Mortgage Calculator
Monthly home loan payment including property tax and insurance, from the home price and down payment
Interactive Sandbox
Adjust values in real-time and observe mathematical cause-and-effect
Exponential Compounding Growth: Returns generate subsequent returns over time t, rapidly accelerating capital growth.
Variable Mechanics
Roles, constraints & impacts
Home Price
Formula Parameter
Down Payment
Formula Parameter
Annual Interest Rate
Formula Parameter
Loan Term
Formula Parameter
Property Tax (per year)
Formula Parameter
Home Insurance (per year)
Formula Parameter
At a Glance
Gotchas, units & real-world use
Formula Nature & Mechanics
Exponential Compounding Growth: Returns generate subsequent returns over time t, rapidly accelerating capital growth.
Common Mistakes & Traps
- Entering annual percentage rate (e.g. 7%) as 7 instead of converting to decimal 0.07.
- Neglecting the compounding frequency (n): monthly compounding produces higher yield than annual.
- Ignoring inflation drag when evaluating long-term nominal returns.
Dimensional Analysis & Units
Currency × (1 + rate)^time = Future Currency ($)
Real-World & Industry Application
Retirement 401(k) / Roth IRA compounding, mortgage amortization schedules, bond yield analysis, and inflation depreciation modeling.
Worked Example: Mortgage
Given:
- price = 400000
- downPercent = 20
- rate = 6.5
- years = 30
- taxRate = 1.2
- insurance = 1500
- Down payment = 20% × $400,000 = $80,000
- Loan amount = $400,000 − $80,000 = $320,000
- Monthly rate r = 6.5% ÷ 12 = 0.5417%, payments n = 30 × 12 = 360
- Principal & interest = $320,000 × r(1 + r)ⁿ ÷ ((1 + r)ⁿ − 1) = $2,022.62
- Property tax = 1.2% × $400,000 ÷ 12 = $400
- Insurance = $1,500 ÷ 12 = $125
- Total monthly payment = $2,022.62 + $400 + $125 = $2,547.62
- Total interest over 30 years = $408,142.36
Answer: 2547.62
Frequently Asked Questions
What is the Mortgage formula?
M = L × r(1 + r)ⁿ ÷ ((1 + r)ⁿ − 1) + tax + insurance. Monthly home loan payment including property tax and insurance, from the home price and down payment.
How do I calculate Mortgage?
Enter Home Price (price), Down Payment (downPercent), Annual Interest Rate (rate), Loan Term (years), Property Tax (per year) (taxRate), Home Insurance (per year) (insurance) into the calculator. It applies M = L × r(1 + r)ⁿ ÷ ((1 + r)ⁿ − 1) + tax + insurance and shows every step of the working.
