M
Money Metric Hubs Precision Finance
LOANS & MORTGAGES CHANNEL

Mortgage Calculator

Calculate complete monthly house payments and analyze amortization schedules.

Calculator Variables

$
$
%
yrs
$
$

Calculation Overview

Estimate your monthly home mortgage payment including principal, interest, taxes, and homeowners insurance.

Mathematical Model & Formula

M = P * [ r(1+r)^n ] / [ (1+r)^n - 1 ]

This formula calculates the exact monthly payment needed to pay off a mortgage within a fixed term, where each payment covers the current monthly interest, and the remainder reduces the principal balance.

Variables Defined:
  • M: Monthly Principal and Interest payment
  • P: Loan principal amount (Purchase price - Down payment)
  • r: Monthly interest rate (Annual rate / 12)
  • n: Total number of payments (Months)

Worked Example Scenario

Scenario: A $300,000 mortgage loan on a 30-year fixed schedule at 6% annual interest.

  1. Principal (P) = $300,000, Monthly rate (r) = 0.06 / 12 = 0.005
  2. Total periods (n) = 30 * 12 = 360 months
  3. Plug in values: $300,000 * [0.005 * (1.005)^360] / [(1.005)^360 - 1]
  4. (1.005)^360 ≈ 6.02257
  5. Solve numerator: 0.005 * 6.02257 ≈ 0.03011
  6. Solve denominator: 6.02257 - 1 = 5.02257
  7. Solve final monthly PI: $300,000 * (0.03011 / 5.02257) ≈ $1,798.65

Result: Monthly Principal & Interest payment is $1,798.65.

Frequently Asked Questions

What is PMI?

Private Mortgage Insurance (PMI) is an extra monthly fee required if your down payment is less than 20% of the home purchase price. It protects the lender from defaults.

Can I shorten my mortgage timeline?

Yes. By paying extra towards the loan principal each month, you bypass front-loaded interest and reduce the term of your loan.

Academic & Regulatory References