What is the formula for a monthly loan payment?

Payment = P x r x (1 + r)^n / ((1 + r)^n - 1), where P is the amount financed, r is the periodic (monthly) interest rate expressed as a decimal, and n is the number of monthly payments. If the rate is 0%, the payment is simply P divided by n.

Is APR the same as the interest rate?

No. The interest rate sets the interest charged on the balance. APR is a broader cost measure that, under the federal Truth in Lending Act, also reflects certain finance charges such as some origination fees, so APR is generally equal to or higher than the note rate.

Why is my lender's payment higher than the calculator result?

A calculator typically shows principal and interest only. A lender quote may add escrowed property taxes and homeowners insurance, mortgage insurance, financed fees, GAP or credit insurance, or a different day-count or first-payment date. Comparing the principal-and-interest line item usually reconciles the difference.

Does a longer term make a loan cheaper?

A longer term generally lowers the monthly payment but typically increases total interest, because the balance is outstanding for more months. Whether that trade-off is worthwhile depends on your budget and goals.

How much of my payment goes to interest?

Interest is charged on the remaining balance, so early payments are mostly interest and later payments are mostly principal. The payment amount stays the same on a fixed-rate loan; only the split changes.

Can I calculate a loan payment without a calculator?

Yes, the formula only needs a scientific calculator that can raise a number to a power. Most borrowers use an online calculator to avoid rounding mistakes and to compare several rate and term combinations quickly.

How to Calculate Loan Payments (Formula + Example)

The short answer

A fixed monthly loan payment is calculated with the standard amortization formula:

Payment = P x r x (1 + r)^n / ((1 + r)^n - 1)

P = amount financed (principal)
r = monthly interest rate = annual rate ÷ 12 ÷ 100
n = total number of monthly payments

Example: a $25,000 loan at a 7.5% annual rate for 60 months works out to about $500.95 per month, roughly $30,056.92 repaid in total and about $5,056.92 of interest. You can reproduce that result in the Loan Calculator, which uses this exact formula.

What a loan payment actually is

On an amortizing loan, every payment does two jobs at once:

It pays the interest that accrued on the outstanding balance since the last payment.
Whatever is left reduces the principal.

Because the payment is level, the split shifts each month. Early on the balance is large, so most of the payment is interest. As the balance falls, the interest portion shrinks and the principal portion grows. Nothing about the payment amount changes on a fixed-rate loan — only the mix.

Most U.S. consumer loans work this way: personal loans, auto loans, student loans and fixed-rate mortgages. Credit cards are different; they use revolving balances with minimum payments, which is why credit card interest behaves differently.

The four inputs that determine your payment

Input	What it means	Effect on the payment
Principal	The amount financed after down payment and trade-in, plus any financed fees	Higher principal, higher payment
Interest rate	The periodic rate charged on the balance	Higher rate, higher payment and more total interest
Term	Number of monthly payments	Longer term, lower payment but generally more total interest
Payment frequency	Usually monthly for U.S. consumer loans	More frequent payments can reduce interest slightly

APR vs. interest rate

The interest rate is used to compute interest on the balance. The APR is a disclosure figure: under the federal Truth in Lending Act and Regulation Z, it expresses the cost of credit as a yearly rate that reflects the interest rate plus certain other finance charges. Because of that, APR is generally equal to or higher than the note rate, and it is the number the Consumer Financial Protection Bureau recommends using when comparing offers. Our longer explainer covers the details: APR vs. interest rate.

When you enter a rate into a payment calculator, you are normally entering the note rate, not the APR.

How the calculation works, step by step

Take a $25,000 loan at 7.5% for 5 years.

Step 1 — Convert the annual rate to a monthly rate. r = 7.5 ÷ 100 ÷ 12 = 0.00625

Step 2 — Count the payments. n = 5 × 12 = 60

Step 3 — Raise (1 + r) to the power of n. (1.00625)^60 ≈ 1.452957

Step 4 — Apply the formula. Payment = 25,000 × 0.00625 × 1.452957 ÷ (1.452957 − 1) ≈ $500.95

Step 5 — Derive the totals. Total repaid = 500.95 × 60 ≈ $30,056.92 Total interest = $30,056.92 − $25,000 ≈ $5,056.92

If the rate is 0% (some promotional auto financing, for example), the formula collapses to principal ÷ number of payments.

The first month, line by line

Item	Amount
Starting balance	$25,000.00
Interest for month 1 ($25,000 × 0.00625)	$156.25
Principal for month 1 ($500.95 − $156.25)	$344.70
Balance after payment 1	$24,655.30

Repeat that arithmetic 60 times and the balance lands on zero at the final payment. That table is what lenders call an amortization schedule.

How the rate changes your payment

Same $25,000, same 60-month term:

Annual rate	Monthly payment	Total interest
7.5%	$500.95	$5,056.92
9.5%	$525.05	$6,502.79

Two percentage points adds about $24 a month here — but roughly $1,446 over the life of the loan. Rate differences look small monthly and large in total.

How the term changes your payment

Same $25,000 at 7.5%:

Term	Monthly payment	Total interest
48 months	$604.47	$4,014.68
60 months	$500.95	$5,056.92
72 months	$432.25	$6,122.20

Stretching from 48 to 72 months cuts the payment by about $172, and increases total interest by roughly $2,107. Neither choice is automatically right; it depends on your cash flow, how long you plan to keep the asset, and what else the money would do.

Want to test your own numbers? The Loan Calculator runs all three scenarios in seconds, and the Personal Loan Calculator applies the same math to unsecured borrowing.

Common mistakes when calculating loan payments

Using the annual rate as the monthly rate. Divide by 12 first, and by 100 to get a decimal.
Entering the APR instead of the note rate, which slightly overstates the payment when fees are included in APR.
Forgetting financed fees. Origination fees deducted from proceeds still accrue interest if they are added to the loan amount.
Ignoring escrow. A mortgage quote usually bundles taxes and insurance into the monthly figure; a principal-and-interest calculator does not.
Assuming the lowest payment is the cheapest loan. Compare total interest, not just the monthly number.
Overlooking prepayment behavior. Extra principal payments reduce future interest, but only if the lender applies them to principal.

When calculator results differ from a lender quote

Calculator output is an estimate of principal and interest. A real quote can differ because of:

escrowed property taxes and homeowners insurance
mortgage insurance such as FHA MIP or conventional PMI
sales tax, title, registration and dealer fees rolled into an auto loan
financed origination fees
optional products such as GAP coverage or extended warranties
a longer gap between closing and the first payment, which adds odd-days interest
daily-simple-interest servicing, common on some auto loans, where payment timing changes the interest charged

None of these change the formula. They change P, r or n — or they sit outside the principal-and-interest figure entirely.

Loan Calculator — any fixed-rate installment loan
Personal Loan Calculator — unsecured loan payments and interest
Auto Loan Calculator — car payments including trade-in and taxes
Mortgage Calculator — home loan principal, interest and amortization
Debt Consolidation Calculator — compare current debts to one new loan

Sources and references

Consumer Financial Protection Bureau, Loan basics and comparing offers
Consumer Financial Protection Bureau, What is an APR?
Truth in Lending Act, Regulation Z, 12 CFR Part 1026
Federal Reserve, Consumer credit statistical release (G.19)

This article is educational information about how loan payments are calculated in the United States. It is not personalized financial advice, and actual terms vary by lender and by borrower.