Use this simple, accurate mortgage payment calculator to quickly estimate your monthly principal and interest payments. By adjusting the loan amount, interest rate, and term, you can understand how each variable impacts your financial commitment.
How to Calculate a Mortgage Payment
Mortgage Payment Formula
The standard formula used to calculate a fixed-rate mortgage payment is the amortization formula, which determines the monthly payment (M) required to pay off the principal and interest over a fixed period.
Variables Explained
- M (Monthly Payment): The total monthly payment amount, including principal and interest.
- P (Principal Loan Amount): The initial amount borrowed.
- i (Monthly Interest Rate): The annual interest rate divided by 12 (and divided by 100 to convert from percentage).
- n (Total Number of Payments): The total number of months in the loan term (Loan Term in Years × 12).
What is a Mortgage Payment?
A mortgage payment is the periodic (usually monthly) payment made by the borrower to the lender. In a traditional mortgage, this payment covers two primary components: Principal and Interest (P&I).
The Principal is the portion of the payment that directly reduces the outstanding loan balance. The Interest is the cost of borrowing the money, calculated based on the remaining principal balance. Early in the loan term, the majority of the payment goes toward interest, but as the principal decreases, more of the payment is directed towards the principal balance.
How to Calculate a Mortgage Payment (Example)
Let’s calculate the monthly payment for a $200,000 loan at 4.5% annual interest over 30 years.
- Identify Variables:
- $P$ (Principal) = $200,000
- Annual Rate ($R$) = 4.5%
- $N$ (Term in Years) = 30
- Calculate Monthly Rate ($i$): $i = (4.5 / 100) / 12 = 0.00375$
- Calculate Total Payments ($n$): $n = 30 \times 12 = 360$
- Apply Formula: $$ M = 200,000 \left[ \frac{0.00375 (1 + 0.00375)^{360}}{(1 + 0.00375)^{360} – 1} \right] $$
- Solve: The resulting monthly payment, M, is approximately $1,013.37.
Frequently Asked Questions (FAQ)
A higher interest rate significantly increases the overall cost of the loan, as more of your monthly payment is allocated to interest rather than reducing the principal. Even a small change in the rate can have a large impact over a 30-year term.
Is this the total amount I pay monthly?No. This calculator provides the Principal and Interest (P&I) portion. Your total housing payment typically includes P&I plus escrow for Property Taxes, Homeowner’s Insurance, and sometimes Mortgage Insurance (PMI).
What is the amortization period?The amortization period is the total length of time, in years or months, over which the loan is scheduled to be completely repaid. Common amortization periods are 15, 20, or 30 years.
What happens if I make extra principal payments?Making extra payments directly toward the principal balance reduces the time it takes to pay off the loan and significantly reduces the total interest paid over the life of the loan, as the interest is calculated on a smaller outstanding balance.