Reviewed by: David Chen, CFA
Certified Financial Analyst with over 15 years of experience in real estate and loan amortization modeling.
Navigate your home purchase with confidence. Use this payment calculator to determine your monthly mortgage obligations based on the loan amount, interest rate, and term.
Mortgage Payment Calculator
Mortgage Payment Formula
The standard fixed-rate mortgage payment formula (solved for Monthly Payment, $M$) is:
$$M = P \left[ \frac{i(1 + i)^n}{(1 + i)^n – 1} \right]$$Where:
- $P$ = Principal Loan Amount
- $i$ = Monthly Interest Rate (Annual Rate / 1200)
- $n$ = Total Number of Payments (Loan Term in Years × 12)
Source: Wikipedia – Mortgage Calculator, Investopedia – Amortization
Variables Explained
- Loan Principal: The initial amount of money borrowed from the lender.
- Annual Interest Rate: The yearly percentage rate charged for borrowing the principal, expressed as a percentage.
- Loan Term (Years): The duration over which the loan is scheduled to be repaid (typically 15 or 30 years).
- Monthly Payment: The fixed amount paid every month, covering both principal and interest.
Related Calculators
What is a Mortgage Payment Calculator?
A mortgage payment calculator is a critical tool for potential homeowners and finance professionals. It uses the loan’s principal, interest rate, and term to project the fixed monthly payment amount required to fully amortize the loan by the end of its term.
The monthly payment covers two components: the interest accrued on the outstanding balance and a portion of the principal. Early payments are heavily skewed toward interest, while later payments consist mostly of principal reduction.
Understanding this breakdown is essential for budgeting and planning. By adjusting inputs like the principal (by changing the down payment) or the term (15 vs. 30 years), users can quickly model different financial scenarios.
How to Calculate a Monthly Payment (Example)
- Determine Inputs: Start with Principal ($200,000), Annual Rate (5%), and Term (30 years).
- Calculate Monthly Rate ($i$): Divide the annual rate by 1200: $i = 5 / 1200 = 0.004167$.
- Calculate Total Payments ($n$): Multiply the term by 12: $n = 30 \times 12 = 360$.
- Apply Formula: Input $P$, $i$, and $n$ into the standard amortization formula.
- Result: For this example, the resulting monthly payment would be $1,073.64.
Frequently Asked Questions (FAQ)
Is the Monthly Payment calculated guaranteed to be my final bill?
No. This calculation covers Principal and Interest (P&I) only. Your actual monthly mortgage bill (PITI) will include Property Taxes, Homeowner’s Insurance, and potentially Private Mortgage Insurance (PMI).
How does the loan term affect total interest paid?
A shorter loan term (e.g., 15 years) results in a higher monthly payment but significantly reduces the total interest paid over the life of the loan compared to a 30-year term, because the principal is paid down faster.
What if I put $0$ in the principal?
The calculator requires a valid positive principal amount to determine payments. A $0$ principal means no loan exists, and the monthly payment would also be $0$. The calculator will prompt you for a valid input.
Can I use this to calculate a bi-weekly payment?
This version is primarily designed for monthly payments. To calculate a bi-weekly payment, you would typically need to adjust the interest calculation and total number of periods (which would be 26 per year).