Mortgage Interest Rate Calculator and Payment Formula

This mortgage calculator estimates the monthly principal-and-interest payment and total interest for a fixed-rate loan. Enter the loan amount, annual interest rate, and term; it returns both amounts using a standard monthly amortization formula. Use a rate supplied by a lender or loan estimate rather than treating the example rate as a market quote.

Formula

The calculator applies the fixed-payment amortization formula. It converts the annual percentage rate to a monthly rate, then calculates the payment that repays the principal and interest in equal monthly installments:

Monthly payment = P × r ÷ [1 − (1 + r)⁻ⁿ]

• P is the loan principal, in dollars.
• r is the monthly interest rate as a decimal: APR ÷ 1200. For an 8% APR, r = 8 ÷ 1200.
• n is the number of monthly payments: loan term in years × 12.

Total interest is calculated as the monthly payment multiplied by the number of payments, minus the original principal: total interest = payment × n − P. The payment is rounded to cents before total interest is calculated, so the total reflects the displayed monthly payment. Actual final payments can differ slightly when a lender adjusts for its precise schedule or rounding.

Worked Example

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

1. Monthly rate: 8 ÷ 1200 = 0.0066667.
2. Number of payments: 5 × 12 = 60.
3. Monthly payment: 20,000 × 0.0066667 ÷ [1 − (1 + 0.0066667)⁻⁶⁰] = $405.53.
4. Total interest: $405.53 × 60 − $20,000 = $4,331.80.

The result is a mathematical illustration, not a quoted mortgage offer. A $20,000 loan is used only to demonstrate the calculation; the example does not suggest a typical mortgage amount or rate.

Assumptions

• The interest rate stays fixed for the full modeled term.
• Payments are equal monthly installments, made at the end of each monthly period.
• Interest accrues monthly using the APR divided by 12.
• The calculation excludes lender fees, taxes, homeowners insurance, mortgage insurance, escrow deposits, and other costs because they are not inputs.
• No extra payments, missed payments, or changes to the loan balance are modeled.

What a Mortgage Interest Rate Means

A mortgage interest rate is the price charged for borrowing the principal, expressed as an annual percentage. In a fixed-rate mortgage, the contractual rate generally remains unchanged during the specified fixed period. In an adjustable-rate mortgage, the rate can change according to the loan’s terms; a single fixed-rate calculation cannot show those later changes.

Do not confuse the interest rate with APR. The interest rate is used to calculate interest on the outstanding loan balance. APR is a broader annualized borrowing-cost measure that can account for certain finance charges as defined by the applicable disclosure method. The calculator accepts APR as a simplified rate input for the payment formula; it does not separately model fees or reproduce a lender’s APR calculation. For an exact comparison, check the lender’s disclosed rate, APR, fees, and assumptions.

Mortgage payments are also often described as PITI: principal, interest, taxes, and insurance. This calculator returns only principal and interest. A payment amount shown by a lender or mortgage servicer may include additional items, such as property taxes, homeowners insurance, mortgage insurance, or escrow. Those costs can make the amount due substantially different from the calculator’s result.

How to Use the Estimate

Enter the principal you expect to borrow—not the home’s purchase price unless you plan to borrow that entire amount. The principal is generally the amount financed after accounting for any down payment and other adjustments. Enter the annual rate as a percentage, such as 6.5 for 6.5%, and enter the repayment term in years.

• Use the rate and term from the same loan offer or scenario. Changing either can change the payment and total interest.
• Compare like with like: a shorter term usually has a higher required monthly principal-and-interest payment but fewer scheduled payments.
• To estimate a different loan scenario, change one input at a time. This makes it easier to see which assumption caused the result to change.
• Ask the lender for the complete payment estimate and itemized costs. The calculator does not determine eligibility, approval, or a household budget.

Because the formula uses a fixed rate and regular payments, it is not a payoff schedule for every mortgage product. It also does not account for additional principal payments, payment dates that vary, rate resets, or lender-specific rounding. Treat its output as an estimate of the basic amortizing loan, not the exact amount due under a contract.

Why Payments and Interest Change

For the same principal and term, a higher interest rate increases the calculated monthly payment and the total interest over the scheduled life of the loan. A longer term spreads repayment over more months, which often lowers the scheduled payment but can increase total interest because the balance remains outstanding for longer. These are formula relationships, not predictions about available rates or the cost of a particular offer.

In a standard amortizing loan, each payment covers interest accrued since the prior payment and pays down some principal. Early in the schedule, the balance is relatively large, so the interest portion is typically larger. As principal is repaid, the balance falls and more of a level payment goes toward principal. The calculator reports aggregate interest, but does not generate a month-by-month amortization table.

Common Questions About Mortgage Rates

A frequent misconception is that the calculator’s payment equals the full monthly housing expense. It does not: property-related charges and lender costs are outside the calculation. Another is that an APR entered here automatically includes all borrowing costs in the output. The formula uses the entered number as its annual rate and does not add fees into the principal or payment.

For adjustable-rate mortgages, introductory or initial-period figures may not remain in effect for the full term. For a loan with changing rates, a single rate-and-term estimate cannot represent future payments reliably. Consult the loan documents for the adjustment structure and use the lender’s disclosures for contract-specific figures.

Frequently Asked Questions

What is the interest rate on a mortgage?
The rate is the annual percentage charged on the amount borrowed. The applicable rate depends on the specific loan offer and its terms; obtain the figure directly from the lender rather than relying on this example.

How do I calculate a mortgage payment from the interest rate?
Convert the annual rate to a monthly decimal by dividing by 1200, then use the fixed-payment formula with the principal and total number of monthly payments. This calculator performs that arithmetic.

Is mortgage APR the same as the interest rate?
No. The interest rate is used to calculate interest on the balance. APR is a broader annualized cost measure that may include certain charges. This calculator does not itemize fees or calculate a lender’s disclosed APR.

Does this estimate include taxes and insurance?
No. It includes principal and interest only. Taxes, homeowners insurance, mortgage insurance, escrow, and fees are not inputs and are not added to the result.

Can I use this for an adjustable-rate mortgage?
Only as a limited illustration for a period when a particular rate applies. The calculator assumes that rate remains fixed for the entire modeled term, so it does not forecast payments after adjustments.

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

Related

• Japan Interest Rate: How the BOJ Rate Works
• Interest Rate Index: Meaning, Uses, and Loan Calculator
• VA Loan Interest Rate Calculator and Payment Guide

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