Quiz: Loan Balance Calculator

Calculate the remaining balance on a fixed-rate loan after any number of payments, along with the monthly payment, principal paid, and interest paid so far.

Quick Facts

Formula
B = M x [1 - (1+i)^-(n-k)] / i
M is the monthly payment, i the monthly interest rate, n the total number of payments, and k the payments already made.
Model
Standard fixed-rate amortization
Assumes equal monthly payments with no missed or extra principal payments.

Your Results

Calculated
Monthly payment
-
Fixed payment each month
Remaining balance
-
Balance after payments made
Principal paid
-
Paid down so far
Interest paid
-
Total interest to date

Ready

Enter your loan amount, rate, term, and payments made, then press Calculate.

How the Loan Balance Calculator works

This calculator finds the remaining balance on a fixed-rate, fully amortizing loan after a given number of monthly payments. It uses the same present-value math a lender uses internally: the balance at any point in time equals the present value of the payments still owed.

The formula

For an original loan amount P, a monthly interest rate i (annual rate divided by 12), and n total scheduled payments, the fixed monthly payment is:

M = P x i x (1 + i)n / [(1 + i)n − 1]

After k payments have been made, the remaining balance is the present value of the n − k payments still outstanding:

B = M x [1 − (1 + i)−(n−k)] / i

If the interest rate is 0%, the payment reduces to M = P / n and the balance reduces to B = P − M×k. The calculator also reports principal paid (P − B) and interest paid (total paid so far minus principal paid).

Worked example

Take a $300,000 loan at 6.5% for 30 years (n = 360 payments). The monthly payment works out to about $1,896. After 5 years (k = 60 payments), the remaining balance is roughly $280,833 — meaning only about $19,167 of principal has been paid off, even though total payments so far add up to about $113,772. The remaining $94,605 went to interest.

Why early payments are mostly interest

  • Interest is charged on the current balance: early in the loan the balance is highest, so the interest portion of each fixed payment is largest and the principal portion is smallest.
  • The split shifts over time: as the balance shrinks, less of each payment goes to interest and more goes to principal — the same fixed payment pays down the balance faster in later years.
  • Extra principal payments compound this effect: any extra amount paid toward principal lowers the balance the very next interest calculation is based on, which is why early extra payments save more total interest than later ones.

Assumptions

This calculator assumes a single fixed interest rate for the whole period entered, equal monthly payments, and no missed or extra payments. Adjustable-rate loans, escrow accounts, capitalized fees, or extra principal payments will make the real balance differ from this baseline estimate — use your lender's official statement or payoff quote for an exact, date-specific figure.

Frequently Asked Questions

How is the remaining loan balance calculated?
The calculator first finds the fixed monthly payment using M = P x i x (1+i)^n / [(1+i)^n - 1], then finds the balance as the present value of the payments still owed: B = M x [1 - (1+i)^-(n-k)] / i, where i is the monthly interest rate, n is the total number of scheduled payments, and k is the number of payments already made.
Why is so little principal paid off in the early years?
Interest is calculated on the outstanding balance each month, and the balance is highest early in the loan. Because the payment is fixed, more of it covers interest when the balance is high, leaving less to reduce principal. As the balance falls, the split gradually shifts toward principal, which is why payoff accelerates in the later years of the loan.
What if I've made extra payments?
This calculator assumes on-time, equal monthly payments with no extra principal paid. If you have made extra payments, your true remaining balance will be lower than this estimate, since extra principal is not reflected in a simple payments-made count. Use your loan's current statement balance for the most accurate figure.
Does this include taxes, insurance, or fees?
No. This tool computes only principal and interest under the loan's amortization schedule. It does not include property taxes, homeowners insurance, private mortgage insurance, HOA dues, or loan fees, which are often bundled into a monthly payment but are not part of the loan balance itself.

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