Mortgage Calculator

A mortgage is a secured loan where the property serves as collateral. Your monthly payment consists of four components — collectively called PITI: **Principal** (the loan amount you're paying down), **Interest** (the lender's fee for borrowing), **Taxes** (property tax, usually escrowed), and **Insurance** (homeowners insurance, also escrowed). Some borrowers also pay PMI (Private Mortgage Insurance) if their down payment is under 20%.

The principal and interest (P&I) portion is what most mortgage calculators focus on. It uses the standard amortization formula: M = P × [r(1+r)^n] / [(1+r)^n − 1], where M is the monthly payment, P is the loan amount, r is the monthly interest rate, and n is the total number of payments.

What makes mortgages interesting mathematically is the way the P&I split changes over time. In the early years, most of your payment goes to interest. As the loan ages, an increasing share goes to principal. This 'reverse compounding' is why prepaying early in the loan saves dramatically more interest than prepaying late.

The two most common loan terms in the US are 15 and 30 years. The shorter term has a higher monthly payment but dramatically less total interest. On a $300,000 loan at 6.5%: the 30-year payment is $1,896/month with $382,000 in total interest; the 15-year payment is $2,613/month with only $170,000 in total interest.

The 15-year saves $212,000 in interest but costs $717/month more. Whether that trade-off is worth it depends on your cash flow and opportunity cost. If you can invest that $717/month at 8% instead, you might come out ahead over 30 years — but only if you actually invest it, which most people don't.

The 30-year mortgage is more flexible: the lower mandatory payment gives you breathing room. You can always pay extra to reduce interest (essentially creating your own 15-year schedule), but you can't easily reduce the 15-year payment if you hit a cash crunch.

Because interest is calculated on the remaining balance each month, early prepayments reduce the balance that future interest is calculated on — creating a compounding effect in your favor. A $10,000 prepayment in year 1 of a 30-year mortgage saves about $21,000 in total interest. The same $10,000 prepayment in year 25 saves only about $700.

This is why financial planners stress that extra payments early in a loan are far more powerful than later. Even $100/month extra in the first 5 years of a 30-year mortgage can cut 3–4 years off the loan and save $30,000+ in interest.

The trade-off, of course, is liquidity. Money put into the mortgage is locked up (unless you refinance or sell). Money kept liquid can be invested, used for emergencies, or deployed elsewhere. For mortgage rates under 4%, investing often wins; for rates above 6%, prepaying is usually better.