Mortgage Calculator

Formula

M = P × r(1+r)^n / ((1+r)^n − 1), where P = loan amount, r = APR/12, n = payments (360 for 30y). Total interest = M×n − P.

LTV = loan ÷ price. PMI required below 20% down; auto-terminates at 78% LTV on conforming loans.

How it works

Enter price, down payment, rate and term. The engine amortizes the loan month by month: each payment covers that month’s interest on the remaining balance, the rest reduces principal. Taxes, insurance, PMI, HOA and other annual costs are spread monthly on top of principal and interest. Extra payments shorten the schedule because they cut principal directly, so less interest accrues next month.

Assumptions

• Fixed rate for the whole term; adjustable rates need the ARM calculator.
• Monthly compounding with payments at month-end; no grace-period float.
• Property tax and insurance held flat unless you set annual increases.

Default result

With Defaults: $400,000 price, 20% down, 30 years, 6.616% APR, taxes 1.2%, insurance $1,500, other $4,000, start January 2026 (payment and totals do not depend on start month; only the payoff calendar date does): Monthly P&I $2,047.09 · total $2,905.42 · payoff 12/2055 in 360 payments · lifetime interest $416,952.82

Worked examples

Standard 30-year purchase

$400,000 price, 20% down ($80,000), 6.616% APR, 30 years, taxes 1.2%, insurance $1,500, other $4,000

Loan $320,000.00 · P&I $2,047.09/mo · total out-of-pocket $1,045,952.82 · interest $416,952.82 — Example calculated with this calculator's formula.

Small extra payment

Same loan plus $200 extra monthly from payment 1

+$200/mo cuts payoff to 4/2049 (280 vs 360 payments) · saves $108,483.10 interest — Example calculated with this calculator's formula.

Frequently asked questions

What is a mortgage and how does it work?

A mortgage is a loan secured by real estate that allows homebuyers to finance the purchase of a property. The borrower agrees to repay the loan over a fixed period (typically 15 or 30 years) through monthly payments that include both principal (the original amount borrowed) and interest (the cost of borrowing). The property serves as collateral, meaning the lender can foreclose if payments are not made.

How is my monthly mortgage payment calculated?

Your monthly payment is calculated using the amortization formula: M = P × [r(1+r)^n] / [(1+r)^n - 1], where P is the loan amount, r is the monthly interest rate (APR/12), and n is total payments (years × 12). The calculator then adds property taxes, insurance, PMI, HOA, and other costs for a complete picture.

What is the difference between a fixed-rate and adjustable-rate mortgage?

A fixed-rate mortgage (FRM) has a constant interest rate for the entire term, providing predictable payments. An adjustable-rate mortgage (ARM) has a rate fixed for an initial period (e.g., 5, 7, 10 years) that then adjusts periodically based on market indices. ARMs start lower but carry future increase risk.

What is PMI and when do I need it?

Private Mortgage Insurance protects the lender if you default. It is required when your down payment is less than 20% of the purchase price. PMI costs 0.3% to 1.9% annually and automatically cancels at 78% LTV or can be requested at 80% LTV.