The math behind every fixed-rate loan payment
Every standard installment loan — car loans, personal loans, student loans, mortgages — uses the same underlying formula to compute a fixed monthly payment that fully pays off the loan by the end of its term:
M = P × [ r(1+r)^n ] / [ (1+r)^n − 1 ]
Where M is the monthly payment, P is the loan amount (principal), r is the monthly interest rate (annual rate divided by 12), and n is the number of monthly payments (the term in months). This calculator applies that formula directly and then runs the full month-by-month schedule so you can see not just the payment amount, but exactly how it’s split between interest and principal every month for the life of the loan.
Why the same payment amount covers a shifting mix of interest and principal
A fixed monthly payment doesn’t mean a fixed split between interest and principal — that split changes every month. Each month, interest is charged on whatever balance is currently outstanding (interest = balance × monthly rate), and whatever is left of the fixed payment after that interest goes toward reducing the principal. Early in the loan, when the balance is at its highest, the interest charge is largest, so a smaller portion of your payment reduces the balance. As the months go by and the balance shrinks, the interest charge shrinks too, freeing up a larger share of the same fixed payment to pay down principal. This is why the balance-over-time chart on this page isn’t a straight line — it declines slowly at first and drops more steeply as the loan matures.
A worked example
Take a $20,000 loan at 7.5% annual interest over 48 months (4 years) — a fairly typical car-loan or personal-loan scenario. The monthly rate is 7.5% ÷ 12 = 0.625%. Plugging into the formula above gives a monthly payment of approximately $483.58. Over the full 48 months, total payments come to about $23,212, meaning roughly $3,212 of that is interest — about 16% of the original loan amount, paid on top of it for the privilege of spreading repayment over four years.
Compare that to the same $20,000 borrowed over just 24 months instead: the monthly payment rises to about $901.60 (nearly double), but total interest drops to roughly $1,638 — less than half of the 48-month scenario’s interest cost, because the balance is outstanding for half as long. This is the fundamental trade-off every borrower faces: shorter terms cost more per month but substantially less overall; longer terms are easier to fit into a monthly budget but cost meaningfully more in total interest.
What this calculator doesn’t include
This tool computes pure principal-and-interest amortization — it doesn’t add loan origination fees, prepayment penalties, credit insurance, or any lender-specific charges some loans include on top of interest. If a lender’s quoted monthly payment differs slightly from what this calculator shows for the same amount, rate, and term, the difference is almost always one of these add-on costs rather than an error in the interest math, since the amortization formula itself is standardized and used identically across virtually every lender.
Reading the amortization chart
The chart plots your remaining loan balance against time, starting at your full loan amount and ending at zero exactly at the final month of your term. The curve is always concave (it bends) rather than a straight diagonal line, precisely because of the shifting interest/principal split described above — the balance drops slowly during the early months when payments are mostly covering interest, then drops faster later as more of each fixed payment goes toward principal. If you’re comparing two different loan terms or rates, look at how much later the “elbow” of faster decline appears — a longer term or higher rate pushes that elbow further out, meaning you spend more of the loan’s life paying mostly interest before meaningfully reducing the balance.
When to also check overpayment
If your loan allows extra payments without penalty, paying more than the required monthly amount reduces the balance faster than this baseline schedule shows, which can meaningfully cut total interest — the mortgage overpayment calculator on this site models that scenario in detail, including a side-by-side comparison chart, and uses the same underlying amortization math as this page.