The maths, with your numbers
What paying extra would do
Every dollar above the payment comes straight off the balance, so the interest stops being charged on it. These are worked out from the loan above.
How the balance falls
The same loan over different terms
| Term | Payment | Total interest | Total repaid |
|---|
A longer term lowers the payment and raises the interest. Your loan is highlighted.
Amortization schedule
Where each payment goes, from the first to the last.
This calculator works out the payment on a fixed-rate loan, and then shows you everything the payment hides: the total interest, the date it ends, what an extra $50 a month would do, and where every single payment goes.
It handles car loans, personal loans, student loans, boat and RV loans, business loans and mortgages, because the arithmetic is the same for all of them. Nothing you type is sent anywhere.
How a loan payment is worked out
An amortizing loan is one where every payment is the same size, and each payment covers the interest that has built up since the last one, with the rest coming off the balance. Early on, most of the payment is interest. Later, most of it is principal. The switch-over point is marked on the chart above.
The payment comes from one formula:
payment = P × i1 − (1 + i)−n
P is the amount borrowed, i is the interest rate for one period (the annual rate divided by the number of payments a year) and n is the number of payments.
We show that formula filled in with your own numbers, above, so you can check it in any other calculator, or by hand.
Why the last payment is a different size
The payment almost never comes out to a round number of cents, so lenders round it, normally up. That rounding leaves a few dollars of difference by the end, which is collected in a slightly smaller final payment. Our schedule does the same thing, which is why the last line is not quite like the others.
Interest rate and APR are not the same thing
The interest rate is what the lender charges on the balance. The APR also includes the fees you pay to get the loan, which is why it is usually the higher number and the more useful one for comparing offers.
As the Consumer Financial Protection Bureau puts it, the interest rate “does not reflect fees or any other charges”, while the APR is “a broader measure of the cost to you of borrowing money”.
Enter an origination fee above and the calculator shows both, along with the cash you actually receive. Personal loan fees are usually taken out of the money sent to you: borrow $20,000 with a 5% fee and $19,000 lands in your account, but you repay all $20,000.
Under federal lending rules, a lender's disclosed APR must be accurate to within one-eighth of a percentage point for a regular loan. Ours is calculated the same way, from the payments and the cash you receive.
Paying extra: what actually happens
On a normal simple-interest loan, paying more than the payment reduces the balance immediately, so the next month's interest is smaller. That is why a small extra amount saves far more than it looks like it should.
Two things to know before you try it.
- Tell the servicer where the money goes. The CFPB's guidance is that a payment is applied to fees first, then interest, then principal. Extra money is not automatically treated as a principal payment, so say so in writing or use the “extra principal” box if the lender has one.
- Check for a prepayment penalty. Some auto and personal loans charge one, though several states ban them.
There is one case where paying extra does not help: a precomputed interest loan, where all of the interest is added at the start. The CFPB is blunt about it: with precomputed interest, “making extra payments does not reduce the principal amount (or interest) owed”. Most loans today are simple interest, but check your agreement before you overpay.
Biweekly payments
Switch the frequency to every two weeks and you make 26 half-payments a year, which is 13 monthly payments instead of 12. That extra payment is where the saving comes from, and you can get the same result by paying a thirteenth of a payment extra each month.
Companies sell biweekly “programs” that do this for you. In 2015 the CFPB sued one of them for charging a $995 setup fee plus an annual fee, on a service borrowers can arrange themselves for nothing.
Choosing a term
The table above runs your loan over every common term. A longer term always lowers the payment and always raises the total interest, and on a car the gap gets expensive quickly: the difference between 48 and 84 months at the same rate is usually thousands of dollars.
The useful question is not “what can I afford each month” but “what is the shortest term whose payment I can afford”. Use the How much I can borrow mode to work backwards from a payment you are comfortable with.
What this calculator does not include
- Taxes, insurance and fees on the thing you are buying. Car sales tax, title and registration, or a mortgage's property tax, homeowners insurance and PMI, are not in the payment here.
- Variable rates. Everything above assumes the rate stays the same for the whole term.
- Daily-accrual differences. Many auto and student loans charge interest by the day, so paying a few days early or late changes the interest slightly. The schedule here uses the standard period-by-period method that lenders use for disclosure.
- Late fees, insurance add-ons and dealer products. If they are financed, add them to the loan amount.
It is an estimate for planning. The number that counts is the one in the lender's own disclosure, and you have the right to see that before you sign.
Quick answers
How do I calculate a loan payment?
Multiply the amount borrowed by the interest rate for one period, then divide by 1 minus (1 + that rate) to the power of minus the number of payments. The calculator above does it and shows the working with your own numbers.
What is the monthly payment on a $25,000 loan?
At 7.5% over five years it is about $501 a month, and you repay about $30,060 in total. Change the amount, rate or term above to see your own figure.
Does paying extra on a loan save money?
On a simple-interest loan, yes: the extra comes off the balance, so less interest is charged from then on. Tell the lender to apply it to principal. On a precomputed-interest loan it does not help, because the interest was added at the start.
Is APR the same as the interest rate?
No. The interest rate is charged on the balance. The APR includes fees as well, so it is usually higher and is the better number for comparing loan offers.
Do biweekly payments pay off a loan faster?
Yes. Paying half the monthly amount every two weeks means 26 half-payments a year, which is 13 monthly payments rather than 12. You can get the same effect by paying a little extra each month, for free.
What is an amortization schedule?
A table showing every payment on the loan: how much is interest, how much comes off the balance, and what is left. You can see the full schedule above and download it as a spreadsheet.
Sources
- Consumer Financial Protection Bureau, “What is amortization?”
- CFPB, “What is the difference between an interest rate and an APR?”
- 12 CFR § 1026.22, Determination of the annual percentage rate (Regulation Z); Appendix J, actuarial method
- CFPB, how a payment is applied: fees, then interest, then principal
- CFPB, simple interest compared with precomputed interest
- CFPB, prepayment penalties
- CFPB, action against a biweekly payment program (2015)