Mortgage Principal & Interest Calculator
Loan Details
Your Monthly Principal & Interest Payment
— Estimated P&I Payment (excluding taxes, insurance, HOA)Total Interest Paid Over Loan Life
— Total InterestTotal Amount Paid Over Loan Life
— Total Principal & InterestUnderstanding Your Mortgage Principal and Interest (P&I)
When you take out a mortgage, the primary components of your monthly payment are Principal and Interest (P&I). Understanding how these are calculated is crucial for budgeting and making informed financial decisions. This calculator helps you estimate your P&I payment based on the loan amount, interest rate, and loan term.
How P&I is Calculated
The most common method for calculating mortgage payments is using the standard amortizing loan formula. This formula ensures that your payment remains constant throughout the life of the loan, with the proportion of principal and interest changing over time.
The formula for the monthly payment (M) is:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
Where:
- P = The principal loan amount (the amount you borrowed).
- i = Your monthly interest rate. This is your annual interest rate divided by 12. For example, if your annual rate is 4.5%, your monthly rate is 0.045 / 12 = 0.00375.
- n = The total number of payments over the loan's lifetime. This is your loan term in years multiplied by 12. For a 30-year loan, n = 30 * 12 = 360.
Example Calculation
Let's say you want to calculate the P&I for a mortgage with the following details:
- Principal Loan Amount (P): $300,000
- Annual Interest Rate: 4.5%
- Loan Term: 30 Years
First, we convert the annual rate to a monthly rate (i):
i = 4.5% / 12 = 0.045 / 12 = 0.00375
Next, we determine the total number of payments (n):
n = 30 years * 12 months/year = 360
Now, we plug these values into the formula:
M = 300,000 [ 0.00375(1 + 0.00375)^360 ] / [ (1 + 0.00375)^360 – 1]
Calculating (1 + 0.00375)^360 gives us approximately 3.839396.
M = 300,000 [ 0.00375 * 3.839396 ] / [ 3.839396 – 1]
M = 300,000 [ 0.0143977 ] / [ 2.839396 ]
M = 300,000 * 0.0050709
M ≈ $1,521.27
So, your estimated monthly Principal & Interest payment would be approximately $1,521.27.
To find the total interest paid, you multiply the monthly payment by the total number of payments and subtract the original principal:
Total Paid = $1,521.27 * 360 = $547,657.20
Total Interest = $547,657.20 - $300,000 = $247,657.20
Important Considerations
Remember that your total monthly housing payment (often called PITI) typically includes more than just Principal and Interest. It usually also includes:
- Taxes (T): Property taxes assessed by your local government.
- Insurance (I): Homeowner's insurance, and potentially Private Mortgage Insurance (PMI) if your down payment is less than 20%.
- HOA Fees: If you live in a community with a Homeowners Association.
This calculator focuses solely on the P&I portion, which is the core debt repayment of your mortgage. Always factor in the other components when determining your overall housing affordability.