The formula for finding your monthly payment
To find your monthly payment when you know the APR, loan amount, and loan term, use this formula:
Monthly Payment = [P × (r × (1 + r)^n)] / [(1 + r)^n − 1]
Where:
- P = the principal (the amount you borrowed)
- r = the monthly interest rate (APR divided by 12, then divided by 100)
- n = the total number of monthly payments (loan term in years × 12)
This is called the amortization formula, and it's what banks and lenders use to calculate what you owe each month. The formula accounts for the fact that early payments cover more interest, while later payments cover more principal.
Key Takeaways
- Convert your APR to a monthly rate by dividing by 12, then by 100 — a 12% APR becomes 0.01 as your monthly rate.
- The amortization formula requires three numbers: the loan amount, the monthly interest rate, and the total number of payments.
- A loan calculator (from your bank, an online tool, or a spreadsheet) will do this math for you in seconds and show you the exact breakdown.
- Your actual monthly payment may differ slightly from the formula if your lender rounds, charges fees, or uses daily interest calculations instead of monthly ones.
Working through a real example
Say you borrow $10,000 at 6% APR over 36 months. First, convert the APR to a monthly rate: 6 ÷ 12 = 0.5, then 0.5 ÷ 100 = 0.005. That's your monthly rate.
Now plug the numbers in: P = $10,000, r = 0.005, n = 36. The formula gives you roughly $299.71 per month. That means you'll pay about $10,789.56 total over three years — the extra $789.56 is the interest your lender collects.
If you stretch the same loan to 60 months instead, your monthly payment drops to about $193.33, but you'll pay roughly $11,599.80 total. Longer terms mean lower monthly payments but more interest paid overall.
Why use a calculator instead of doing it by hand
The formula works, but the exponents make it tedious and error-prone to calculate by hand. Most people use one of three tools: a loan calculator on their lender's website, a free online calculator (search "loan payment calculator"), or a spreadsheet like Excel or Google Sheets.
In Excel, the function is =PMT(rate, nper, pv). For the example above, you'd type =PMT(0.005, 36, -10000) and it returns your monthly payment instantly. The negative sign on the loan amount tells the spreadsheet you're borrowing money, not lending it.
Most online calculators ask you to enter the loan amount, APR, and term in years or months, then show your monthly payment and a full amortization schedule — a month-by-month breakdown of how much interest and principal you pay each time.
What the APR actually includes
The APR (Annual Percentage Rate) is supposed to reflect the true cost of borrowing by including not just the interest rate but also certain fees the lender charges. However, what counts as a "fee" varies by loan type.
For credit cards, the APR is usually just the interest rate. For mortgages, auto loans, and personal loans, the APR may include origination fees, closing costs, or points — but not all fees. Property taxes, insurance, and HOA fees on a mortgage don't count toward APR, for example.
This matters because two lenders might quote different APRs for the same loan if one charges more upfront fees. The APR is meant to make comparison easier, but you still need to read the loan estimate or disclosure document to see what you're actually paying.
When your actual payment differs from the formula
The formula assumes interest compounds monthly and that your payment is exactly the same every month. Real loans sometimes work differently.
Some lenders use daily interest calculations, which means your payment may be a few cents higher or lower depending on how many days are in each month. Others round payments to the nearest dollar or add fees (like loan insurance or servicing fees) that aren't part of the APR. A few loans have variable rates, meaning the APR changes over time, so your payment changes too.
Always check your loan documents or ask your lender for the exact payment amount rather than relying only on the formula. The formula is accurate for standard fixed-rate loans, but it's a starting point, not a may provide.
How changes to the loan affect your payment
If you want to see how different choices change your monthly payment, the formula shows you instantly. Borrowing more money raises your payment proportionally — double the principal, and your payment roughly doubles. A higher APR also raises your payment, though not as dramatically as you might expect on short loans.
The term length has the biggest effect on how much you pay each month. Stretching a five-year loan to ten years cuts your monthly payment roughly in half, but you'll pay nearly twice as much interest overall. Shortening the term does the opposite: higher monthly payments, but much less interest paid.
Use a calculator to run different scenarios before you commit. Most lenders let you choose your term, and seeing the trade-off between monthly affordability and total interest cost helps you decide what works for your budget.
Frequently Asked Questions
Is the formula different for credit cards?
Credit cards don't use the amortization formula because you don't have a fixed term or payment. Instead, interest accrues daily on your balance, and you can pay any amount you want each month. If you want to know how long it will take to pay off a credit card balance, you need a different calculator that accounts for minimum payments and daily compounding.
What if the APR changes during the loan?
If your loan has a variable rate, the formula only works for the current rate. Your payment will change when the rate changes. Fixed-rate loans keep the same APR and payment for the entire term. Check your loan documents to see whether your rate is fixed or variable.
Why does my lender's payment differ from what the formula gives me?
The most common reasons are rounding, daily interest calculations instead of monthly ones, and fees added to your payment that aren't part of the APR. Always use the payment amount your lender provides on your loan estimate or disclosure document — that's the legally required figure and reflects how they actually calculate it.
Can I use this formula to compare loans from different lenders?
Yes. Calculate the monthly payment for each loan using the same formula, then compare. But also look at the total amount you'll pay over the life of the loan — a lower monthly payment sometimes means paying much more interest overall. The loan estimate from each lender will show both the monthly payment and the total interest cost.
What's the difference between APR and interest rate?
The interest rate is just the cost of borrowing money. The APR includes the interest rate plus certain fees, so it's supposed to be a more complete picture of what the loan costs. For some loans (like mortgages), the APR can be noticeably higher than the interest rate because it includes closing costs.