Interest Loan Formula: Calculate Monthly Payments

The interest loan formula calculates a fixed monthly payment from the amount borrowed, annual percentage rate (APR), and loan term. Enter those three figures to estimate the monthly payment and total interest over the full term.

Formula

For a loan repaid in equal monthly installments, the payment is calculated using:

Payment = P × r ÷ [1 − (1 + r)⁻ⁿ]

P is the starting loan principal, in dollars.
r is the monthly interest rate as a decimal. With an APR entered as a percentage per year, r = APR ÷ 1,200. For example, 8% APR gives r = 8 ÷ 1,200.
n is the number of monthly payments. For a term in years, n = years × 12.

The calculator rounds the monthly payment to cents. It estimates total interest as the rounded monthly payment multiplied by the number of payments, minus the original principal. This is the standard level-payment amortization formula: each installment covers interest accrued for the period and pays down some principal.

Worked Example

Using the calculator’s default inputs—$20,000 principal, 8% APR, and a five-year term:

Convert APR to a monthly decimal rate: r = 8 ÷ 1,200 = 0.0066667.
Convert the term to payments: n = 5 × 12 = 60.
Substitute into the payment formula: $20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰].
The monthly payment is approximately $405.53, rounded to the nearest cent.
Using the rounded payment, total payments are $405.53 × 60 = $24,331.80. Estimated total interest is $24,331.80 − $20,000 = $4,331.80.

Because the payment is rounded to cents, the final installment on an actual loan can differ slightly from the regular payment. The lender’s schedule may also apply its own payment and interest conventions.

Assumptions

The interest rate remains fixed throughout the modeled term.
Payments are equal, made monthly, and occur at the end of each payment period.
Interest is modeled monthly using APR divided by 12.
The calculation excludes fees, taxes, insurance, PMI, and escrow; it includes none of these unless separately entered.

How the Interest Loan Formula Works

A loan balance does not fall by the full payment amount each month. At the beginning, interest is calculated on a relatively large outstanding balance, so a greater share of each payment goes toward interest. As principal is paid down, the interest portion generally shrinks and more of the same scheduled payment reduces principal. This changing division is called amortization.

The formula finds the payment that, under its assumptions, brings the balance to zero after n payments. A simple-interest calculation such as principal × annual rate × years can estimate interest in some contexts, but it does not produce the scheduled payment for a conventional amortizing loan. Applying a flat rate to the original principal for every month would ignore the fact that principal is being repaid.

When to Use It and How to Read the Results

Use the formula for an estimate when you know the loan amount, APR, and repayment term and expect regular monthly payments at a fixed rate. It can help illustrate how the payment and total interest respond when one input changes. It is not a lender quote or a complete loan-cost comparison.

Monthly payment is the modeled recurring principal-and-interest installment, not necessarily the entire amount due on a bill.
Total interest is the estimated interest paid across all modeled installments, not the total amount repaid.
Total payments in the example equal principal plus interest only under the calculation’s assumptions.

For example, a payment that excludes taxes, insurance, or escrow may be lower than a real monthly housing expense. Fees and other charges can also affect the amount financed or the overall cost. Obtain the relevant figures from the lender’s disclosure and check whether the quoted APR and term match the inputs used here.

Common Mistakes and Limits

Entering a percentage as a decimal: Enter 8 for 8% APR, not 0.08. The calculator converts the annual percentage to a monthly decimal rate.
Mixing annual and monthly terms: This version takes years and multiplies by 12. Do not enter 60 for a five-year term; that would be interpreted as 60 years.
Confusing APR with the periodic rate: APR is entered as a yearly percentage, while the formula uses APR divided by 1,200 as the monthly rate. Actual contracts may specify interest calculations differently.
Assuming total interest is exact: The estimate uses a payment rounded to cents. Real schedules may adjust the final payment because of rounding, payment dates, or other contract details.
Using it for a changing-rate or irregular-payment loan: A single fixed-payment formula does not represent a rate that changes, skipped or extra payments, fees rolled into the balance, or a different payment frequency.

The formula is useful for understanding standard amortization, but the result depends on the inputs and assumptions. It does not determine eligibility, approval, or the full cost of borrowing.

Frequently Asked Questions

What is the formula for monthly loan interest payments?
For a fixed-rate, fully amortizing loan, payment = P × r ÷ [1 − (1 + r)⁻ⁿ], where P is principal, r is the monthly rate as a decimal, and n is the number of monthly payments.

How do I convert APR to a monthly interest rate?
When APR is entered as a percentage per year and interest is modeled monthly, divide the APR by 1,200. For instance, 8% ÷ 1,200 is about 0.006667 per month.

Does the monthly payment include interest?
Yes. In this formula each level payment includes both interest for the period and repayment of principal. The mix changes over time even though the scheduled payment remains level.

How do I calculate total interest on a loan?
For this estimate, multiply the monthly payment rounded to cents by the number of payments, then subtract the original principal. The result excludes charges not represented in the inputs.

Why does my lender’s payment differ from this estimate?
The loan may have fees, a different interest calculation or payment schedule, a variable rate, or other included costs. Rounding and payment timing can also change figures; compare the calculator assumptions with the lender’s disclosure.

This result is an estimate, and the lender’s disclosure gives the exact figures.

Formula used

in p | Loan amount | $ | 20000 | 1 | 100000000
in apr | Interest rate (APR) | % | 8 | 0.01 | 100
in yrs | Loan term | years | 5 | 0.0833 | 50
out pmt | Monthly payment | $ | p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)) | 2
out int | Total interest | $ | pmt * yrs * 12 - p | 2

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Method: the standard loan formula for this calculation, fixed rate and monthly compounding unless stated, rounded as each result states. Not financial advice; no lender, rate or product is recommended. See formulas and assumptions, the disclaimer or report an error.