How the loan payment formula works
An amortizing loan is repaid in equal installments, each of which covers the interest that accrued over the period and then applies whatever is left to the principal. The installment size comes from the standard annuity formula: payment = P * i * (1 + i)^n / ((1 + i)^n - 1), where P is the amount borrowed, i is the interest rate for one payment period, and n is the total number of payments. This calculator uses exactly that formula, then builds the schedule period by period from it.
The period rate is the annual rate divided by the number of periods in a year. Choosing monthly divides by 12, biweekly divides by 26, and weekly divides by 52. The term you enter in years and months is converted the same way, so a 30 year term becomes 360 monthly periods, 780 biweekly periods, or 1,560 weekly periods. If you enter a rate of zero, the formula collapses to principal divided by the number of periods, which the calculator handles as a separate case rather than dividing by zero.
Once the payment is known, each row of the schedule is computed as interest = current balance * period rate, principal = payment - interest, and new balance = old balance - principal. Interest is always taken first, which is why early payments on a long loan move the balance so little. On a 30 year loan at a typical rate, more than half of the first year of payments is interest.
Worked example: a 300,000 loan at 6.5 percent
Take the calculator defaults: 300,000 borrowed, 6.5 percent annual interest, 30 year term, monthly payments. The period rate is 0.065 / 12 = 0.00541667 and n is 360. Running the formula gives a monthly payment of 1,896.20. Multiplied across 360 payments, that is 682,633.47 paid in total, of which 382,633.47 is interest. The interest exceeds the amount borrowed, which is normal for a long term at that rate.
The first payment breaks down as interest of 300,000 * 0.00541667 = 1,625.00 and principal of 1,896.20 - 1,625.00 = 271.20. After that payment the balance is 299,728.80. By payment 180, the halfway point in time, the balance is still above 200,000, because principal reduction accelerates only as the interest portion shrinks.
Switching the frequency to biweekly on the same loan gives a payment of 874.76 every two weeks across 780 periods, or 682,311.79 in total. The small difference from the monthly figure comes from the compounding period changing, not from paying extra. This calculator treats biweekly as 26 true periods per year at one twenty sixth of the annual rate, so it is not the same thing as the accelerated biweekly plans some lenders sell, where you pay half a monthly payment every two weeks and therefore make the equivalent of 13 monthly payments a year.
What the extra payment field does
The extra payment field adds a fixed amount to every scheduled payment, applied entirely to principal. The calculator keeps the base payment from the original formula, then in each period subtracts principal plus the extra amount from the balance. The loop stops as soon as the balance reaches zero, so the schedule ends early and the final payment is trimmed to whatever is actually owed rather than overshooting.
On the 300,000 example, adding 200 per month ends the loan after 277 payments instead of 360, a little over 23 years, and total interest falls to roughly 279,185 from 382,633. The savings figure shown by the calculator is the difference between the interest on the unchanged schedule and the interest actually paid, and the time saved is the number of periods removed from the original term.
Two limits are worth knowing. First, the calculator assumes the extra amount is paid every single period without interruption; skipping months changes the result materially. Second, it assumes your lender applies extra money to principal immediately rather than holding it as a prepaid future installment. Some servicers do the latter by default, which produces no interest savings at all, so the instruction to apply extra funds to principal has to be given explicitly.
What the total does not include
This is a pure principal and interest calculator. It does not model origination fees, discount points, application fees, or any other closing cost, so the total payment figure is not the total cost of borrowing. A loan with a lower rate and two points of origination can easily cost more than a higher rate loan with no fees, and nothing in this tool will reveal that. Comparing annual percentage rate figures from lender disclosures is the way to catch it.
It also does not model insurance, property tax, escrow, late fees, or prepayment penalties. For a mortgage, those items often add several hundred dollars a month to what actually leaves your account, which is why the mortgage calculator on this site is a better fit for a home loan. For a car loan, sales tax and registration are excluded here as well.
Finally, the schedule assumes a fixed rate for the entire term. Adjustable rate loans, introductory teaser rates, and any loan whose payment resets partway through will not be described correctly by this model. The payoff date it reports is derived from the start month you enter plus the number of periods, and takes no account of a first payment date that falls outside the normal cycle, which lenders commonly set.
The mistake people make with loan comparisons
The most common error is comparing two loans on monthly payment alone. A longer term always produces a smaller payment and almost always produces more total interest. The 300,000 loan at 6.5 percent costs 1,896.20 a month over 30 years and 382,633 in interest; the same loan over 15 years costs about 2,613 a month but only around 170,000 in interest. The payment is worse and the loan is much cheaper, and looking only at the first number hides that completely.
The second common error is reading the total interest figure as a fee you could avoid. Interest is the price of having money now, spread over time; the only way to reduce it materially is to borrow less, borrow for less time, or borrow at a lower rate. Refinancing into a fresh 30 year term at a lower rate can raise total interest even though the payment drops, because the clock restarts.
A third error is ignoring the payment frequency setting. Weekly and biweekly schedules produce smaller individual payments that look cheaper at a glance, but the comparison that matters is the annual total. Change the frequency and check the total payment line rather than the per period line.