How a fixed monthly payment pays down a loan
Understand how interest and principal split each month, why the payoff formula rounds up, and how a bigger payment cuts total interest.
Every payment splits into interest and principal
Each month the lender first charges interest on whatever you still owe, calculated as the balance times the monthly rate. At 18% APR the monthly rate is 1.5%, so on a $10,000 balance the first month's interest is $150. Your $250 payment covers that $150 and the remaining $100 chips away at the principal. As the balance falls, the interest slice shrinks and more of each fixed payment goes to principal, which is why the loan pays off faster and faster toward the end.
Where the payoff formula comes from
Because the balance changes every month, the number of payments is not a simple division. The tool solves the amortization equation for the month count using logarithms, then rounds up because you cannot make a fraction of a payment. That rounding is why a $10,000 loan at 18% with $250 payments lands on 62 whole months rather than 61 and a half. The last of those months needs only a partial payment to finish the job.
Why the last payment is smaller
After 61 full payments the leftover balance on that $10,000 loan is only about $134, so a 62nd full $250 payment would overshoot. This calculator trims the final payment to that remaining balance plus its one month of interest, which is why the total paid comes to $15,386.23 rather than 62 times $250. Modeling the capped final payment keeps the total interest figure of $5,386.23 honest instead of slightly inflated.
When a payment is too small to win
There is a floor below which a loan never dies. If your payment only equals or undercuts the first month's interest, the principal never drops and the balance holds steady or grows. A $3,000 balance at 24% APR accrues $60 of interest in month one, so a $50 payment leaves you further behind every month and the tool flags it as impossible. Clearing the interest threshold is the first requirement; paying comfortably above it is what shortens the term and slashes total interest.