This calculator module and its accompanying content have been reviewed for financial accuracy and compliance by a certified financial analyst.
Use our comprehensive and easy-to-use mortgage calculator to quickly determine your estimated monthly loan payments. Understanding your monthly obligation is the first crucial step in planning your home purchase.
How to Calculate Mortgage Payments
Mortgage Payment Formula
$$ M = P \left[ \frac{r(1+r)^n}{(1+r)^n - 1} \right] $$
Where:
- P = Principal loan amount
- r = Monthly interest rate (Annual Rate / 1200)
- n = Total number of payments (Term in Years × 12)
Variables Explained
The calculation relies on three primary variables input into the calculator:
- Loan Principal: The total amount of money borrowed from the lender.
- Annual Interest Rate: The yearly percentage rate charged on the loan balance. This is converted to a monthly rate for calculation.
- Loan Term (Years): The duration over which the loan is scheduled to be repaid (e.g., 15, 20, or 30 years).
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What is a Mortgage Payment Calculation?
A mortgage payment calculation determines the fixed amount you must pay the lender each month for the duration of the loan term. This monthly payment, often called P&I (Principal and Interest), is mathematically derived to ensure the loan balance is fully paid off by the final scheduled payment.
The calculation is a function of compounding interest. Early in the loan term, a large portion of the payment goes toward interest, while later payments consist primarily of principal repayment. The goal is to provide a consistent, predictable payment amount that simplifies budgeting for the borrower.
How to Calculate Mortgage Payment (Example)
- Identify Variables: Assume a $200,000 principal (P), a 6% annual rate (I), and a 30-year term (Y).
- Calculate Monthly Rate (r): Divide the annual rate by 1200: $6 / 1200 = 0.005$.
- Calculate Total Payments (n): Multiply the term by 12: $30 \times 12 = 360$ payments.
- Apply the Formula: Substitute these values into the formula to find M. For this example, the monthly payment (M) would be approximately $1,199.10.
- Review Amortization: The total interest paid over 30 years would be $231,675.24, showing the significant impact of compounding interest.
Frequently Asked Questions (FAQ)
Is the calculated monthly payment my total housing cost?
No. The calculated payment only covers Principal and Interest (P&I). Your total monthly housing cost (often called PITI) typically includes Property Taxes, Homeowner’s Insurance, and sometimes Private Mortgage Insurance (PMI).
How does a shorter loan term affect the payment?
A shorter loan term (e.g., 15 years vs. 30 years) results in a significantly higher monthly payment because the principal is paid off faster. However, the total amount of interest paid over the life of the loan is substantially lower.
What is amortization?
Amortization is the process of paying off debt over time in fixed, regular installments. Each payment consists of both principal and interest, but the ratio of interest to principal shifts over the loan term.
What is the difference between APR and Interest Rate?
The Interest Rate is the annual cost of the borrowed money. The Annual Percentage Rate (APR) is a broader measure of the cost, including the interest rate plus other fees and costs (like origination fees) associated with the transaction, expressed as a yearly percentage.