How to Calculate a Loan Payment
To calculate a loan payment, use the amortization formula: the monthly payment equals the loan amount times the monthly rate times (1 plus the monthly rate) to the power of the number of payments, divided by (1 plus the monthly rate) to the power of the number of payments minus 1. The monthly rate is the APR divided by 12. The free loan payment calculator above applies the formula instantly, and this page works through it step by step so you can check the result by hand.
The formula looks forbidding, but it has only three inputs: the loan amount, the monthly interest rate, and the number of payments. Once those are known, the payment follows, and every other figure — the total paid, the total interest, the payoff date, and the split between principal and interest in each payment — follows from the payment. Below are the steps, the worked examples, and the shortcuts for comparing loans.
The Loan Payment Formula
With P as the loan amount, r as the monthly interest rate (APR divided by 12), and n as the number of monthly payments, the monthly payment M is P times r times (1 + r) to the power n, divided by (1 + r) to the power n minus 1. If the APR is zero, the payment is simply the loan amount divided by the number of months — a $25,000 loan over 60 months at 0% costs $416.67 a month, with no interest at all.
The formula exists because the payment must do two jobs at once: pay the interest charged that month, and reduce the balance so that it reaches exactly zero on the last payment. A payment that only covered the interest would never reduce the balance, and a payment that only reduced the balance would leave the interest unpaid. The formula finds the single fixed amount that does both over the term you choose.
Step 1 — Find the monthly rate
Divide the APR by 12. For a 7.5% APR, the monthly rate is 0.625%, or 0.00625. For a 9% APR it is 0.75%, or 0.0075. For a 6% APR it is 0.5%, or 0.005. This is the r in the formula, and it is also the rate that charges the first month’s interest on the full loan amount.
Step 2 — Count the payments
Multiply the term in years by 12. A 4-year loan has 48 payments, a 5-year loan has 60, and a 3-year loan has 36. This is the n in the formula, and it is the exponent that makes the formula work: the longer the term, the smaller the payment, but the more interest you pay in total.
Step 3 — Apply the formula and check the first payment
Plug the three numbers in and work out the payment, then check it against the first payment’s split: the first month’s interest is the loan amount times the monthly rate, and the principal is the payment minus that interest. For the default $25,000 loan at 7.5% over 60 months, the payment is $500.95, the first month’s interest is $156.25, and the first month’s principal is $344.70, leaving a balance of $24,655.30. If your hand calculation gives a different first-month interest, the monthly rate is wrong.
Worked Examples: Calculating Payments by Hand
Each row below is a loan worked through the formula, with the monthly payment, the total paid, and the total interest, all from the calculator above. Try the formula on the first row and check your answer against the table.
| Loan | APR | Term | Monthly rate | Monthly payment | Total interest |
|---|---|---|---|---|---|
| $25,000 | 7.5% | 60 months | 0.625% | $500.95 | $5,056.92 |
| $15,000 | 9% | 48 months | 0.75% | $373.28 | $2,917.23 |
| $20,000 | 6% | 60 months | 0.5% | $386.66 | $3,199.36 |
| $10,000 | 12% | 36 months | 1% | $332.14 | $1,957.15 |
| $10,000 | 7.5% | 36 months | 0.625% | $311.06 | $1,198.24 |
The last two rows are the lesson in one pair: the same $10,000 over the same 36 months costs $332.14 a month at 12% and $311.06 a month at 7.5%. The payment differs by $21.08 a month, and the total interest differs by $758.91 — $1,957.15 against $1,198.24. That is the price of a 4.5-point rate difference, and it is why your credit score matters so much when you borrow. The $15,000 row shows the middle case: at 9% over 48 months, the payment is $373.28, the first payment is $112.50 of interest and $260.78 of principal, and the last payment is $2.78 of interest and $370.50 of principal.
How to Use the Loan Payment Calculator
The calculator is the fast way to apply the formula, and it also builds the schedule the formula alone does not show.
- Enter the loan amount. This is the principal you borrow, before interest.
- Enter the APR. Use the APR from the loan offer, because the APR includes fees.
- Enter the term in years. Common terms are 3, 5 or 7 years for personal and auto loans.
- Read the payment, the total, and the interest. The result box shows all three, plus the payoff month.
- Read the first payment’s split. The schedule shows the first 12 payments in detail: interest, principal, and balance for each.
- Try an extra payment. Add $50 a month and watch the interest and the payoff date change.
On the default loan, the first payment’s split is $156.25 of interest and $344.70 of principal. By payment 12 the interest has fallen to $131.80 and the principal has risen to $369.15. By payment 60 the interest is just $3.11 and the principal is $497.84. That progression is the amortization schedule, and it is what the formula is really calculating.
What the First Payment Tells You
The first payment is the most informative number after the payment itself, because it shows how front-loaded the interest is. The table below compares the first payment on four loans, all from the calculator above.
| Loan | Monthly payment | First interest | First principal | Balance after payment 1 |
|---|---|---|---|---|
| $25,000 at 7.5%, 5 years | $500.95 | $156.25 | $344.70 | $24,655.30 |
| $15,000 at 9%, 4 years | $373.28 | $112.50 | $260.78 | $14,739.22 |
| $20,000 at 6%, 5 years | $386.66 | $100.00 | $286.66 | $19,713.34 |
| $10,000 at 12%, 3 years | $332.14 | $100.00 | $232.14 | $9,767.86 |
Two patterns stand out. First, the first month’s interest is simply the loan amount times the monthly rate: $25,000 times 0.625% is $156.25, and $10,000 times 1% is $100.00. Second, the principal share is smallest when the rate is highest: on the 12% loan, only $232.14 of the $332.14 payment reduces the balance in month 1. That is why high-rate loans feel like they never shrink — in the early months, they barely do.
Common Mistakes When Calculating a Loan Payment
The formula is exact, so mistakes come from the inputs, not the maths.
- Using the annual rate as the monthly rate. The monthly rate is the APR divided by 12. Using 7.5% a month instead of 0.625% gives a payment nobody could afford.
- Using the interest rate instead of the APR. When fees exist, the APR is higher than the interest rate, and the APR is the honest price of the loan.
- Counting the term in years instead of months. A 5-year loan has 60 payments, not 5. The exponent n must be in months.
- Forgetting that the payment is principal plus interest. The $500.95 payment is not $500.95 of principal — in month 1, only $344.70 is principal.
- Comparing payments without comparing interest. A lower payment on a longer term costs more in total interest: $383.46 a month for 7 years costs $7,210.38 of interest, against $500.95 a month for 5 years at $5,056.92.
- Ignoring the payoff date. The payment and the term together decide when the loan ends: December 2026 plus 60 payments is November 2031.
Where You Will Use the Formula
The formula is the same for every fixed-rate loan, and the usual cases are the ones below.
- Personal loans. Check the payment before you sign, and compare two offers by their APR, not their payment.
- Auto loans. The average new-car loan in late 2026 was $44,664 at 7.0%, or $884.40 a month over 60 months.
- Student loans. The standard 10-year payment is the baseline every other repayment plan is compared against.
- Refinancing. Run the old loan and the new loan through the formula and compare the total interest, not just the payment.
- Extra payments. The formula with an extra amount shows the new payoff date and the interest saved.
Tips for Accurate Results
Five habits keep the calculation exact.
- Divide the APR by 12 first. Write the monthly rate down before touching the formula.
- Convert years to months. Multiply the term by 12 and use that as n.
- Check the first month’s interest. Loan amount times monthly rate should match the schedule’s first interest figure.
- Check the total. Monthly payment times the number of payments should equal the total paid: $500.95 times 60 is $30,056.92.
- Use the calculator to verify. Enter the same three numbers above and compare the payment with your hand calculation.
Loan Payment Calculation Quick Answers
The figures people look up most often when calculating a loan payment.
| Question | Answer |
|---|---|
| Payment on $25,000 at 7.5% for 5 years | $500.95 a month |
| Payment on $15,000 at 9% for 4 years | $373.28 a month |
| Payment on $20,000 at 6% for 5 years | $386.66 a month |
| Monthly rate at 7.5% APR | 0.625% |
| First interest on $25,000 at 7.5% | $156.25 |
Related tools on this site: the main loan payment calculator, the mortgage calculator for a home loan, the auto loan calculator for a car purchase, and the compound interest calculator for the other side of interest. The CalculatorSoup loan calculator is another independent check on the same formula.
Frequently Asked Questions
What is the formula for a monthly loan payment?
The monthly payment equals the loan amount times the monthly rate times (1 plus the monthly rate) to the power of the number of payments, divided by (1 plus the monthly rate) to the power of the number of payments minus 1. The monthly rate is the APR divided by 12.
How do I calculate a loan payment without a calculator?
Divide the APR by 12 to get the monthly rate, multiply the term in years by 12 to get the number of payments, then apply the formula. For most people, the practical answer is to use the calculator above — but the first month’s interest, loan amount times monthly rate, is an easy hand check.
How much is the payment on a $15,000 loan at 9% for 4 years?
The monthly payment is $373.28, the total paid is $17,917.23, and the total interest is $2,917.23. The loan pays off in November 2030 with the first payment in December 2026.
Why is the first payment mostly interest?
Because the interest is charged on the full balance, which is at its largest in month 1. On a $25,000 loan at 7.5%, the first month’s interest is $156.25 of the $500.95 payment. As the balance falls, the interest falls and the principal share rises.
What is the difference between APR and interest rate?
The interest rate is the cost of borrowing the balance. The APR adds the fees to the interest rate and expresses the total as a yearly rate. When fees exist, the APR is higher, and it is the honest number for comparing loan offers.
Disclaimer: This calculator is for general information only and is not financial advice. Rates shown are reference ranges, not live quotes, and change weekly. The payment shown is principal and interest only and excludes taxes, insurance, fees and PMI. Check your loan offer before borrowing.