The monthly loan payment formula
For a fixed-rate loan repaid in equal monthly installments, calculate M = P × i/[1 − (1 + i)^(-N)]. P is the financed principal, i is the monthly decimal interest rate, and N is the number of payments. This answers how large each regular payment must be to repay the balance over the stated term. It does not calculate an interest-only payment, a credit-card minimum, or a balloon repayment.
Write down the three inputs before calculating. A purchase price is not necessarily the amount borrowed, an annual percentage is not a monthly decimal, and a four-year loan does not have four monthly installments. The worked example below uses an illustrative 12,000 principal, 8% nominal annual rate, and 48 months. These numbers demonstrate the arithmetic; they are not current market rates or a lender offer.
Turn the offer into consistent inputs
Convert the annual percentage to a decimal and divide by twelve: i = 8/100/12 = 0.0066666667 approximately. Keep the full value during the calculation instead of rounding it to 0.0067. Convert four years to N = 4 × 12 = 48 months. The assumption here is an annual rate divided into twelve equal periodic rates, with each payment made at the end of its monthly period.
Suppose an item costs 15,000 and you pay 3,000 upfront. Without other financed charges, P = 15,000 − 3,000 = 12,000. A 300 fee added to the loan would instead make principal 12,300; the same fee paid separately would not change this formula's principal. Use the stated amount financed when available. Do not silently add an upfront expense twice by including it in both the loan and a separate cost comparison.
Work through a 48-month example
Substitute the values: M = 12,000 × (0.08/12)/[1 − (1 + 0.08/12)^(-48)]. The numerator is 80, but that is only one month's interest on the initial balance. Dividing by the complete denominator gives approximately 292.9550681, displayed as 292.96. A payment of only 80 would not reduce principal in this model, so it could not clear the debt in 48 months.
The first cent-rounded payment contains 80.00 interest and 212.96 principal, leaving 11,787.04. The next month's interest is approximately 78.58, and its principal portion is 214.38, leaving 11,572.66. These two rows provide a practical cross-check of the payment. For a full explanation of why that allocation changes over time, continue with Loan Amortization Explained rather than treating the total installment as interest.
Reproduce the result in a spreadsheet
A compatible spreadsheet payment function can evaluate =-PMT(8%/12,48,12000). The leading minus sign presents the outgoing payment as a positive amount under the usual cash-flow sign convention. An equivalent direct expression is =12000*(8%/12)/(1-(1+8%/12)^(-48)). Both calculate the unrounded annuity payment, so use a two-decimal display format without first reducing the stored precision of the rate.
If a rate cell already stores 8% as 0.08, divide that cell by twelve only; dividing by one hundred again makes the rate too small. If it stores the plain number 8, divide by both one hundred and twelve. Use a positive whole payment count, ensure principal is in one currency, and confirm the payment timing option is end of period. A spreadsheet using beginning-of-period payments solves a different problem.
Compare a longer term without hiding total interest
Keeping principal at 12,000 and the annual rate at 8%, a 72-month term gives a formula payment of approximately 210.40. Relative to 292.96 over 48 months, that lowers the regular monthly amount by about 82.56. The reduction is a cash-flow comparison, not evidence of a cheaper loan. The longer schedule leaves principal outstanding for an additional two years under the same interest-rate assumption.
NumUtility's cent-rounded ledger gives total payments of 14,061.77 and interest of 2,061.77 for 48 months. At 72 months, total payments are 15,148.71 and interest is 3,148.71. The longer model therefore adds 1,086.94 of interest. Compare these totals alongside monthly payment and term; if a real offer also changes the rate or fees, record those changes explicitly rather than attributing everything to duration.
Handle zero interest and final-payment rounding
At zero interest, use M = P/N because the ordinary fraction becomes zero divided by zero. A 12,000 principal over 48 months then requires 250.00 per month and no modeled interest. If the division does not produce a whole number of cents, a cent-rounded schedule may need a slightly different final payment even at a zero rate. Separately billed fees are still outside the interest formula.
In the 8% example, 48 × 292.96 equals 14,062.08, while the ledger totals 14,061.77. The 0.31 difference comes from rounding and the final adjusted payment of 292.65. NumUtility rounds monthly interest to cents and carries balances in integer cents. A provider using daily accrual or different posting rules may calculate another total. Do not force a contractual statement to match a simplified schedule by changing inputs without an explanation.
Separate the interest rate from APR and extra costs
For this payment model, use the contractual interest rate rather than automatically using APR. APR can incorporate additional borrowing charges, so its purpose differs from the periodic accrual input. Compare the disclosed APR and fees alongside the modeled payment. NumUtility does not calculate APR from an offer's cash flows, determine whether a fee is legally included, or provide a regulatory disclosure.
A loan with changing rates, irregular payments, or additional principal payments needs a model that follows those events. This calculator uses scheduled monthly payments only, accepts whole-month terms, and does not model early payoff. USD, CAD, GBP, and AUD are formatting labels, not switches for national lending conventions. Confirm how the actual agreement converts its quoted annual rate, accrues interest, and allocates payments before using an estimate to check an offer.
Verify your calculation before comparing offers
Enter 12,000, 8, and 48 in the Loan Calculator to reproduce the example. Check the first interest amount, the remaining principal after payment one, the final zero balance, and the totals. Then change only the term to 72 to isolate duration. Preserve a record of principal, rate basis, month count, rounding method, and excluded costs so another reader can reproduce the same calculation.
This is an educational estimate, not financial advice, an affordability assessment, or a lending recommendation. It does not evaluate income, other debts, eligibility, or whether borrowing is appropriate. Use the lender's written terms for a real transaction and qualified guidance when needed. A useful comparison identifies both what the formula measures and what remains outside it, rather than ranking offers solely by whichever number produces the lowest installment.