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.

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The mortgage payment formula

The standard fixed-rate mortgage payment formula is:

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

Where:

• M = estimated monthly payment (principal and interest only)
• P = the loan amount (home price minus down payment)
• r = the monthly interest rate (annual rate divided by 12)
• n = 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.

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

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

Suppose you borrow $400,000 at an annual rate of 6.5% for 30 years.

• P = 400,000
• r = 0.065 / 12 = 0.005417
• n = 30 x 12 = 360

M = 400,000 x [0.005417(1.005417)^360] / [(1.005417)^360 - 1]

M = 400,000 x [0.005417 x 6.9913] / [6.9913 - 1]

M = 400,000 x 0.03788 / 5.9913

Estimated monthly payment: approximately $2,528.

Over 360 payments, you would pay approximately $910,080 total. 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.

Where each payment goes: principal vs. interest

Mortgage payments are front-loaded with interest. In the early years, most of each payment covers interest. Over time, the balance shifts toward principal.

For the $400,000 loan at 6.5% described above:

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. It explains why extra payments early in the loan save the most interest.

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%:

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

The 15-year term costs approximately $956 more per month but saves approximately $282,880 in interest. That is a significant difference. Whether it 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 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)
• Spend no more than 36% of gross monthly income on total debt (housing plus car payments, student loans, credit cards)

For a household earning $8,000/month gross:

• 28% of $8,000 = $2,240 maximum housing cost
• 36% of $8,000 = $2,880 maximum total debt

If property taxes and insurance add approximately $500/month, that leaves $1,740 for principal and interest. Based on the formula, that 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.

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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: varies by property and coverage level
• PMI: required if down payment is below 20%, typically 0.5% to 1% of loan amount per year
• HOA fees: if applicable, can range from $100 to $500+ per month
• Maintenance: a common estimate is 1% of home value per year

For example, on a $500,000 home, property taxes of 1.5% add approximately $625/month. Insurance might add $150/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.

Key takeaways

• The mortgage formula is M = P x [r(1+r)^n] / [(1+r)^n - 1], where r is the monthly rate and n is total payments
• A $400,000 loan at 6.5% for 30 years has an estimated monthly payment of approximately $2,528 and approximately $510,080 in total interest
• Early payments are mostly interest; the balance shifts toward principal over time
• A 15-year term on the same loan saves approximately $282,880 in interest but costs $956 more per month
• The 28/36 rule suggests spending no more than 28% of gross income on housing
• The calculator estimates principal and interest only; taxes, insurance, PMI, and maintenance are additional costs

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