Monthly payment, total interest and amortization for a fixed-rate loan.
Standard amortization: pmt = P · r / (1 − (1 + r)^−n) where r = APR/12 and n = months. Each payment is constant, but the interest share shrinks each month.
A fixed-rate installment loan — a car loan, a personal loan, the consumer credit you take to spread out a big purchase — is the most common loan product after a mortgage. The lender asks for a constant monthly payment over a fixed number of months. The headline trade-off is length × rate × principal: longer terms shrink the monthly payment but inflate the total interest paid. People consistently underestimate that inflation. A 7-year car loan vs a 5-year car loan at the same rate looks like a small monthly saving but costs hundreds or thousands more in interest. This calculator surfaces the three numbers that matter — the monthly payment, the total paid over the life of the loan, and the total interest — plus the first-month split between interest and principal, which is the leading-edge view of the amortization schedule.
Standard amortization: pmt = P · r / (1 − (1 + r)^−n), where P is principal, r is the monthly rate (APR ÷ 12), and n is the number of monthly payments (years × 12). Total paid = pmt × n. Total interest = total paid − P. First-month interest = P × r; first-month principal = pmt − first-month interest. Each subsequent month the interest share shrinks because the outstanding balance shrinks; the principal share grows correspondingly. This is amortization: the payment is constant but its composition shifts month by month. Setting r = 0 (a 0 % loan) collapses the formula to pmt = P / n by L'Hôpital's rule on the ratio.
Enter the loan amount (principal), the annual rate (APR — what the lender quotes; the calc converts to monthly rate internally), and the term in years. The result panel shows the monthly payment as the headline KPI plus the total paid, total interest, the first-month interest/principal split, and the interest-as-a-percentage-of-principal — a powerful single number for comparing loan offers.
Car loan: P = 18 000 €, APR = 5.5 %, 5 years. - Monthly rate: 5.5 / 12 = 0.4583 %. - n = 60. - Pmt = 18 000 × 0.004583 / (1 − (1.004583)^−60) = 343.97 €. - Total paid: 343.97 × 60 = 20 638 €. - Total interest: 2 638 € = 14.65 % of principal. - First-month interest = 18 000 × 0.004583 = 82.50 €; first-month principal = 343.97 − 82.50 = 261.47 €.
APR vs nominal rate. Banks sometimes quote a "nominal" rate that omits fees and sometimes the true APR that includes origination, broker, and insurance fees. The pmt formula here treats whatever you enter as the interest-only APR. If your lender's APR includes fees (the standard EU "TAEG" definition does), the resulting pmt will be slightly higher than the actual cash payment because the fees are already amortized into the rate; for a precise number, get the lender's amortization schedule directly.
Longer term illusion. Stretching from 5 to 7 years on the same 18 000 € / 5.5 % loan drops the payment from 344 € to 261 € (−24 %), but the total interest jumps from 2 638 € to 3 951 € (+50 %). That is not a small difference — it's a year of payments paid in pure interest. The calc displays both so the trade-off is visible.
Variable-rate loans. The formula assumes a fixed rate. Variable-rate or adjustable loans (ARM mortgages, some lines of credit) shift the payment when the rate moves. The first-month numbers are still useful as an entry-point estimate, but the totals will drift.
Bullet repayment / interest-only. Some loans defer principal until a final balloon payment. The calc does not model this — it amortizes uniformly. A bullet loan at 5.5 % APR pays 0 % principal monthly and 100 % interest, then a single 18 000 € principal payment at month 60. The interest cost is the same first-month value × 60 — much higher than amortized.
Early repayment. Paying extra principal in any given month shortens the loan. The calc does not expose an early-repayment input; if you're shopping for a loan, ask the lender whether early repayment incurs a penalty (in France, banks may charge up to 6 months of interest on the prepaid amount, capped at 3 % of the outstanding capital).