The Home Buyer's Guide to Mortgage Math

Everything you need to understand about mortgage calculations. Covers the payment formula, amortization, rate comparisons, and how different loan terms change total cost.

mortgage home-buying real-estate

The mortgage payment formula

The standard fixed-rate mortgage payment formula is:

\[M = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1}\]

Where M is the estimated monthly payment (principal and interest only), P is the loan amount (home price minus down payment), r is the monthly interest rate (annual rate divided by 12), and n is the total number of monthly payments (loan term in years x 12).

This formula produces a fixed payment that, if made every month for the full term, pays off both principal and interest by the final payment. The companion guide on understanding your mortgage payment covers how interest rates and loan terms affect this number in detail.

Try it yourself

Estimate your monthly mortgage payment, total interest, and total cost based on loan amount, interest rate, and term.

Open Mortgage Calculator

Worked example: $400,000 at 6.5% for 30 years

With P = 400,000, r = 0.065 / 12 = 0.005417, and n = 360, the estimated monthly payment is approximately $2,528. Over 360 payments, the total paid is approximately $910,080. Subtract the $400,000 principal and you get approximately $510,080 in interest. The total cost of the loan is more than double the amount borrowed, which is why the interest rate matters so much on a 30-year term.

Second example: $250,000 at 7% for 30 years

Here P = 250,000, r = 0.07 / 12 = 0.005833, and n = 360. The estimated monthly payment is approximately $1,663. Total paid over 30 years comes to approximately $598,772, meaning roughly $348,772 goes to interest. Even on a smaller loan, the interest charges over three decades nearly match the original balance. This is the mathematical consequence of a long term combined with a rate above 6%. Borrowers who can qualify for a lower rate save tens of thousands on the same principal amount. A single half-point reduction from 7% to 6.5% on this $250,000 loan drops the monthly payment by about $80 and saves approximately $28,800 over the full term.

Where each payment goes: principal vs. interest

Mortgage payments are front-loaded with interest. In the early years, most of each payment covers interest because the lender calculates interest on the remaining balance, and that balance is highest at the start.

Period	Approximate interest portion	Approximate principal portion
Year 1 (first payment)	$2,167	$361
Year 15	$1,484	$1,044
Year 25	$775	$1,753
Year 30 (final payment)	$14	$2,514

In the first payment, roughly 86% goes to interest. By year 25, roughly 69% goes to principal. This pattern is called amortization. Each small principal payment reduces the balance, which reduces the next month’s interest charge, which frees up more of the next payment for principal. The effect compounds over time. That is why extra payments early in the loan save the most interest; they shrink the balance that generates interest charges for every remaining month. See mortgage payment breakdown for a detailed year-by-year walkthrough.

The real cost of “just one more percent”

Many borrowers focus on the monthly payment without fully considering how rate differences compound over the life of the loan. For a $400,000 loan over 30 years:

Interest rate	Estimated monthly payment	Total interest
5.5%	$2,271	$417,560
6.0%	$2,398	$463,353
6.5%	$2,528	$510,080
7.0%	$2,661	$557,726

The difference between 5.5% and 7.0% is $390 per month. Over 30 years, the higher rate costs approximately $140,166 more in interest. This is why even small rate reductions from paying discount points, improving credit scores, or shopping among lenders can pay off significantly. A borrower who spends $4,000 in points to drop from 7.0% to 6.75% would save approximately $68 per month. That point cost is recovered in about 59 months, and everything after that is net savings.

15-year vs. 30-year terms

Shorter terms mean higher monthly payments but dramatically less total interest. For a $400,000 loan at 6.5%:

Loan term	Estimated monthly payment	Total interest
15 years	$3,484	$227,200
30 years	$2,528	$510,080

The 15-year term costs approximately $956 more per month but saves approximately $282,880 in interest. That savings comes from two sources: you repay the principal in half the time, and the faster principal reduction means less interest accumulates each month. Whether this tradeoff makes sense depends on your monthly cash flow and other financial obligations.

How down payment size affects the loan

The down payment reduces the loan principal, which lowers both the monthly payment and total interest. For a $500,000 home at 6.5% for 30 years:

Down payment	Loan amount	Estimated monthly payment	Total interest
5% ($25,000)	$475,000	$3,002	$605,720
10% ($50,000)	$450,000	$2,844	$573,840
20% ($100,000)	$400,000	$2,528	$510,080

A 20% down payment also eliminates the requirement for private mortgage insurance (PMI), which typically costs 0.5% to 1% of the loan amount per year. On a $400,000 loan, that is an extra $167 to $333 per month until you reach 20% equity. The down payment calculator shows how different down payment amounts change the loan.

Common mistakes in mortgage math

One frequent error is comparing monthly payments without accounting for total cost. A 30-year loan at 6.5% looks cheaper per month than a 15-year loan at the same rate, but the 30-year option costs $282,880 more over its lifetime. Monthly affordability matters, but the total interest column tells the full story.

Another mistake is ignoring how rounding affects real payments. Lenders calculate interest on the exact remaining balance to the penny, not on rounded numbers. The formula gives an estimated figure; the actual amortization schedule your lender provides may differ by a few dollars due to rounding conventions and the way partial cents are handled.

A third common error is assuming the quoted annual rate directly represents the cost of borrowing. The annual percentage rate (APR) includes origination fees and other costs, making it a more accurate comparison tool between loan offers. Two loans with the same interest rate but different fee structures will have different APRs, and the lower APR is usually the cheaper loan overall.

The 28/36 rule for affordability

A common guideline for mortgage affordability is the 28/36 rule: spend no more than 28% of gross monthly income on housing costs (mortgage payment, taxes, insurance), and no more than 36% on total debt (housing plus car payments, student loans, credit cards).

For a household earning $8,000 per month gross, 28% is $2,240 maximum housing cost. If property taxes and insurance add approximately $500 per month, that leaves $1,740 for principal and interest, which supports an estimated loan of approximately $275,000 at 6.5% for 30 years.

These are guidelines, not strict rules. Lenders may approve more or less depending on credit score, savings, and other factors. The home affordability calculator runs these numbers for your specific income.

Try it yourself

Estimate how much house you can afford based on income, debts, down payment, and current interest rates.

Open Home Affordability Calculator

What the calculator does not include

A mortgage payment calculator estimates the principal and interest portion of your payment. Your actual monthly housing cost will also include property taxes (typically 0.5% to 2.5% of home value per year, depending on location), homeowner’s insurance, PMI if the down payment is below 20%, HOA fees (if applicable, ranging from $100 to $500+ per month), and maintenance (a common estimate is 1% of home value per year).

On a $500,000 home, property taxes of 1.5% add approximately $625 per month and insurance might add $150 per month. These costs can add $800 or more to the base mortgage payment. Always factor in these expenses when evaluating affordability. Consult a mortgage professional for estimates specific to your situation.