Calculate Loan Payments and Remaining Balance

This calculator estimates the fixed monthly payment and total interest for a fully amortizing loan when you enter the loan amount, annual percentage rate (APR), and term. It does not calculate a changing balance for a chosen payment date; the balance can be found from the payment schedule using the formula explained below.

Formula

The monthly payment is the level-payment amortization formula: M = P × r ÷ [1 − (1 + r)⁻ⁿ]. Here, P is the amount borrowed in dollars, r is the monthly interest rate as a decimal, and n is the number of monthly payments. Convert the annual APR entered as a percentage to a monthly decimal by calculating r = APR ÷ 1200; convert the term in years to months with n = 12 × years.

Total interest in this calculator is I = M × n − P, where M is the monthly payment rounded to cents. The formula assumes the same payment each month and a constant rate. It models a loan paid off exactly at the end of its stated term.

Worked Example

Using the calculator’s default inputs—$20,000 principal, 8% APR, and a five-year term—the monthly rate is 0.08 ÷ 12, or 0.0066667, and the number of payments is 5 × 12 = 60.

1. Substitute the values: M = 20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰].
2. Evaluate the formula and round the monthly payment to cents: $405.53 per month.
3. Calculate total interest using that rounded payment: $405.53 × 60 − $20,000 = $4,331.80.

These are estimates under the stated assumptions. A lender’s payment schedule can differ because of rounding, payment dates, fees, or contract terms.

Assumptions

• The interest rate stays fixed throughout the full term.
• Payments are made monthly, with the first payment one month after the loan begins.
• Interest is treated as compounding monthly at APR ÷ 12.
• Fees, taxes, insurance, mortgage insurance, and escrow are not included unless they are part of the principal entered.

How to Calculate a Balance After Payments

The calculator reports the scheduled payment and total interest over the entire term, not the balance after a particular number of payments. To estimate that balance, first use the monthly payment M from the calculator, then enter the number of completed payments as k in this formula:

B_k = P(1 + r)^k − M × [(1 + r)^k − 1] ÷ r

B_k is the estimated remaining principal after payment k; P, r, and M have the definitions above. For example, after 12 payments on the default loan, the formula gives a balance of about $16,393.45. The balance is not simply the original principal minus 12 payments, because each payment first covers interest accrued for that period and only the remainder reduces principal.

For a zero-interest loan, the balance formula’s division by r is undefined; the corresponding balance is P − M × k, subject to a floor of zero once the loan is paid off. Actual payoff quotes may also include accrued interest through a specific date or other contract amounts, so this estimate is not a payoff statement.

How to Use and Interpret the Results

• Enter the principal amount, not the total of all scheduled payments.
• Enter APR as a percentage per year: for example, enter 8 for 8%, not 0.08.
• Enter the term in years. The calculator converts it to monthly payments.
• Read the first result as the scheduled monthly loan payment, then use total interest to see the interest implied by that payment over the full term.

The calculated payment represents principal and interest only. A billed amount may be different if the loan includes separate charges, variable-rate changes, irregular payment dates, or other items not represented by these inputs. The total-interest result also uses the payment rounded to cents, so it is the sum implied by that displayed payment—not an unrounded theoretical total.

Common Errors and Formula Limits

A frequent mistake is mixing an annual rate with a monthly period. Since the payment is monthly, the rate must be converted to a monthly decimal; the expression APR ÷ 1200 does both percentage-to-decimal and annual-to-monthly conversion. Another mistake is treating the loan term as months when the input asks for years.

This standard formula fits fixed-rate, fully amortizing loans with equal monthly payments. It does not accurately represent interest-only arrangements, balloon payments, variable rates, daily simple-interest calculations, skipped payments, or extra principal payments. If you make extra payments, the balance and payoff timing change; calculate each period using the actual payment and lender’s interest method rather than assuming the original schedule still applies.

For a changing balance, use the lender’s transaction history or amortization schedule when exact figures matter. The formula is useful for a consistent estimate, but it cannot account for details that were not entered.

Frequently Asked Questions

How do I calculate a monthly loan payment?
Convert APR to a monthly decimal, convert the term to months, and apply M = P × r ÷ [1 − (1 + r)⁻ⁿ]. This calculator performs that calculation and rounds the payment to cents.

How do I calculate my remaining loan balance?
Use the balance formula B_k = P(1 + r)^k − M[(1 + r)^k − 1] ÷ r, where k is the number of completed monthly payments. For an exact payoff amount, request a dated payoff figure from the lender.

Does a monthly payment include taxes and insurance?
Not in this calculation. It estimates principal and interest only; taxes, insurance, mortgage insurance, escrow, and fees are excluded unless included in the amount borrowed.

Why does my lender’s number differ from this estimate?
Differences can result from payment timing, daily interest, rounding rules, fees, rate changes, or contract terms. Compare the assumptions and use the lender’s disclosed schedule for the exact figures.

Does paying extra reduce the balance?
Extra amounts applied to principal generally change the future balance path, but their effect depends on how and when the lender applies them. This calculator does not model extra payments.

This is estimate arithmetic for education, not financial advice; the lender’s disclosure gives the exact figures.

Related

• Unsecured Loan Interest TDS Section: Section 194A
• Interest Loans to Pay Off Credit Cards: Cost Calculator
• Interest Loan Types and How They Work

in p | Loan amount | $ | 20000 | 1 | 100000000
in apr | Interest rate (APR) | % | 8 | 0.01 | 100
in yrs | Loan term | years | 5 | 0.0833 | 50
out pmt | Monthly payment | $ | p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)) | 2
out int | Total interest | $ | pmt * yrs * 12 - p | 2