Use this house mortgage payment calculator to quickly estimate your monthly principal and interest payment. Understand the impact of different loan amounts, interest rates, and loan terms on your budget.
House Mortgage Payment Calculator
House Mortgage Payment Calculator Formula
The standard formula used to calculate the fixed monthly payment ($M$) required to amortize a loan is:
$$M = P \cdot \frac{r(1+r)^n}{(1+r)^n – 1}$$Formula Sources: Investopedia – Mortgage Calculation, Consumer Financial Protection Bureau (CFPB)
Variables Explained
- Loan Amount ($P$): The total principal amount borrowed.
- Annual Interest Rate ($R$): The nominal annual interest rate (e.g., 6.5%).
- Loan Term ($T$): The length of time over which the loan is repaid, in years.
- Monthly Payment ($M$): The fixed amount paid by the borrower every month.
- Monthly Rate ($r$): The annual rate divided by 1200 ($r = R / 1200$).
- Total Payments ($n$): The number of months in the term ($n = T \times 12$).
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- Rent vs. Buy Analysis Tool
- Home Equity Loan Payment Calculator
What is a House Mortgage Payment Calculator?
A house mortgage payment calculator is a simple financial tool designed to help prospective and current homeowners estimate their monthly obligation for a home loan. By inputting the principal loan amount, the annual interest rate, and the loan term, the calculator applies the standard amortization formula to determine the fixed monthly payment (principal and interest only). This amount is crucial for budgeting, allowing individuals to assess affordability before committing to a mortgage.
The calculated payment does not typically include escrow items like property taxes, homeowner’s insurance, or mortgage insurance (PMI). These factors can significantly increase the total payment, which is why it is often referred to as the P&I (Principal and Interest) payment. Using the calculator for sensitivity analysis—testing how payments change when the rate or term is adjusted—is a critical step in the home buying process.
How to Calculate a Monthly Mortgage Payment (Example)
Let’s use an example: Loan Amount ($P$) = $200,000, Annual Rate ($R$) = 5.0%, Term ($T$) = 30 Years.
- Convert the annual rate to monthly rate ($r$): $r = 5.0\% / 12 / 100 = 0.0041667$.
- Calculate the total number of payments ($n$): $n = 30 \text{ years} \times 12 \text{ months/year} = 360 \text{ payments}$.
- Apply the monthly payment formula:
$$M = 200,000 \cdot \frac{0.0041667(1+0.0041667)^{360}}{(1+0.0041667)^{360} – 1}$$
- Calculate the numerator: $0.0041667 \times (4.467745) \approx 0.0186158$.
- Calculate the denominator: $4.467745 – 1 = 3.467745$.
- Final calculation: $M = 200,000 \times (0.0186158 / 3.467745) \approx 200,000 \times 0.0053682 \approx \$1,073.64$.
Frequently Asked Questions (FAQ)
Is the payment calculated here my final monthly bill?
No. The result is the monthly Principal and Interest (P&I) portion. Your final bill will include escrow payments for property taxes, homeowner’s insurance, and potentially Private Mortgage Insurance (PMI).
How does the loan term affect my payment?
A shorter term (e.g., 15 years) results in a much higher monthly payment but significantly less total interest paid over the life of the loan. A longer term (e.g., 30 years) lowers the monthly payment but increases the total interest paid.
What is the difference between Annual Rate and APR?
The Annual Rate (Nominal Rate) is the simple rate used to calculate interest. The Annual Percentage Rate (APR) is a broader measure of the cost of the loan, including the nominal rate plus certain fees and closing costs, but the calculator uses the simpler nominal rate for the P&I calculation.
Can this calculator solve for the maximum loan I can afford?
Yes. If you enter your desired Monthly Payment, the Annual Rate, and the Term, the calculator can work backwards to solve for the maximum Principal Loan Amount you can afford with that payment.