What a loan payment is made of
A fixed-rate loan is repaid with equal monthly payments. Each payment first covers the interest that accrued on the outstanding balance during the month; whatever is left reduces the balance. Early on, most of each payment is interest because the balance is large. Near the end, almost all of it is principal. This pattern is called amortization, and the table under the calculator shows it month by month. With the default loan of $20,000 at 6.5%, the first month’s interest is $20,000 × 6.5% ÷ 12 = $108.33 of the $391.32 payment.
How to use this calculator
The calculator works out the monthly payment and the total cost of a fixed-rate loan, or the interest rate behind a payment you have been quoted.
What to enter
- What do you want to find? Monthly payment (the default) or Interest rate. The choice decides whether you enter a rate or a payment.
- Loan amount: the amount you borrow, in dollars, from $1 to $1,000,000,000. Default $20,000.
- Annual interest rate: the loan’s nominal yearly rate, before fees, from 0% to 100%. Default 6.5%. It is shown when you find the monthly payment.
- Loan term: the repayment period in whole years, from 0 to 50. Default 5. Use 0 only together with Additional months.
- Monthly payment: the payment you have been quoted, in dollars. It is shown only when you find the interest rate, and it must be above 0.
Advanced options
The next four fields sit in the Advanced options group. At their defaults they leave the result exactly as it would be without them.
- Additional months: 0 to 11 months added to the loan term, for a term such as 2 years and 6 months, or 9 months with a Loan term of 0. Default 0. A term of 0 years and 0 months shows “Enter a period of at least one month.”
- Upfront fee: a fee the lender keeps when the loan starts, such as an origination fee, as a percent of the loan amount from 0% to 20%. Default 0%, no fee. You receive the loan amount minus the fee and repay the full amount, so the payment does not change.
- First payment month and First payment year: when your first payment is due, with years from 2000 to 2079. Both start as Not set.
What the results mean
- Monthly payment: the amount due each month, shown to the cent. When you find the interest rate, it is the payment you entered.
- Annual interest rate: the rate you entered or, when you find the interest rate, the rate the calculator found, which then becomes the main result.
- Number of payments: 12 for each year of the term, plus the additional months.
- Total interest: Total paid minus the loan amount.
- Total paid: the monthly payment times the number of payments.
- Upfront fee: the fee in dollars, the loan amount times the fee percent.
- Amount you receive: the loan amount minus the fee.
- Total cost (interest plus fee): the total interest plus the upfront fee.
- APR with the fee: the annual percentage rate, the yearly rate at which your monthly payments repay the amount you receive. With a fee it is higher than the Annual interest rate.
- Last payment: the month and year of the final payment. For the default loan with a first payment in March 2026, it is February 2031.
The four fee rows appear only when Upfront fee is above 0, and Last payment only when both First payment month and First payment year are set. Under the results, the Chart tab of the result details draws the remaining balance, the Table tab lists every payment split into interest and principal (Download CSV, in the More menu, saves it as a file), and the Math tab repeats the steps with your own numbers. The two worked examples below go through full calculations, and “How it’s calculated” lists the formula and its sources.
The formula
With principal P, a monthly interest rate r (the nominal annual interest rate R divided by 12) and n monthly payments, the payment M is
M = P · r / (1 − (1 + r)^−n)
For a term of t years and m additional months, n = 12·t + m. If the rate is zero, there is no interest to spread, and the payment is simply P ÷ n. Total paid is T = M × n, and total interest is I = T − P. With a first payment month S, the last payment falls in month L = S + n − 1.
With an upfront fee f, a percent of P, the fee is F = P × f, you receive Q = P − F, and the total cost is K = I + F. The APR is 12·a, where a is the monthly rate at which the same payment M repays the amount received:
Q = M · (1 − (1 + a)^−n) / a
This follows Regulation Z, the US Truth in Lending rule: §1026.18 defines the amount financed, which here is the amount you receive, and §1026.22 sets how the APR is measured against it. Like the rate behind a payment, a cannot be solved for directly, so the calculator finds it by search.
A worked example
Borrow $10,000 at a 5% annual interest rate over 5 years. The monthly rate is 5% ÷ 12 = 0.4167%, and there are 60 payments:
M = 10,000 × 0.004167 / (1 − 1.004167^−60) ≈ 188.71
The payment is $188.71. The calculator keeps the unrounded payment (188.7123…), so the sixty payments add up to $11,322.74 and the loan costs $1,322.74 in interest. In the first month the interest is $10,000 × 0.004167 = $41.67, and $147.05 goes to principal; by the last month only about $0.78 is interest. Because the schedule uses the exact payment and rounds each figure to the cent only for display, interest and principal can differ by a cent from the payment shown in a row, and the balance ends at exactly 0.
A larger, longer loan shows how much the term matters: $200,000 at 6% over 30 years costs $1,199.10 a month and $231,676.38 in interest, more than the amount borrowed.
A worked example with an upfront fee
Take the default loan, $20,000 at 6.5% over 5 years, and enter 5 under Upfront fee. Without the fee, the payment is $391.32 and the total interest $3,479.38.
- The fee is $20,000 × 5% = $1,000.00, which the lender keeps when the loan starts.
- You receive $20,000 − $1,000.00 = $19,000.00 but repay the full $20,000, so the payment stays $391.32 and the interest stays $3,479.38.
- The Total cost (interest plus fee) is $3,479.38 + $1,000.00 = $4,479.38.
- The APR with the fee is 8.66%, the yearly rate at which sixty payments of $391.32 repay $19,000.00. That is 2.16 percentage points above the 6.5% that interest is charged at.
The same fee raises the APR more on a shorter loan, because it is spread over fewer payments. The fee works the same way when you find the interest rate: $20,000 repaid at $400 a month over 5 years has an Annual interest rate of 7.42%, and with a 2% fee you receive $19,600.00 and the APR with the fee is 8.27%.
Finding the rate behind a payment
Sometimes you know the amount, the term and the payment, but not the rate, for example when a dealer quotes a monthly figure. There is no closed-form way to solve the formula for r, so the calculator searches for the rate at which the formula reproduces your payment. Choose “Interest rate” under What do you want to find? and enter the payment. The solved rate becomes the main result, and the payment you entered is shown below it. If the payment is too small to ever repay the balance, the calculator says so and shows no rate.
How to compare offers
Two loans with the same payment can differ a lot in total cost. Compare the total interest, not just the monthly figure, and check the term: stretching a loan lowers the payment but, at any rate above 0%, raises the interest. To see two offers side by side, press Compare. It copies the loan into a second scenario that you can change, and a table lists the results of both.
The rate entered here is the loan’s nominal interest rate. The annual percentage rate (APR) that US lenders must disclose under Regulation Z also counts upfront charges such as an origination fee: it measures the cost against the money you actually receive. To see it, enter the fee under Upfront fee in Advanced options and read the APR with the fee row. A lender’s APR can still differ if it counts other charges too, or if the fee is added to the loan instead of being taken from the money you receive.
Common kinds of loans
The calculator fits any loan with a fixed rate and equal monthly payments, whatever the money is for. Loans are often described by what secures them and by what they pay for.
- Secured loans are backed by collateral, an asset the lender can take if the loan is not repaid. The car bought with an auto loan and the home bought with a mortgage are the usual examples.
- Unsecured loans have no collateral. The lender relies on your promise to repay, judged from your credit history and income.
- Personal loans pay out a lump sum that can be used for many purposes and is repaid in fixed payments over a set term. They are often unsecured, though some are secured by savings or a vehicle.
- Auto loans pay for a car or other vehicle, and the vehicle secures the loan: the lender holds a lien on it until the loan is repaid.
- Student loans pay for education. In the US they come from the federal government or from private lenders, and they are usually unsecured. Repayment often starts after you leave school. A plan with equal monthly payments follows the formula here; a plan whose payment depends on your income does not.
The kind of loan does not change the arithmetic: the payment depends only on the amount, the rate and the term.
FAQ
Does the calculator include fees or insurance?
It includes one upfront fee. Open Advanced options and enter the fee under Upfront fee, as a percent of the loan amount. The result then adds the fee, the Amount you receive, the Total cost (interest plus fee) and the APR with the fee. Other charges, such as insurance, property-tax escrow or fees billed each month, are not included, so a payment that bundles them is higher than the one shown here.
How does the interest rate change the payment and the total cost?
Each month's interest is the balance times the monthly rate, so a higher rate raises both the payment and the total interest, and a lower rate cuts both. The default loan, $20,000 over 5 years at 6.5%, costs $391.32 a month and $3,479.38 in interest. If a lender asks $400 a month for the same amount and term, the rate behind that payment is 7.42% and the interest comes to $4,000.00, so less than one percentage point more adds $8.68 a month and $520.62 in all. At 0% there is no interest, and the payment is the amount divided by the number of payments, so $12,000 over 2 years is $500.00 a month.
How does the loan term change the payment and the total cost?
A longer term spreads the amount over more payments, so each payment is smaller. But the balance comes down more slowly and is charged interest for longer, so at any rate above 0% the total interest rises. $10,000 at 5% costs $188.71 a month over 5 years and $1,322.74 in interest. Over 2 years and 6 months the payment rises to $355.29, but the interest falls to $658.81, about half. At any rate above 0%, lengthening a loan lowers the payment and raises the total cost; shortening it does the opposite.
How does the loan amount change the payment and the total cost?
At the same rate and term, the payment and the total interest are proportional to the amount. $200,000 at 6% over 30 years costs $1,199.10 a month and $231,676.38 in interest. Borrow a quarter more, $250,000 on the same terms, and both rise by a quarter, to $1,498.88 a month and $289,595.47 in interest. An upfront fee grows with the amount too, because it is a percent of it.
How can I tell whether a payment fits my budget?
The calculator does not judge that and uses no income rule. It gives the figures to set against your own budget. The Monthly payment is due every month, the same amount each time, for the Number of payments shown. Set the First payment month and the First payment year, and the Last payment row shows when the payments end. The payment covers principal and interest only, so insurance, taxes and other costs that come with the loan are extra. Total paid is the sum of all the monthly payments, and with an upfront fee, Amount you receive is the money you actually get. At any rate above 0%, a payment made smaller by a longer term means more payments and a larger Total paid.
Why is my lender's payment a few cents different?
Lenders round differently, may count days rather than months, and sometimes start interest from the funding date. The formula here is the standard monthly annuity used in textbooks.
Can I use it for a mortgage or car loan?
Yes, any fixed-rate, fully amortizing loan with equal monthly payments follows the same formula. Variable-rate loans change over time and need a different model. For a mortgage, the payment here is principal and interest only; property tax and home insurance, often paid into escrow together with the payment, come on top.
Where is the rate shown when I solve for the interest rate?
The solved annual interest rate becomes the main result, and the payment you entered is shown below it with the totals.