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Finance formula

How to calculate loan payment

The loan payment formula spreads principal and interest over a fixed number of monthly payments.

See the formulaOpen calculator
Direct answer
Formula
M = P * r * (1 + r)^n / ((1 + r)^n - 1)

Use the table below to match each symbol with the right input. Keep units consistent before you start.

Loan payment formula
Start here when you only need the equation and variable names.
Formula
M = P * r * (1 + r)^n / ((1 + r)^n - 1)

The loan payment formula spreads principal and interest over a fixed number of monthly payments.

Variable meanings
Check each symbol, meaning, and unit before you calculate.
SymbolNameDescriptionUnit
MMonthly paymentFixed payment due each month.currency per month
PPrincipalAmount borrowed.currency
rMonthly rateAnnual percentage rate divided by 12.Depends on inputs
nNumber of paymentsTotal monthly payments over the loan term.months
When to use this formula
Check that your situation matches the formula before you trust the result.
  • Works for fixed-rate installment loans such as personal loans, auto loans, or student loans.
Step-by-step method
Follow these steps when you are solving it by hand.
  1. 1Convert APR to a monthly decimal rate.
  2. 2Multiply years by 12 to get the number of payments.
  3. 3Apply the amortization formula.
  4. 4Multiply the payment by the number of months to estimate total paid.
Examples
These sample numbers show the order of operations and units.
Five-year auto loan
P
$25,000
APR
6%
n
60 months
  1. 1.r = 0.06 / 12 = 0.005
  2. 2.M = 25000 * 0.005 * (1.005)^60 / ((1.005)^60 - 1)
  3. 3.M = 483.32
Result
The monthly payment is about $483.32.
Three-year personal loan
P
$10,000
APR
8%
n
36 months
  1. 1.r = 0.08 / 12 = 0.0066667
  2. 2.M = 10000 * r * (1 + r)^36 / ((1 + r)^36 - 1)
  3. 3.M = 313.36
Result
The monthly payment is about $313.36.
Mistakes to avoid
Small input or unit errors can change the answer a lot.
  • Using an annual rate where the loan payment formula needs a monthly or period rate.
  • Entering 8 instead of 0.08 when the formula calls for a decimal rate.
  • Comparing results across different time periods without converting them first.
  • Rounding each step instead of rounding the final answer.
Open the Loan Calculator
Open the calculator for the answer without rewriting the formula.

Enter your values in the related calculator, then compare the output with the hand method above.

Open Loan Calculator
FAQs
Short answers for common formula questions.
Can I calculate Loan payment by hand?

Yes. Write the units next to each value, convert rates or measurements first, and round only the final answer.

Why does my Loan payment result differ from another calculator?

Most differences come from rounding, unit conversions, rate timing, or a slightly different version of the formula.

When is the Loan Calculator better than hand math?

Open the Loan Calculator to check several scenarios or skip the hand arithmetic.