← All Guides
🏠

Complete Guide to Home Buying Math

✍️
By Derek Jordan, BA Business Marketing  ·  Updated May 2026  ·  Reviewed for accuracy

Buying a home involves more financial calculations than any other decision most people will make. This guide walks through every number: affordability ratios, mortgage payment math, the true cost of different down payment amounts, PMI breakpoints, closing cost estimation, the rent-vs-buy breakeven analysis, and when refinancing makes sense. Each section links to the calculator you need to run your own numbers.

How to use this guide: Work through the sections in order if you are starting the home-buying process. Jump to specific sections if you need answers to particular financial questions. Use our step-by-step Home Buying Guide for the process-oriented walkthrough — this page focuses purely on the math.

Affordability: The Numbers Lenders Check

Lenders evaluate two debt-to-income (DTI) ratios. The front-end ratio divides your total housing costs (mortgage principal, interest, taxes, insurance, HOA) by gross monthly income — target under 28%. The back-end ratio adds all other debt payments (car loans, student loans, credit cards, personal loans) and divides by gross income — must be under 43% for most conventional loans (some programs allow up to 50%).

Your credit score determines your interest rate, which has an enormous impact on affordability. On a $350,000 loan, the difference between a 6.0% rate (760+ score) and a 7.0% rate (680 score) is $230/month or $83,000 in total interest over 30 years. If your score is below 740, spending 6–12 months improving it before buying is often the highest-return financial decision you can make. Read our How Credit Scores Work and What Is a Good DTI Ratio? guides.

1
Calculate What You Can Afford
Run the DTI ratios and find your comfortable price range.

Down Payment and PMI Math

The conventional wisdom of 20% down exists because it eliminates PMI (Private Mortgage Insurance). PMI typically costs 0.5–1.0% of the loan amount annually, adding $100–$300/month to your payment. But waiting years to save 20% while renting has its own costs — rising home prices and continued rent payments.

Down PaymentOn $400K HomeLoan AmountMonthly PMI (est.)Total Upfront Cash Needed
3% (conventional)$12,000$388,000$200–$325$20,000–$27,000
3.5% (FHA)$14,000$386,000$215–$270 (MIP)$22,000–$29,000
10%$40,000$360,000$150–$300$48,000–$55,000
20%$80,000$320,000$0$88,000–$95,000

Total upfront cash includes down payment + estimated closing costs (2–5% of loan). PMI rates vary by credit score, LTV, and insurer. FHA MIP cannot be cancelled (unlike conventional PMI) unless you refinance to conventional.

The PMI removal strategy: Conventional PMI automatically cancels at 78% LTV (loan-to-value) based on the original purchase price, or you can request removal at 80% LTV. Accelerating principal payments can reach 80% LTV faster. On a $360,000 loan at 6.5%, it takes about 8 years to reach 80% LTV through normal payments. Adding $200/month extra to principal reduces this to about 5.5 years. Use the PMI Calculator to model your specific scenario.

2
Model Your Mortgage Scenarios
Compare loan terms, interest rates, and down payment amounts.

15-Year vs. 30-Year: The Interest Difference

The 15-year mortgage saves massive interest and typically comes with a lower rate (0.25–0.75% less). On a $300,000 loan: the 30-year at 6.5% costs $1,896/month with $382,633 in total interest. The 15-year at 5.75% costs $2,491/month with $148,370 in total interest. The 15-year saves $234,000 in interest but requires $595/month more in cash flow.

A flexible middle ground: take the 30-year but make extra principal payments when cash flow allows. This preserves the lower minimum payment as a safety net while still reducing interest. Paying an extra $300/month on a 30-year $300,000 loan at 6.5% cuts the payoff from 30 years to about 21 years and saves roughly $130,000 in interest. Read our 15 vs. 30-Year Mortgage Analysis and Should You Pay Off Your Mortgage Early? for the detailed comparison.

Closing Costs: The Expense Nobody Plans For

Closing costs run 2–5% of the loan amount and are due at closing on top of your down payment. On a $350,000 home with 10% down ($315,000 loan), expect $6,300–$15,750 in closing costs. This includes loan origination fees (0.5–1%), appraisal ($400–$700), title insurance ($1,000–$3,000), attorney fees, recording fees, prepaid insurance, and escrow setup (property tax and insurance reserves).

Plan for 13–15% of the purchase price in total upfront cash (down payment + closing costs + moving + initial home setup). Many first-time buyers plan only for the down payment and are caught short. Read our How to Compare Mortgage Offers guide to understand how closing costs vary between lenders.

3
Estimate Closing Costs and Total Cash Needed
Calculate all upfront expenses beyond just the down payment.

Rent vs. Buy: The Breakeven Analysis

The rent-vs-buy decision comes down to timeline and total cost. Transaction costs (realtor commissions, closing costs, moving) run 8–10% of the home’s value round-trip. You need enough appreciation and equity building to overcome this cost. In most markets, the breakeven point where buying becomes cheaper than renting is 3–5 years. If you expect to move sooner, renting and investing the down payment may be the better financial choice.

The true comparison must include all homeownership costs (mortgage, taxes, insurance, maintenance, opportunity cost of down payment) vs. all renting costs (rent, renter’s insurance, investment returns on the money you would have used for a down payment). Read our Renting vs. Buying in 2026 for the current market analysis.

4
Compare Renting vs. Buying
Run the full financial comparison for your specific situation and timeline.

After Purchase: Refinancing and Equity

Once you own, two financial calculations become relevant: refinancing (when does a lower rate justify the closing costs?) and equity access (should you tap equity through a HELOC or cash-out refinance?). For refinancing, divide closing costs by monthly savings to get the break-even month. Only refinance if you will keep the home longer than that. A 0.75–1.0% rate reduction typically justifies the cost. Read our Refinancing Calculator Guide and HELOC vs. Cash-Out Refi comparison.

5
Optimize After Purchase
Model refinancing scenarios, HELOC options, and extra payment impact.
How much house can I afford?
Front-end DTI under 28%, back-end under 43%. Conservative rule: 3–4x gross annual income. On $100K income, target $300K–$400K. Remember: lender approval maximum ≠ comfortable affordability.
How does down payment affect total costs?
Below 20% requires PMI ($100–$300/month). Larger down payment = smaller loan = less interest + no PMI. The difference between 10% and 20% down on a $400K home is roughly $35K–$60K in total additional cost over 30 years.
15-year or 30-year mortgage?
15-year saves 50–60% in total interest with a lower rate, but payments are ~40% higher. Flexible alternative: take 30-year, make extra principal payments when possible. This preserves the lower minimum as a safety net.
When does refinancing make sense?
Divide closing costs by monthly savings = break-even months. Only refinance if you’ll keep the home longer. A 0.75–1.0% rate reduction usually justifies it. Also consider: removing PMI, converting ARM to fixed, or switching to 15-year.
When is buying better than renting?
Typically when you’ll stay 3–5+ years. Transaction costs run 8–10% round-trip. The true comparison must include all ownership costs (mortgage, taxes, insurance, maintenance, opportunity cost) vs. rent + investment returns on what you’d have spent on a down payment.
📚 Sources: [1] CFPB — Owning a Home Guide [2] Freddie Mac — Mortgage Research and Data [3] NAR — Real Estate Market Statistics [4] FHFA — House Price Index