The formula for monthly payment starts with your loan amount, interest rate, and term length

To find your monthly payment, you need three pieces of information: the principal (the amount you borrowed), the annual percentage rate (APR), and the loan term (how many months you have to repay it). The APR tells you what percentage of the loan you pay in interest each year, but you have to convert it to a monthly rate and then explore a specific formula to get the actual payment amount.

The standard formula is called the amortization formula. It looks like this:

M = P × [r(1 + r)^n] / [(1 + r)^n − 1]

Where M is your monthly payment, P is the principal, r is the monthly interest rate (APR divided by 12), and n is the total number of months. This formula assumes you make equal payments every month and that the interest compounds monthly, which is how most consumer loans work.

Key Takeaways

  • Convert your APR to a monthly rate by dividing by 12, then convert that percentage to a decimal by dividing by 100.
  • The amortization formula requires your loan amount, monthly interest rate, and total number of months to calculate the exact payment.
  • A $10,000 loan at 6% APR over 60 months results in a monthly payment of approximately $193, with the exact amount depending on how your lender rounds.
  • Online calculators and spreadsheet formulas handle the math automatically, but understanding the steps helps you verify the result.
  • Your actual payment may differ slightly from the calculated amount because lenders round, and some loans have fees or variable rates.

Converting APR to a monthly interest rate

The APR is an annual figure, so the first step is to break it into a monthly rate. Divide the APR by 12. If your APR is 6%, the monthly rate is 6 ÷ 12 = 0.5%.

Then convert that percentage to a decimal, which is what the formula requires. Divide by 100: 0.5 ÷ 100 = 0.005. This decimal (0.005) is the value you use for r in the formula.

This conversion is the same for any APR. A 12% APR becomes 1% monthly, or 0.01 as a decimal. An 18% APR becomes 1.5% monthly, or 0.015 as a decimal.

Working through a concrete example

Let's say you borrow $10,000 at 6% APR and have 60 months (5 years) to repay it. Here's how the formula works:

First, set up your values: P = 10,000, r = 0.005 (the 6% APR converted to a monthly decimal), n = 60.

Next, calculate (1 + r)^n, which is (1.005)^60. This equals approximately 1.3489. Then multiply r by this result: 0.005 × 1.3489 = 0.006745. Subtract 1 from (1 + r)^n: 1.3489 − 1 = 0.3489. Divide the numerator by the denominator: 0.006745 ÷ 0.3489 = 0.01933. Finally, multiply by the principal: 10,000 × 0.01933 = $193.30.

Your monthly payment would be approximately $193.30. The exact amount depends on how many decimal places your lender carries through the calculation and whether they round at the end.

Using a spreadsheet or calculator instead of doing it by hand

Most people do not calculate this by hand. Spreadsheet programs like Excel and Google Sheets have a built-in function called PMT that does the work. In Excel, the syntax is =PMT(rate, nper, pv). The rate is your monthly interest rate (APR divided by 12), nper is the number of months, and pv is the loan amount (entered as a negative number).

For the $10,000 loan example, you would type =PMT(0.005, 60, -10000) and the spreadsheet returns -193.33. The negative sign is just how Excel displays it; your actual payment is $193.33.

Online loan calculators work the same way but do the math behind the scenes. You enter the loan amount, APR, and term, and the calculator shows your monthly payment when ready. These tools are useful for checking your math or exploring what happens if you change the term or interest rate.

Why your actual payment might differ from the calculated amount

The formula gives you the theoretical payment, but the actual amount you owe each month may be slightly different. Lenders round to the nearest cent, and different lenders round at different points in the calculation. A payment calculated as $193.326 might be rounded to $193.33 by one lender and $193.32 by another.

Some loans also include fees that are not part of the interest calculation—origination fees, servicing fees, or insurance premiums. These are added to your payment or rolled into the principal, changing the final monthly amount. Always check your loan agreement to see what is included in the stated payment.

Variable-rate loans complicate things further. If your APR can change during the loan term, your monthly payment will change too. The formula only works for fixed-rate loans where the APR stays the same for the entire term.

What happens if you change the loan term or interest rate

The formula shows how sensitive your payment is to both the rate and the length of the loan. Stretching a loan over more months lowers the monthly payment but increases the total interest you pay. A $10,000 loan at 6% APR costs $193.33 per month over 60 months, but only $172.61 per month over 84 months—yet you pay significantly more interest overall.

A higher APR raises your monthly payment directly. That same $10,000 loan at 9% APR over 60 months costs $207.58 per month instead of $193.33. The difference compounds over the life of the loan.

You can use the formula or a calculator to run these scenarios before you commit to a loan, which helps you understand the trade-offs between a lower payment and a lower total cost.

Frequently Asked Questions

Do I need to know the formula to find my monthly payment?

No. A calculator or spreadsheet does the math for you. Understanding the formula helps you verify the result and see why changing the rate or term changes your payment, but you do not need to calculate it by hand.

What if my loan has a different compounding period?

Most consumer loans compound monthly, so dividing the APR by 12 is correct. Some loans compound daily or quarterly. Check your loan documents to see the compounding frequency, then divide the APR by the number of periods per year instead of 12.

Does the formula work for credit cards?

Credit cards do not use a fixed term or principal, so the formula does not explore the same way. Credit card interest compounds daily, and your payment depends on your balance and the card issuer's minimum payment policy. You can use the formula to estimate what a fixed payment would be if you wanted to pay off a specific balance in a specific number of months.

Why is my actual payment different from what the formula gives me?

Lenders round to the nearest cent, and some include fees or insurance in the payment. Check your loan agreement for the exact payment amount and what it covers. Small differences (a few cents) are normal rounding; larger differences usually mean a fee is included.

Can I use this formula if my interest rate changes?

The formula only works for fixed-rate loans. If your rate adjusts during the loan term, you would need to recalculate the payment each time the rate changes, treating the remaining balance as a new loan with the new rate and remaining term.