What the payment calculator does
Given a loan amount, an annual interest rate and a number of payments, the calculator returns the fixed payment per period, the total paid and the total interest — for monthly, bi-weekly or weekly schedules. It is the general form of the mortgage, auto-loan and personal-loan calculators: use it for any amortizing debt, including equipment finance, business loans, student loans and buy-now-pay-later plans, and to compare how a different payment frequency changes the cost.
The formula
Payment = P × r(1 + r)ⁿ / ((1 + r)ⁿ − 1)
P = amount borrowed
r = rate per period = annual rate ÷ periods per year (12 monthly, 26 bi-weekly, 52 weekly)
n = total number of payments
$50,000 at 6% over 360 monthly payments:
r = 0.005, n = 360 → payment ≈ $299.78/month, total ≈ $107,919, interest ≈ $57,919Monthly vs bi-weekly vs weekly
Changing frequency alone barely changes the cost: 26 bi-weekly payments of half the monthly amount cost about the same as 12 monthly payments. The famous saving from “bi-weekly mortgage payments” comes from paying half the monthly amount every two weeks — which is 26 halves, or 13 full monthly payments a year instead of 12. That extra payment goes to principal and shortens the loan.
| Schedule on $50,000 at 6%, 30 years | Payment | Payments per year | Total interest | Paid off in |
|---|---|---|---|---|
| Monthly | $299.78 | 12 | $57,919 | 30 years |
| Bi-weekly (true bi-weekly amortization) | $138.30 | 26 | $57,520 | 30 years |
| Half the monthly payment every two weeks | $149.89 | 26 | $46,500 | ≈ 25 years |
The calculator computes the true amortized payment for each frequency. To model the accelerated version, enter the monthly figure ÷ 2 as a bi-weekly overpayment in a mortgage calculator with extra-payment support.
Reading the results
- Payment amount is fixed for the life of a fixed-rate loan; the split between interest and principal shifts toward principal over time.
- Total interest is the true cost of borrowing. Compare it, not the payment, when weighing a longer term.
- Total paid = payment × number of payments; fees charged up front are not included — add them to the principal if they are financed.
Solving for the other variables
- How much can I borrow for a given payment? Rearrange:
P = payment × ((1 + r)ⁿ − 1) / (r(1 + r)ⁿ). At 6% over 60 months, a $500 payment supports about $25,860. - What rate am I paying? There is no closed form; the Interest Rate Calculator solves it numerically from the payment, amount and term.
- How long to pay off at a chosen payment?
n = −log(1 − rP/payment) ÷ log(1 + r), valid only when the payment exceeds the first period's interest.