This calculator uses industry-standard financial formulas to ensure accuracy and compliance with common lending practices.
Determine your estimated monthly mortgage payment instantly and understand the full amortization schedule for your loan.
The Mortgage Calculator
Estimated Monthly Payment:
$0.00
Calculation Steps & Amortization Summary
Enter your inputs and click ‘Calculate’ to see the detailed breakdown.
The Mortgage Calculator Formula
The standard formula used to calculate the fixed monthly payment (M) required to amortize a loan of Principal (P) over n months at a monthly interest rate (r) is:
$$M = P \frac{r(1+r)^n}{(1+r)^n – 1}$$Where:
- $r = \text{Annual Interest Rate} / 1200$ (Monthly rate as a decimal)
- $n = \text{Loan Term in Years} \times 12$ (Total number of payments)
Formula Source: Investopedia, Bankrate
Variables Explained
- Loan Principal ($P$): The initial amount borrowed. This is the house price minus your down payment.
- Annual Interest Rate ($R$): The yearly rate charged by the lender, expressed as a percentage.
- Loan Term ($N$): The length of time over which the loan will be repaid, expressed in years (e.g., 15, 30).
- Monthly Payment ($M$): The fixed amount paid every month, which includes both principal and interest.
What is the Mortgage Calculator?
A mortgage calculator is an essential financial tool used by prospective homeowners and refinancers. It helps estimate the fixed monthly mortgage payment required to pay off a loan over a specified term. By adjusting the loan amount, interest rate, and term length, users can quickly model different financial scenarios to determine affordability.
Beyond the simple monthly payment, these calculators are crucial for understanding the amortization process—how much of each payment goes toward interest versus the principal balance over the life of the loan. This insight is key for long-term financial planning.
How to Calculate the Mortgage Payment (Example)
Let’s calculate the monthly payment for a loan with the following details:
- Identify Variables: Principal ($P$) = $250,000; Annual Rate ($R$) = 6.0%; Term ($N$) = 30 years.
- Calculate Monthly Rate ($r$): $r = 6.0\% / 1200 = 0.005$.
- Calculate Total Payments ($n$): $n = 30 \times 12 = 360$ payments.
- Apply Formula Components:
- $(1+r)^n = (1.005)^{360} \approx 6.022575$
- $r(1+r)^n = 0.005 \times 6.022575 \approx 0.030113$
- $(1+r)^n – 1 = 6.022575 – 1 = 5.022575$
- Solve for Monthly Payment ($M$): $$\frac{0.030113}{5.022575} \approx 0.0059955$$ $$M = P \times 0.0059955 = 250,000 \times 0.0059955 = \$1,498.88$$ The estimated monthly payment is **$1,498.88**.
Frequently Asked Questions (FAQ)
Is the monthly payment fixed for the entire term?
Yes, for a standard fixed-rate mortgage, the principal and interest portion of your monthly payment remains constant for the life of the loan. This calculator assumes a fixed rate.
Does this calculation include property taxes or insurance?
No. The calculated monthly payment only covers the principal and interest (P&I). Actual monthly payments often include escrow for property taxes and homeowner’s insurance (PITI).
What is amortization?
Amortization is the process of paying off debt over time in fixed installments. In the early years of a mortgage, a larger portion of the payment goes toward interest, while in later years, more goes toward the principal.
What happens if the annual rate is 0%?
If the rate is 0%, the loan is interest-free, and the monthly payment simplifies to the Principal divided by the total number of payments ($P/n$).