Mortgage Calculator

The formula

Principal and interest use the standard amortising loan formula:

M = P x r x (1 + r)^n / ((1 + r)^n - 1)

Where P is the loan amount, r is the monthly interest rate (annual rate divided by 12), and n is the number of monthly payments. Property tax, insurance, PMI and HOA are added on top, which is why the headline rate never matches the real monthly cost.

Worked example

$400,000 home, 20 percent down, 6.5 percent for 30 years, 1.1 percent property tax, $1,800 insurance:

Loan amount: $400,000 - $80,000 = $320,000
Principal and interest: $2,022.62 per month
Property tax: $4,400 / 12 = $366.67
Insurance: $1,800 / 12 = $150.00
Total: about $2,539 per month
Total interest over 30 years: roughly $408,000

The striking part is the last line: at 6.5 percent over 30 years you pay more in interest than the house cost. That is not an argument against buying, but it is an argument for a shorter term or extra payments.

How lenders judge affordability

Ratio	Typical limit	What it means
Front-end (housing only)	28% of gross monthly income	Total housing cost including tax and insurance
Back-end (all debt)	36% of gross monthly income	Housing plus car loans, student loans, credit cards
Down payment	20% to avoid PMI	Below 20% usually adds mortgage insurance
Cash reserves	2 to 6 months of payments	Lenders verify you can survive a job loss

Common mistakes

Budgeting only principal and interest. Tax, insurance, PMI and HOA often add 25 to 40 percent on top.
Forgetting maintenance. A common rule is 1 percent of home value per year. On a $400,000 house that is $4,000 annually, or $333 a month.
Ignoring closing costs. Expect 2 to 5 percent of the purchase price, paid in cash at closing.
Choosing 30 years without checking 15. A shorter term can cut total interest by more than half, though the payment rises.
Assuming PMI lasts forever. It usually can be removed at 20 percent equity. Ask the lender for the exact removal process in writing.

Frequently asked questions

What is PMI and when does it apply?

Private mortgage insurance is usually required when the down payment is below 20 percent of the purchase price. It typically costs 0.3 to 1.5 percent of the loan amount per year and can usually be removed once you reach 20 percent equity.

How much house can I afford?

A common guideline keeps total housing costs at or below 28 percent of gross monthly income, and total debt payments at or below 36 percent.

Does a longer term lower my payment?

Yes, but it sharply increases total interest. A 30 year loan has a lower monthly payment than a 15 year loan but usually costs far more over the full term.

Should I pay extra each month?

Extra payments go straight to principal, which shortens the term and cuts interest significantly. Even $100 a month makes a visible difference over 30 years. Confirm with the lender that extra payments are applied to principal, not to future scheduled payments.

Is a fixed or adjustable rate better?

Fixed rates cost more upfront but remove the risk of a payment shock. Adjustable rates start lower and can be reasonable if you are certain you will sell or refinance before the first reset.

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