Payment Calculator
Four loan unknowns — payment, amount, term, rate. Give the calculator any three and it solves for the fourth, at the payment frequency you actually use.
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One Calculator, Four Questions
Most loan tools answer a single question — "what is the payment?" — because the payment has a tidy formula. Real borrowing asks three harder questions just as often. A dealer quotes a payment and a term, and the unknown that matters is the rate hiding inside them. A budget fixes the payment you can carry, and the unknown is how much you can borrow, or how long a balance will actually take to clear. Each unknown needs its own mathematics: the term comes from logarithms, and the rate has no formula at all — it is found by narrowing in on the value that makes the payment equation balance, which this calculator does to three decimal places.
Worked Example: The $320,000 Mortgage, Solved Four Ways
The calculator opens on a $320,000 loan at 6.8% APR over 30 years, monthly. Solving for the payment gives $2,086.16 a month; over 360 payments the interest totals $431,017.82, and the first year is the most lopsided — $21,656.01 of interest against $3,377.92 of principal. Now change one thing at a time. Solve for the amount instead, telling it you can pay $2,000 a month at 6.5% for 30 years, and it works backwards to the loan that payment carries. Solve for the term on a $25,000 balance at 9.9% with a $500 payment and it answers 64.7 months — 61 payments, the last one smaller. Solve for the rate on $18,000 repaid at $360 a month for 60 months and it finds 7.42% APR — the check to run whenever a seller quotes you a payment and a term but not a rate.
Payment Frequencies, Honestly
The frequency changes the arithmetic, not just the calendar: the per-period rate is the APR divided by the payments per year, and the number of payments is the term multiplied by that same count. Biweekly is the interesting case — 26 payments a year at half the monthly size adds up to a thirteenth monthly payment annually, which is why the worked example's interest falls by $349.04 when it is switched to biweekly. Weekly, semi-monthly, quarterly and annual modes follow the same rule, so a quote in any frequency can be compared with any other on equal terms.
Payment Calculator Facts at a Glance
- The worked example: $320,000 at 6.8% APR for 30 years costs $2,086.16 a month and $431,017.82 in total interest — more than half the amount borrowed.
- The interest rate is the only loan variable with no direct formula; this calculator solves it numerically to three decimal places.
- A payment that does not exceed the interest charged each period never reduces the balance — the calculator rejects it and shows the period interest.
- Biweekly payments total 13 monthly payments a year, which is where their interest saving comes from.
Frequently Asked Questions
What can this payment calculator solve for?
Any one of the four loan variables, given the other three: the payment (from amount, rate and term), the loan amount you can carry (from payment, rate and term), the time to pay off (from amount, rate and payment), or the interest rate implied by the other three — the mode most loan calculators refuse to touch, because the rate has no closed-form formula and must be solved numerically, as it is here.
How is a loan payment calculated?
The payment is the amount that exactly retires the loan in equal instalments: payment = principal × r ÷ (1 − (1 + r)^−n), where r is the per-period rate (APR divided by the payments per year) and n is the number of payments. For the worked example — $320,000 at 6.8% APR over 360 monthly payments — r is 0.005667 and the formula gives $2,086.16 a month.
What is the monthly payment on a $320,000 loan at 6.8% for 30 years?
$2,086.16. Year one alone carries $21,656.01 of interest against $3,377.92 of principal — early payments are mostly interest, which is normal amortisation. Over the full 30 years the interest totals $431,017.82, so the loan costs $751,017.82 all in. Run the same figures in the calculator above to see the year-by-year schedule.
What happens if the payment does not cover the interest?
The loan never pays off — the balance grows instead of shrinking, which is called negative amortisation. This calculator detects it and says so: on a $25,000 loan at 9.9% APR, the interest charged in the first month is $206.25, so any monthly payment at or below that figure is rejected with the exact interest amount shown. Raise the payment above it and the term solver takes over — at $500 a month that same loan clears in 64.7 months, so 61 payments with a smaller final one.
How is this payment calculator different from the Loan Calculator?
The Loan Calculator answers one question — the payment — from amount, rate and term, monthly only. This calculator solves for whichever variable you do not know, including the interest rate and the payoff term, and it works in weekly, biweekly, semi-monthly, monthly, quarterly or annual payments, with a year-by-year schedule for every answer. If you already know all four variables and want a full month-by-month schedule, the Amortization Calculator is the deeper tool.
Do biweekly payments pay a loan off faster?
Two separate effects are at work. A biweekly schedule makes 26 half-size payments a year — the equivalent of 13 monthly payments, one extra — and interest is charged more often on a shrinking balance. On the worked example, switching the $320,000 loan at 6.8% to biweekly payments of $962.40 cuts total interest from $431,017.82 to $430,668.78, a saving of $349.04 over the life of the loan. The calculator uses true biweekly periods (rate = APR ÷ 26), not a monthly payment split in two.