Fact-Checked by David Chen, CFA. This calculator uses industry-standard compound interest formulas to ensure accurate mortgage principal and interest calculations. Always consult a licensed financial advisor for personalized advice.
Welcome to the Free Home Mortgage Calculator. Determine your monthly payment, maximum affordable principal, or even the required interest rate and loan term by leaving one variable blank. Get accurate results for better financial planning.
Free Home Mortgage Calculator
Calculated Monthly Payment
$0.00
Please enter three values to solve for the fourth, or four values to check for consistency.
Mortgage Payment Formula
M = P [ i (1 + i)^n ] / [ (1 + i)^n - 1 ]
Where:
M = Monthly Payment
P = Principal Loan Amount
i = Monthly Interest Rate (Annual Rate / 12)
n = Total Number of Payments (Term in Years * 12)
Formula Sources: Investopedia – Mortgage, Consumer Finance Bureau – Mortgage Tools, Bankrate – Payment Calculation
Variables Explained
- Loan Principal ($): The initial amount of money borrowed.
- Annual Interest Rate (%): The yearly cost of borrowing, expressed as a percentage.
- Loan Term (Years): The duration over which the loan is scheduled to be repaid (e.g., 15 or 30 years).
- Monthly Payment ($): The fixed amount paid every month to cover both principal and interest.
Related Calculators
Explore other essential financial tools for your long-term planning:
- Amortization Schedule Calculator
- Refinance Savings Estimator
- Loan Interest-Only Calculator
- Rent vs. Buy Analysis Tool
What is a Free Home Mortgage Calculator?
A free home mortgage calculator is a crucial online tool designed to estimate the costs associated with home financing. Its primary function is to help prospective homeowners and refinancers quickly determine their expected monthly mortgage payments based on the loan amount, interest rate, and repayment term.
Beyond finding the monthly payment, advanced versions—like this one—can solve for any missing variable. This allows a user to ask, “If I can afford a \$2,000 monthly payment (M), how large of a principal (P) can I afford given current rates and terms?” This flexibility makes it invaluable for setting realistic housing budgets.
Understanding these figures upfront helps prevent unforeseen financial strain, making the initial stages of home buying much clearer and less stressful. It is the first step toward sound long-term financial planning.
How to Calculate Monthly Payment (Example)
Let’s use an example: Principal = \$250,000, Annual Rate = 6.0%, Term = 30 Years.
- Convert Annual Rate: Divide the 6.0% annual rate by 12 months to get the monthly interest rate: $i = 0.06 / 12 = 0.005$.
- Calculate Total Payments: Multiply the term by 12: $n = 30 \times 12 = 360$ total payments.
- Apply Formula Components: Calculate the numerator part: $i(1+i)^n = 0.005(1.005)^{360} \approx 0.005 \times 6.022575 \approx 0.030113$.
- Apply Formula Components: Calculate the denominator part: $(1+i)^n – 1 = (1.005)^{360} – 1 \approx 6.022575 – 1 = 5.022575$.
- Final Calculation: Divide the numerator by the denominator, then multiply by the principal: $M = 250,000 \times (0.030113 / 5.022575) \approx \$1,498.88$.
Frequently Asked Questions (FAQ)
Is the monthly payment calculated here inclusive of property taxes and insurance?
No. This calculator determines the Principal and Interest (P&I) portion of your payment only. You must separately budget for taxes, insurance, and HOA fees, which are often bundled into your final escrow payment (PITI).
Why is the annual interest rate used in the formula?
The annual interest rate (APR) is the standard quoted rate. However, since mortgage payments are made monthly, the formula converts the APR into a monthly rate (i) to accurately reflect the compounding interest over the repayment period.
What is amortization?
Amortization is the process of gradually paying off a debt over time in fixed installments. In the early years of a mortgage, the majority of your payment goes towards interest, and over time, the balance shifts to paying down the principal.
Can I solve for the Loan Term (Years)?
Yes. By leaving the Loan Term blank and providing the other three variables (Principal, Rate, and Payment), the calculator uses a logarithmic formula to determine the exact number of years and months required to pay off the loan.