Free loan calculator that solves for any missing value. Enter any three of amount, rate, term and payment, and get the fourth plus the total interest.
Any three of the four fix the fourth, so the one being worked out is hidden.
Estimates only, for a fixed-rate loan with equal monthly payments and no fees. A lender's quote may differ because of origination fees, insurance, a different compounding or day-count convention, or the rate you are actually offered.
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A loan is fixed by four numbers: how much you borrow, the interest rate, how long you take to repay it, and the monthly payment. Any three of them determine the fourth. Most calculators only ever go one direction, from amount and rate and term to a payment. This one solves in all four directions, so you can also ask how much you can borrow on a payment you can afford, what rate a quoted payment really implies, and how long a balance will take to clear at a fixed monthly amount.
An amortising loan charges interest each month on the balance still outstanding, and whatever is left of your payment reduces that balance. Because the balance falls, the interest portion shrinks and the principal portion grows with every payment, even though the payment itself never changes. The standard payment formula is just the amount that makes the balance land on exactly zero at the end of the term. Reverse it and you get the borrowing power of a given payment; solve it for the term and you get a payoff date; solve it for the rate and you recover the rate behind a payment a lender quoted without one.
Monthly Payment Formula
Start from the payment you can comfortably afford and work backwards to the loan amount it supports, before a salesperson anchors you to a bigger number.
If an offer names a monthly payment but not a rate, recover the rate from the amount, the payment and the term, then compare it against a bank's published rates.
Fix the amount you can put toward a balance each month and see how many months it clears in, and how much interest that costs.
A longer term always lowers the payment and always raises the total interest. The term table prices both sides of that trade in the same view.
Payment, loan amount, interest rate and term are all solvable. Fill in any three and the fourth appears, instead of being forced to guess and re-guess until you land on the number you wanted.
Dealers, retailers and some lenders quote a monthly payment and stay quiet about the rate. Given the amount, the payment and the term, this recovers the rate implied by that offer so you can compare it with anyone else's.
Two comparison tables hold everything else fixed and move one thing. One shows what a longer term really costs in interest; the other shows what a rate a point higher or lower does to the same loan.
Each worked step states an equation whose left side genuinely evaluates to its right side, so you can verify the result on any calculator rather than taking it on faith.
Payments are quoted in whole cents the way a lender bills them, and the final instalment is trimmed to close the balance exactly rather than overshooting it.
All four variables of a fixed-rate loan: the monthly payment, the loan amount, the annual interest rate and the term. Enter any three and it returns the fourth. Payment, amount and term have closed-form solutions; the rate does not, so it is found by searching for the rate that reproduces your payment exactly, and the worked steps show that check.
An amortization calculator answers one question in depth: given an amount, a rate and a term, what does every single payment look like month by month. This one answers a different question, which is what any missing variable has to be. If you want the full month-by-month schedule and the effect of extra payments, use the amortization calculator; if you are still working out the loan itself, start here.
Choose "Interest rate" as what you want to work out, then enter the amount financed, the monthly payment and the number of payments. There is no formula that isolates the rate, so the calculator narrows in on the rate whose payment matches yours to the cent. This is how you compare a payment-only offer with a rate you have been quoted elsewhere.
Choose "Loan amount", then enter the payment you can manage, the rate you expect and the term. The answer is the present value of that stream of payments. Remember it is the loan amount, not the purchase price: any deposit, trade-in, tax or fee sits on top of it.
It depends on the loan, which is exactly why both comparison tables are shown. Shortening the term always cuts total interest but raises the payment, sometimes steeply. A lower rate cuts the interest and the payment together, but the available spread is usually narrower than the spread of terms on offer.
Because the regular payment is rounded to whole cents, the schedule almost never lands on exactly zero. Lenders bill the rounded amount every month and trim the final instalment to close the balance, so the calculator does the same and tells you when the last payment differs.
The interest rate is what is charged on the balance. The APR also folds in fees such as origination charges, spreading them across the term, so it is usually the higher of the two and is the fairer basis for comparing offers. This calculator works from the interest rate, so enter the APR instead if you want an estimate that carries the fees.
Yes. At zero interest the payment is simply the amount divided by the number of months, and the total of payments equals the amount borrowed. The worked steps switch to that simpler form so nothing divides by zero.