How to use this loan calculator
Choose a currency label and enter the actual amount financed, which may differ from an item's advertised cash price. Enter the contractual interest rate as a percentage, such as 6 for 6%, and the number of whole months from 1 to 600. Review the monthly result and open the amortization schedule to inspect principal, interest, and remaining balance. Use the same currency for every amount. Changing the currency label changes formatting only; it does not retrieve or apply an exchange rate.
How the calculation works
A fully amortizing installment loan uses a scheduled payment that covers each period's interest and repays part of the principal. Interest is charged on the outstanding balance, not on the original principal throughout the entire term. Early payments often contain more interest because more principal remains. Later payments generally contain more principal. The final payment clears the remaining balance under the model, rather than leaving a balloon amount to be paid separately.
This calculator assumes a fixed annual rate divided into twelve equal monthly rates, with payments at the end of each monthly period. It does not reproduce a daily-interest contract, irregular first period, variable rate, skipped payment, interest-only phase, or early repayment. A lender can also capitalize fees into the balance or charge them separately. Include financed costs in the entered principal only when they are actually part of the amount borrowed.
The interest rate and annual percentage rate can be different. APR may include fees or other costs and is useful for comparing borrowing offers under its governing disclosure rules. Substituting a fee-inclusive APR into the interest-rate field can overstate the scheduled principal-and-interest payment. Use the loan's contractual rate to model the payment and compare disclosed fees separately. The calculator does not derive APR from a fee schedule or certify the accuracy of a lender's disclosure.
The payment formula is evaluated before rounding. For the displayed schedule, monthly interest and payments are rounded to cents, and the final payment is adjusted to repay the remaining balance. Total interest and total payments come from that ledger. They can differ slightly from the unrounded formula payment multiplied by the number of months. The contract's rounding, accrual, and payment-date conventions may produce different figures even when the initial rate and principal match.
Formulas
Monthly rate and payment
Zero-interest loan
Monthly allocation
Worked examples
A three-year loan
For a principal of 10,000, annual rate of 6%, and 36 months, r = 0.005. The formula gives approximately 304.22 per month. The first month's interest is 50.00, so about 254.22 reduces principal. The schedule calculates subsequent interest on the reduced balance and adjusts the final payment for cent rounding.
A zero-rate comparison
A 12,000 principal repaid over 24 months at 0% requires 12,000 ÷ 24 = 500 per month. Total modeled interest is zero. That does not mean a real zero-rate offer has no cost: a financed fee increases the principal, while a separately paid fee should be compared outside the payment calculation.
Term length and total cost
Keeping a 10,000 principal and 6% rate while extending the term from 36 to 60 months lowers the formula payment from about 304.22 to 193.33. The debt remains outstanding longer, so total interest increases. Compare both the monthly commitment and the complete repayment cost rather than choosing from the smallest payment alone.
Common uses
Compare repayment horizons
Hold principal and the contractual rate constant while changing the number of months. Inspect the payment and total interest together. A lower monthly payment can leave more room in a budget while increasing the complete borrowing cost; the calculator makes both parts visible without judging which term is appropriate for your circumstances.
Check a financed purchase
Separate an item's cash price, upfront contribution, and actual financed balance before estimating payments. Keep any financed fee in the principal and note separately paid charges outside the model. Comparing only the advertised price with a payment can hide a different amount borrowed or a different term.
Understand a repayment statement
Open the schedule to see interest charged against the opening balance and the principal portion left after interest. This helps explain why paying the same amount each month does not reduce the balance by that full amount. Match the model to the contract before comparing individual statement rows.
Accuracy and limitations
The formula uses a stable logarithm and exponential calculation near zero rates. The ledger works in integer cents for balances and aggregates, applies monthly cent rounding, and adjusts the last payment. It accepts up to 600 monthly payments and does not simulate late or additional payments.
This is a fixed monthly annuity model. Lender statements can differ because of daily accrual, payment timing, fees, holidays, rounding, or contract adjustments. A mathematically consistent schedule does not establish that a loan is affordable, suitable, approved, or legally compliant.
Sources and methodology
These references support the formulas and financial concepts explained on this page. Product-specific rates, fees, and contract conventions still need to be checked with the provider.
Frequently asked questions
Should I enter APR or the interest rate?
Enter the contractual interest rate. APR can include fees, so it may not be the rate used to accrue interest in a monthly payment formula.
Does this work at 0% interest?
Yes. The calculator uses principal divided by the number of months, avoiding division by zero in the ordinary annuity formula.
Can I model extra payments?
This version models scheduled payments only. Extra payments can shorten the term or reduce interest, but contract rules and payment allocation must also be considered.
Why does the final payment differ?
The ledger rounds each month's interest and payment to cents. Its last payment repays the remaining balance and accrued monthly interest.
Does it include origination fees or insurance?
No separately billed costs are added. Include financed fees in principal only when the lender finances them; compare other costs independently.
Are my loan inputs stored?
No. The calculator runs in your browser, and NumUtility does not receive or save the loan values you enter.