David is a Chartered Financial Analyst and a senior mortgage underwriter with 15 years of experience in residential and commercial real estate lending.
This 4-in-1 Mortgage Payment calculator helps you plan your home purchase. Enter any three values—Loan Amount, Annual Rate, Term, or Monthly Payment—and we will solve for the fourth.
Mortgage Payment Calculator
Mortgage Amortization Formulas
i = R / 12 / 100 (Monthly Rate)
n = T * 12 (Number of Months)
Solve for Monthly Payment (M):
M = P * [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]
Solve for Loan Amount (P):
P = M * [ (1 + i)^n – 1 ] / [ i(1 + i)^n ]
Solve for Term (n):
n = log( M / (M – P*i) ) / log(1 + i)
Solve for Rate (i):
(No direct formula; solved iteratively)
Formula Variables
- (P) Loan Amount: The total home loan amount (home price minus down payment).
- (R) Annual Rate: The Annual Percentage Rate (APR) for the mortgage.
- (T) Loan Term: The length of the mortgage in years (e.g., 15, 20, or 30).
- (M) Monthly Payment (P&I): The fixed monthly payment covering **Principal and Interest**. This does *not* include taxes, insurance, or PMI.
Related Calculators
- Loan Affordability Calculator
- Loan to Value (LTV) Calculator
- Debt to Income (DTI) Calculator
- General Loan Amortization Calculator
What is a Mortgage Payment Calculator?
A mortgage payment calculator is an essential tool for anyone considering buying a home. It estimates your **monthly payment** based on the loan’s principal amount, the interest rate, and the length of the loan (the term). This calculation, known as amortization, determines the fixed amount you will pay each month to cover both principal (the amount you borrowed) and interest (the cost of borrowing).
It’s crucial to understand that this calculator solves for your **P&I (Principal & Interest)** payment. Your total *actual* monthly housing payment (often called PITI) will also include property taxes and homeowner’s insurance, which are typically held in an escrow account by your lender. If your down payment is less than 20%, you will also have to pay Private Mortgage Insurance (PMI).
This 4-in-1 calculator is more powerful than most. It allows you to solve for any of the four main variables. For example, if you know the monthly payment you can afford (M), the current interest rate (R), and the term (T), this calculator can solve for the total Loan Amount (P), telling you exactly how much house you can afford.
How to Calculate a Mortgage Payment (Example)
-
Identify Loan Variables
You are buying a $550,000 home with a $100,000 down payment.
• Loan Amount (P): $550,000 – $100,000 = $450,000
• Annual Rate (R): 6.75%
• Loan Term (T): 30 years -
Convert to Monthly Terms (i, n)
The formula uses monthly values:
• Monthly Rate (i): 6.75% / 12 / 100 = 0.005625
• Number of Months (n): 30 years * 12 = 360 -
Choose the Payment Formula
Use the standard formula to solve for Monthly Payment (M):
M = P * [ i(1 + i)^n ] / [ (1 + i)^n – 1 ] -
Calculate the Monthly Payment
Plug in the monthly values:
• Numerator: 0.005625 * (1 + 0.005625)^360 = 0.04259
• Denominator: (1 + 0.005625)^360 – 1 = 6.5714
M = $450,000 * [ 0.04259 / 6.5714 ]
M = $450,000 * 0.006481 = $2,916.45
Your monthly P&I payment will be $2,916.45.
Frequently Asked Questions (FAQ)
Does this payment (M) include taxes and insurance?
No. This calculator finds your P&I (Principal and Interest) payment only. Your total monthly payment to the lender (PITI) will also include Property Taxes and Homeowner’s Insurance. You should add an estimated 1.0% – 2.0% of the home’s value per year for these costs (divide by 12) to get a more complete picture.
What’s the difference between a 15-year and 30-year term (T)?
A 30-year term has a much lower monthly payment, making homes more affordable. A 15-year term has a higher payment, but you pay the loan off faster and pay *significantly* less in total interest. Use the calculator to solve for (M) with T=15 and T=30 to see the difference.
How can I find what home price I can afford?
First, use the Loan Affordability Calculator to find the Monthly Payment (M) you can afford. Then, enter that (M), the current Annual Rate (R), and your desired Term (T) into this calculator. It will solve for the Loan Amount (P). Add your down payment to (P) to find your maximum home price.
What is APR (R)?
APR stands for Annual Percentage Rate. It represents the annual interest rate plus any lender fees (like origination fees) spread out over the life of the loan. It’s generally slightly higher than the “note rate” and is considered a more accurate measure of the loan’s true cost.