owed after a specified number of regular payments. Enter the original loan amount, APR, term, and payments already made to estimate the balance, along with the scheduled monthly payment.

Formula

For a fixed-rate loan with level monthly payments, the balance after k payments is:

B_k = P(1 + r)^k − M × ((1 + r)^k − 1) / r

The scheduled payment is calculated as M = P × r / (1 − (1 + r)⁻ⁿ), rounded to the nearest cent. The calculator uses that rounded payment in the balance formula.

• B_k is the estimated remaining balance in dollars.
• P is the original amount borrowed in dollars.
• r is the monthly interest rate as a decimal: APR ÷ 1200.
• k is the number of monthly payments made.
• M is the scheduled monthly payment in dollars.
• n is the full term in months: years × 12.

The balance formula accounts for two effects: interest makes the unpaid balance grow between payments, while each payment reduces it. Early in an amortizing loan, more of a payment generally goes toward interest because interest is charged on a larger balance. As principal falls, the interest portion falls and more of each level payment reduces principal.

Worked Example

Using the calculator defaults: original loan amount P = $20,000, APR = 8%, term = 5 years, and k = 12 payments made.

1. Convert the annual percentage rate to a monthly decimal: r = 8 ÷ 1200 = 0.0066667.
2. Convert the term to months: n = 5 × 12 = 60.
3. Calculate and round the monthly payment: M = $20,000 × 0.0066667 ÷ (1 − (1.0066667)⁻⁶⁰) = $405.53.
4. Substitute into the balance formula: B₁₂ = $20,000(1.0066667)¹² − $405.53 × ((1.0066667)¹² − 1) ÷ 0.0066667 = $16,470.19.
5. The scheduled payments made total 12 × $405.53 = $4,866.36. This total is not the principal reduction: part of each payment covered interest.

Small differences can arise if a lender uses a different payment date, daily interest, or a payment amount that differs by a cent from the rounded schedule.

Assumptions

• The interest rate stays fixed for the modeled period.
• Payments are equal, made monthly, and made at the end of each payment period.
• Interest accrues monthly using APR divided by 12.
• The estimate excludes fees, taxes, insurance, PMI, escrow, and any extra payments or payment adjustments.

When to Use the Remaining-Balance Calculation

This calculation is useful when you want an estimate of the principal still outstanding at a point in a standard repayment schedule—for example, after a year of payments or halfway through a fixed-term loan. It can help explain an amortization statement or provide a starting estimate for a payoff discussion. It does not itself calculate a lender’s exact payoff quote, which may include interest accrued since the last payment and other amounts specified by the lender.

Enter the count of payments that have actually been made, not the number remaining. If no payment has been made, use zero; the balance should then equal the original amount. The payment count must also make sense for the term. The tool permits a broad range of entries, so check that payments made do not exceed the number of scheduled months in your loan.

How to Read the Result and Its Limits

The headline is an estimated unpaid balance immediately after the stated number of monthly payments. The separate payment figure is the scheduled amount, and “Payments made in dollars” is that amount multiplied by the number of payments. Neither the payment total nor the remaining balance alone tells you the total cost of borrowing: interest already paid is not included in the balance.

The equation assumes a conventional, fully amortizing loan: a fixed rate, a consistent payment interval, and a payment large enough to repay principal and interest over the term. The monthly rate convention is APR divided by 12. A contract that accrues interest daily, uses irregular payment dates, changes its rate, or applies payments differently can produce a different balance.

Common Errors and Related Questions

• Mixing up APR and the monthly rate: For this formula, an APR entered as 8 means 8 percent per year; divide by 1200 to get the monthly decimal. Do not enter 0.08 in the APR field.
• Using the wrong payment count: The formula needs completed payments. A payment that is due but not yet made should not be counted as completed.
• Rounding too early: Keep full precision in intermediate calculations and round the scheduled payment to cents as shown. Repeatedly rounding the monthly interest or balance can create small differences.
• Treating the estimate as a payoff quote: A payoff amount on a particular date may differ because interest accrues between scheduled payments and the lender may account for contract-specific items.

Frequently Asked Questions

How do I calculate my remaining loan balance?
Find the monthly rate by dividing APR by 1200, calculate the scheduled monthly payment, then use the balance formula with the number of payments already made. The calculator performs those steps for a fixed-rate monthly schedule.

Does the formula include interest?
Yes. It includes interest accrued over the modeled payment periods and subtracts the scheduled payments. It does not add interest that accrues after the last modeled payment.

Is the remaining balance the same as the payoff amount?
Not necessarily. A payoff amount for a specific date can include interest accrued since the last scheduled payment and other contract-specific items. Request an exact figure from the lender.

Can I use this formula if I made extra payments?
Not accurately with the standard inputs alone. Extra payments reduce principal differently from the level-payment schedule. Use the actual payment and balance history or a calculator that models extra payments.

Why does my lender’s balance differ by a few dollars?
Possible reasons include daily rather than monthly interest accrual, different payment dates, rounding, a variable rate, fees, or extra or missed payments. Compare the calculator’s assumptions with the loan statement.

This result is an estimate; the lender’s disclosure gives the exact figures.

Related

• Loan Balance Payoff Calculator: Estimate Your Remaining Debt
• Loan Balance Transfer Calculator: Estimate Savings
• Lifetime Balance Transfer Calculator: Estimate Payoff Time

in p | Original loan amount | $ | 20000 | 1 | 100000000
in apr | Interest rate (APR) | % | 8 | 0.01 | 100
in yrs | Loan term | years | 5 | 0.0833 | 50
in k | Payments made | - | 12 | 0 | 600
out bal | Remaining loan balance | $ | max(0, p * (1 + apr / 1200) ^ k - round(p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12), 2) * ((1 + apr / 1200) ^ k - 1) / (apr / 1200)) | 2
out pmt | Monthly payment | $ | round(p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)), 2) | 2
out paid | Payments made in dollars | $ | pmt * k | 2