Loan fundamentals
How are loan payments calculated?
A fixed monthly loan payment is calculated from the amount borrowed, the periodic interest rate, and the number of payments. The payment is set high enough to cover each month's interest and reduce the balance to zero by the end of the term.
The four inputs behind the payment
A standard fixed-rate installment-loan calculation uses four pieces of information:
- Principal: the amount borrowed before future interest.
- Annual interest rate: the fixed percentage used to calculate interest on the outstanding balance.
- Periodic rate: for monthly payments, the annual rate divided by 12.
- Number of payments: the loan term in years multiplied by 12 for a monthly schedule.
Changing any one of these inputs changes the result. A larger principal or higher rate raises the payment. A longer term usually lowers the payment but keeps the balance outstanding longer.
Calculate a monthly loan payment with the same fixed-rate assumptions.
The fixed-payment formula
For principal P, monthly rate r, and n payments, the required payment is:
If the annual rate is 6%, the monthly rate is 0.06 ÷ 12, or 0.005. When the rate is exactly 0%, the formula simplifies to principal divided by the number of payments.
The formula calculates a level principal-and-interest payment. It does not mean the interest and principal portions are level. Interest is calculated on the remaining balance, so the split changes every month. The amortization schedule guide explains that movement.
Worked example
Calculate a $20,000 five-year loan
Inputs: $20,000 principal, 6% fixed annual rate, 60 monthly payments, and no extra payment.
The monthly rate is 0.5%. Applying the fixed-payment formula gives a required payment of $386.66. Across the complete schedule, estimated payments total $23,199.36: the original $20,000 principal plus $3,199.36 of interest.
The first month includes $100.00 of interest and $286.66 of principal. By the final month, only about $1.92 is interest because the remaining balance is much smaller. The final payment can differ by a fraction of a cent before display rounding.
Reproduce this loan in the calculator →Interest rate, APR, and total payment are different
The interest rate is the price charged on the outstanding principal. APR can include the interest rate plus certain loan fees, so it can be useful when comparing offers. The Consumer Financial Protection Bureau explains the distinction between rate and APR.
A mortgage's total monthly payment may also include property taxes, homeowners insurance, mortgage insurance, or escrow. CFPB guidance distinguishes that total from the principal-and-interest payment. A basic installment-loan calculator cannot infer those additional costs.
When the estimate may differ from a lender
Real contracts may use daily interest, specific payment dates, fees, variable rates, prepayment rules, or different rounding. Some loans include balloon payments or interest-only periods and therefore do not follow the level-payment model described here.
Use the result to understand a scenario, then compare it with the disclosures from the lender. The complete implementation assumptions are listed on the methodology page.
Common questions
Frequently asked questions
What determines a monthly loan payment?
For a fixed-rate, fully amortizing loan, the principal, annual interest rate, number of monthly payments, and payment frequency determine the required principal-and-interest payment.
Does a calculated loan payment include every cost?
No. A basic loan payment calculation usually excludes origination fees, taxes, insurance, escrow, late fees, and optional products.
Is APR the rate used in the payment formula?
Not necessarily. APR may include certain fees as well as interest. This site uses the entered fixed annual rate to calculate monthly interest and does not model separate fees.
Why does a longer loan have a lower payment but more interest?
The same principal is spread across more payments, reducing each required payment. The remaining balance also accrues interest for more months, which can increase total interest.