What is a Mortgage?
A mortgage is a type of loan used to purchase real estate, where the property itself serves as collateral. The borrower agrees to pay back the loan, plus interest, over a set period (typically 15 or 30 years) through regular monthly payments.
Each monthly payment consists of two parts: principal (reducing the loan balance) and interest (the cost of borrowing). In the early years, a larger portion goes toward interest; as the loan matures, more goes toward principal. This is known as amortization.
The down payment is the upfront amount paid by the buyer. A 20% down payment is standard and typically avoids the need for Private Mortgage Insurance (PMI). A larger down payment reduces both the monthly payment and total interest paid.
Mortgage Payment Formula
Monthly mortgage payments are calculated using the standard amortization formula:
Where:
- M = Monthly payment
- P = Principal loan amount (home price minus down payment)
- r = Monthly interest rate (annual rate ÷ 12 ÷ 100)
- n = Total number of payments (years × 12)
Example: $400,000 Home at 6.5% Interest
Scenario: Purchase a $400,000 home with 20% down at 6.5% interest over 30 years.
Step 1: Calculate Loan Amount
Loan = $400,000 − $80,000 = $320,000
Step 2: Convert Rate
Step 3: Calculate Monthly Payment
M = $320,000 × [0.005417 × 1.005417³⁶⁰] / [1.005417³⁶⁰ − 1]
M ≈ $2,023/month
Result
- Monthly Payment: $2,023
- Total Paid: $728,280 over 30 years
- Total Interest: $408,280