What is Mortgage Calculator?
A comprehensive mortgage calculator evaluates total monthly housing costs—including Principal, Interest, Taxes, and Insurance (PITI)—along with long-term interest costs over the life of the loan.
How to Use This Calculator
- Enter the home purchase price.
- Specify down payment amount or percentage.
- Enter current mortgage interest rate and loan duration.
- Review your monthly PITI commitment and total lifetime borrowing charges.
The Mathematical Formula & Variables
Monthly P&I = [Principal * r * (1 + r)^n] / [(1 + r)^n - 1] where r = annual rate / 12 and n = term in months
Variables Definition
| Symbol / Variable | Name | Description |
|---|---|---|
P |
Loan Principal | Home price minus down payment. |
r |
Monthly Interest Rate | Annual interest rate divided by 12 months. |
n |
Payment Months | 360 months for a 30-year loan; 180 months for a 15-year loan. |
Step-by-Step Worked Example
Scenario: $400,000 home with 20% down ($80,000 down, $320,000 loan) at 6.8% for 30 years.
- Monthly interest rate = 0.068 / 12 = 0.005667.
- Number of months = 30 * 12 = 360.
- Principal & Interest = $2,085.15 / month.
- Taxes & Insurance = ($4,800 + $1,500) / 12 = $525.00 / month.
- Total monthly PITI = $2,085.15 + $525.00 = $2,610.15.
Result: Monthly Payment = $2,610.15 (P&I: $2,085.15)
Frequently Asked Questions
What is the benefit of a 15-year mortgage over a 30-year?
A 15-year mortgage carries lower interest rates and cuts total lifetime interest paid by more than 60%, but requires higher monthly payments due to the accelerated amortization schedule.