Use the most accurate house mortgage calculator to estimate your monthly loan payments, total interest paid, and understand the true cost of borrowing for your new home.
House Mortgage Calculator
House Mortgage Calculator Formula
The standard fixed-rate mortgage payment is calculated using the following amortizing loan formula, which determines the principal and interest portion of your monthly payment:
M = P [ i(1 + i)ⁿ / ( (1 + i)ⁿ – 1 ) ]
Formula Source: Investopedia: Mortgage Payment
Variables Explained
Understanding the key variables is essential for accurate mortgage calculation:
- Loan Principal Amount (P): The total amount of money borrowed from the lender. This is the house price minus your down payment.
- Annual Interest Rate (R): The yearly cost of the loan, expressed as a percentage. This is converted to a monthly rate for the formula.
- Loan Term (N): The repayment period in years (e.g., 15, 20, or 30 years). This is converted to the total number of payments (months).
- Monthly Payment (M): The resulting payment (Principal and Interest portion) calculated by the formula.
Related Calculators
Explore other financial tools to better manage your home financing and investments:
- HELOC Payment Calculator
- Mortgage Refinance Break-Even Calculator
- Amortization Schedule Generator
- Property Tax Estimator
What is a House Mortgage Calculator?
A house mortgage calculator is a crucial online tool that helps prospective and current homeowners estimate the monthly cost of financing a home. By inputting the loan amount, the annual interest rate, and the repayment term, the calculator instantly solves for the required principal and interest payment (P&I).
This tool is essential for budgeting, as the calculated P&I is the core component of your total monthly housing cost, which also includes property taxes, homeowner’s insurance, and sometimes HOA fees. Financial experts recommend using this tool early in the home-buying process to establish an affordable price range and compare different loan products.
How to Calculate a House Mortgage Payment (Example)
Let’s use an example to illustrate the calculation steps manually:
- Identify Variables: Assume a loan of $200,000 (P), an annual rate of 4.5% (R), and a 30-year term (Y).
- Convert to Monthly Terms:
- Monthly Rate (i): 4.5% / 12 = 0.00375 (or 0.375%)
- Total Months (n): 30 years * 12 months/year = 360 payments
- Calculate the Compounding Factor: Compute $(1 + i)^n$, which is $(1 + 0.00375)^{360} \approx 3.84751$.
- Apply the Formula: Plug the values into the formula: $$M = 200,000 \times \frac{0.00375 \times 3.84751}{3.84751 – 1}$$
- Solve for M: $M = 200,000 \times \frac{0.014428}{2.84751} \approx 200,000 \times 0.00506685 \approx \$1,013.37$.
Frequently Asked Questions (FAQ)
Is the result from this calculator my final house payment?
No. The result is only the Principal and Interest (P&I) portion. Your final monthly payment (PITI) will also include Property Taxes, Homeowner’s Insurance, and potentially Private Mortgage Insurance (PMI) if your down payment is less than 20%.
What is the difference between APR and Interest Rate?
The Interest Rate is the simple cost of borrowing money. The Annual Percentage Rate (APR) is a broader measure of the total cost of the loan, including the interest rate and other charges (like closing costs, origination fees) expressed as a yearly percentage.
How does a shorter loan term affect my payment?
A shorter term (e.g., 15 years vs. 30 years) results in a significantly higher monthly payment (M) but a much lower total interest paid over the life of the loan, as you pay off the principal faster and benefit from fewer compounding periods.
Can this calculator solve for the Loan Principal if I know my desired Monthly Payment?
This version is primarily designed to calculate the Monthly Payment (M). However, advanced users can re-arrange the formula P = M / [ i(1 + i)ⁿ / ( (1 + i)ⁿ – 1 ) ] and perform the calculation manually or use a specialized reverse calculator.