Chartered Financial Analyst and former Senior Mortgage Broker with 15+ years experience in residential lending and loan structuring.
The **Mortgage Calculator** estimates your monthly principal and interest payment for a home loan. Use this tool to solve for the missing variable: Loan Principal, Monthly Payment, Annual Interest Rate, or Loan Term (Months).
Mortgage Calculator
Instructions: Enter values for any three of the four parameters (P, F, V, Q) to solve for the missing one.
Loan Parameters
Mortgage Amortization Formula
The core calculation for the Principal and Interest (P&I) portion of a mortgage payment uses the standard Amortization formula. Note that $i = R/12$ is the monthly interest rate, and $R$ is the annual rate.
Monthly P&I Payment ($M$):
$$M = P \left[ \frac{i(1+i)^N}{(1+i)^N – 1} \right]$$This calculator solves for $P$, $M$, $R$, or $N$ using rearrangement and iterative solving methods where necessary.
Formula Source: Consumer Financial Protection Bureau (CFPB)Variables Explained (P, F, V, Q – Parameters)
- $P$ (Loan Principal): The amount borrowed, which is the home price minus your down payment.
- $M$ (Monthly Payment, $F$): The fixed monthly payment amount covering Principal and Interest (P&I).
- $R$ (Annual Interest Rate, $V$): The annual rate (APR) applied to the loan.
- $N$ (Loan Term in Months, $Q$): The total number of months in the loan term (e.g., 180 months for 15 years, 360 months for 30 years).
Related Home Loan Calculators
Further optimize your home buying and mortgage strategy:
- Loan Term Calculator
- Refinance Savings Calculator
- Early Payoff Calculator
- Debt-to-Income Ratio Calculator
What is a Mortgage?
A mortgage is a loan used to finance the purchase of real estate, which serves as collateral for the loan. Mortgages are typically long-term commitments, with standard repayment terms spanning 15 or 30 years. The core payment structure involves amortization, meaning each regular payment partially reduces the outstanding principal balance while covering the accrued interest.
The total monthly payment on a mortgage often includes not only the Principal and Interest (P&I) but also escrow payments for Property Taxes and Homeowner’s Insurance, often referred to by the acronym PITI. Lenders use a potential borrower’s Debt-to-Income (DTI) ratio to determine eligibility and maximum loan size, making the affordability check a critical step before pre-approval.
How to Calculate Mortgage Payment (Example)
Imagine a \$300,000 Loan ($P$) at a 6% Annual Rate ($R$) over 30 years ($N=360$ months). We are solving for $M$ (Monthly P&I Payment):
- Step 1: Determine the Monthly Interest Rate ($i$)
$i = 6\% / 12 = 0.005$
- Step 2: Calculate the Amortization Factor
Factor $\approx i(1+i)^N / ((1+i)^N – 1)$ where $N=360$. Factor $\approx 0.005995$
- Step 3: Apply the Monthly Payment Formula
The Monthly Payment $M = P \times \text{Factor} = \$300,000 \times 0.005995 \approx \mathbf{\$1,798.65}$.
The total interest paid over 30 years would be $\$347,514$, demonstrating how significantly interest impacts the total cost of a long-term loan.
Frequently Asked Questions (FAQ)
PITI stands for Principal, Interest, Taxes, and Insurance. It represents the total monthly housing payment, with P&I going to the lender and T&I usually placed in an escrow account managed by the lender.
PMI is a monthly insurance premium required if the borrower’s down payment is less than 20% of the home’s purchase price. It protects the lender, not the borrower, in case of default.
Your credit score is a major factor. Borrowers with higher credit scores (typically above 740) are generally offered the lowest interest rates because they are viewed as lower risk by lenders.
A fixed-rate mortgage has an interest rate that remains the same for the entire loan term. An ARM has an initial fixed period, after which the interest rate can fluctuate based on a market index.