What is the remaining balance formula?

Bk = L(1 + r)k − P × [(1 + r)k − 1] ÷ r, where L is the original loan, P the payment, r the rate per period and k the number of payments made.

Is there another way to calculate it?

Yes. The balance equals the present value of the remaining payments: P × [1 − (1 + r)−(n−k)] ÷ r. Both give the same answer.

Why have I repaid so little principal?

Early payments are mostly interest because interest is charged on the large starting balance.

Is this the same as my payoff amount?

It is the principal balance. A payoff quote may add interest accrued since the last payment and any fees.

Remaining Loan Balance Formula

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Remaining Loan Balance Calculator

The remaining balance formula tells you how much of a loan is still outstanding after a given number of payments, without building a full amortization table. It treats the loan as money growing at the loan rate, L(1 + r)^k, minus the future value of the payments you have made, P × [(1 + r)^k − 1] ÷ r. The difference is the principal still owed.

Formula

B_k = L(1 + r)^k − P × (1 + r)^k − 1r

Where

B_k: balance still owed after k payments
L: original loan amount
P: regular payment
r: interest rate per period
k: number of payments already made

Calculator

Loan amount

Annual interest rate (%)

Loan term (years)

Payments per year

Payments already made (k)

Result and step-by-step solution

Remaining balance

232,635.89

After 60 of 360 payments you have repaid 17,364.11 of principal and 72,568.47 of interest.

Rate per period and number of payments
r = 6%12 = 0.005; n = 30 × 12 = 360
Discount term
(1 + r)⁻ⁿ = (1 + 0.005)⁻³⁶⁰ = 0.16604193
Apply the payment formula
P = 250,000.00 × 0.0051 − 0.16604193 = 1,498.88
Growth factor over k payments
(1 + 0.005)⁶⁰ = 1.34885015
Balance formula
B = 250,000.00 × 1.34885015 − 1,498.88 × 1.34885015 − 10.005 = 232,635.89

How to use the formula

This is the number a lender uses for a payoff quote (before any fees or daily interest), and the one you need when deciding whether to refinance, sell a property or make an extra payment. The calculator first works out the regular payment from the loan terms and then applies the balance formula, and it also tells you how much principal and interest you have paid so far.

On a 250,000 mortgage at 6% over 30 years, the monthly payment is 1,498.88. After 60 payments, 89,932.58 has been paid but the balance is still 232,635.89: only 17,364.11 of principal has been repaid and 72,568.47 has gone to interest. That front-loading of interest is why extra payments early in a loan save so much; see the amortization schedule for the payment-by-payment view.

Frequently asked questions

What is the remaining balance formula?: B_k = L(1 + r)^k − P × [(1 + r)^k − 1] ÷ r, where L is the original loan, P the payment, r the rate per period and k the number of payments made.
Is there another way to calculate it?: Yes. The balance equals the present value of the remaining payments: P × [1 − (1 + r)^−(n−k)] ÷ r. Both give the same answer.
Why have I repaid so little principal?: Early payments are mostly interest because interest is charged on the large starting balance.
Is this the same as my payoff amount?: It is the principal balance. A payoff quote may add interest accrued since the last payment and any fees.

Last reviewed: September 26, 2026. Calculations run in your browser and were checked against numpy-financial, SciPy and published spreadsheet examples.