Welcome to the Mortgage Payment Calculator. Use this tool to quickly estimate your monthly payments, total interest paid, and total cost of a new home loan based on the principal amount, annual interest rate, and loan term in years.
Mortgage Payment Calculation
Mortgage Calculator Formula
The standard formula for calculating a fixed-rate mortgage payment is:
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 (Years × 12)
Formula Sources: Investopedia, CFPB
Variables Explained
- Principal Loan Amount: The total amount of money borrowed.
- Annual Interest Rate: The percentage of the loan balance charged as interest each year. This is divided by 12 to get the monthly rate (i).
- Loan Term (Years): The total duration (in years) over which you agree to repay the loan. This is multiplied by 12 to get the total number of payments (n).
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What is the Mortgage Calculator Formula?
The mortgage calculator formula is based on an amortization model. Amortization is the process of gradually paying off debt over a fixed period of time through regular, fixed payments. In the early years of the loan, a larger portion of your monthly payment goes toward interest, and a smaller portion goes toward reducing the principal balance.
As the loan matures, this ratio reverses, and more of each payment goes toward the principal. The formula is designed to ensure that by the final payment date, the entire principal balance, plus all accrued interest, is paid off completely. This calculator simplifies the complex mathematics behind this process into a single, reliable estimate.
How to Calculate Mortgage Payments (Example)
Let’s calculate the monthly payment for a $150,000 loan over 30 years at a 5% annual interest rate.
- Determine Variables:
- Principal (P) = $150,000
- Annual Rate (r) = 5% or 0.05
- Term (Years) = 30
- Calculate Monthly Rate (i): $$i = \frac{r}{12} = \frac{0.05}{12} = 0.0041667$$
- Calculate Total Payments (n): $$n = \text{Years} \times 12 = 30 \times 12 = 360$$
- Apply the Formula: $$M = 150,000 \cdot \frac{0.0041667(1+0.0041667)^{360}}{(1+0.0041667)^{360} – 1}$$
- Solve for M:
The calculation yields a Monthly Payment (M) of approximately $805.23.
Frequently Asked Questions (FAQ)
Is the monthly payment always the same?
Yes, for a fixed-rate mortgage, the principal and interest portion of your payment remains constant throughout the life of the loan. However, your total escrow payment (for taxes and insurance) may fluctuate annually.
Does this calculation include property tax or insurance?
No, this calculator determines only the Principal and Interest (P&I) portion of your payment. It does not include Property Taxes, Homeowner’s Insurance, or Private Mortgage Insurance (PMI).
What is amortization?
Amortization is the process of paying off a debt over time in installments. With a mortgage, the amortization schedule shows how much of each payment goes to interest and how much goes to the principal balance.
Why is the total interest paid so high?
Interest accrues on the remaining principal balance. Because mortgage terms are long (e.g., 30 years), the compound effect of interest over hundreds of payments results in the total interest often equaling or exceeding the original principal amount.