How to Calculate a Weighted Average Interest Rate

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Mortgage Payment Calculator

Understanding Your Mortgage Payment

A mortgage is a long-term loan used to purchase a property. The monthly mortgage payment is a crucial figure that impacts your budget and financial planning. It's typically composed of several parts, often referred to by the acronym PITI:

  • Principal: This is the actual amount of money you borrowed to buy the home. Each payment you make reduces the principal balance.
  • Interest: This is the cost of borrowing the money. Lenders charge interest based on the outstanding principal balance and the interest rate.
  • Taxes: Property taxes are typically paid annually but are often collected by your lender in monthly installments and held in an escrow account.
  • Insurance: Homeowners insurance premiums are also often collected monthly by your lender and held in escrow. If you have an FHA or VA loan, Private Mortgage Insurance (PMI) or Mortgage Insurance Premium (MIP) might also be included.

The formula used to calculate the principal and interest (P&I) portion of your monthly mortgage payment is a standard amortization formula:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]

Where:

  • M = Your total monthly mortgage payment (Principal & Interest)
  • P = Your loan principal (the amount you borrowed)
  • i = Your monthly interest rate (annual rate divided by 12)
  • n = The total number of payments over the loan's lifetime (loan term in years multiplied by 12)

This calculator focuses on the Principal and Interest (P&I) portion of your payment. Remember that your total housing cost will likely be higher due to property taxes and homeowner's insurance, which can vary significantly by location and the specifics of your policy.

Example Calculation:

Let's say you are taking out a mortgage with the following details:

  • Loan Principal (P): $250,000
  • Annual Interest Rate: 6.5%
  • Loan Term: 30 years

First, we convert the annual interest rate to a monthly interest rate:

i = 6.5% / 12 = 0.065 / 12 ≈ 0.00541667

Next, we determine the total number of payments:

n = 30 years * 12 months/year = 360 payments

Now, we plug these values into the formula:

M = 250000 [ 0.00541667(1 + 0.00541667)^360 ] / [ (1 + 0.00541667)^360 – 1]

Calculating this yields a monthly Principal & Interest payment of approximately $1,580.37.

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