Mortgage Calculator
Understanding Mortgages: A Comprehensive Guide
What is a Mortgage?
A mortgage is a loan used to purchase real estate. The property serves as collateral for the loan, which is paid back over time with interest. Homeowners make regular payments, typically monthly, to repay the loan.
Mortgages are commonly used to buy homes, but they can also be used for investment properties or refinancing existing mortgages.
Mortgage Formula and Mathematical Explanation
The mortgage formula calculates the monthly payment based on the loan amount, interest rate, and loan term. The formula is derived from the present value of an annuity formula:
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| P | Principal (loan amount) | $ | Depends on home price and down payment |
| r | Monthly interest rate | % | 0-10 |
| n | Number of payments (loan term in months) | Months | 120-360 |
The monthly mortgage payment (M) is calculated as:
M = P * r * (1 + r)^n / ((1 + r)^n - 1)
Practical Examples
Example 1: $250,000 Home with 20% Down Payment and 30-Year Mortgage at 3% Interest
Loan amount: $200,000 (after 20% down payment)
Interest rate: 3%
Loan term: 30 years (360 months)
Monthly mortgage payment: $843.21
Total interest paid: $143,739.95
Total cost: $343,739.95
Example 2: $400,000 Home with 10% Down Payment and 15-Year Mortgage at 2.5% Interest
Loan amount: $360,000 (after 10% down payment)
Interest rate: 2.5%
Loan term: 15 years (180 months)
Monthly mortgage payment: $1,910.15
Total interest paid: $63,645.00
Total cost: $423,645.00
Related Tools and Internal Resources
- Mortgage Calculator - Estimate your monthly mortgage payment and total interest paid.
- Refinance Calculator - Determine if refinancing your mortgage makes financial sense.
- Home Affordability Calculator - Calculate how much home you can afford based on your income and expenses.