$100,000 is the benchmark salary everyone uses for home-buying math, so let us run the numbers three ways.
Assumptions for all three cases: $100k gross annual income ($8,333/month). $400/month in existing debt (a modest car payment). 6.75% 30-year fixed mortgage rate. 1.1% property tax (national average). $120/month home insurance. No HOA.
Case 1: 20% down, moderate DTI (33%). Max monthly payment: 33% × $8,333 − $400 = $2,350. Working backwards through the payment equation, this supports a home price of approximately $320,000 with $64,000 down and a $256,000 loan. Monthly: $1,660 P&I + $293 tax + $120 insurance = $2,073. Under cap with $277 of headroom.
Case 2: 10% down, same DTI. Same $2,350 cap, but the smaller down payment means a bigger loan per dollar of price, and PMI adds ~$50/month per $100k borrowed. Net result: approximately $295,000 home price. Lower purchase power, but you close two years sooner by saving half as much down payment.
Case 3: 3.5% down (FHA), same DTI. FHA also adds mandatory MIP. Max home price drops to roughly $270,000. You can enter the market with $9,500 down, but you are paying MIP for the life of the loan (or until you refinance into conventional at 20% equity).
What changes the answer most. Bigger effects than the down payment amount: your existing debt ($400 vs $0 swings the budget by $12k of home price), your rate (6.75% vs 5.75% adds roughly $35k of purchasing power), and your local property tax (NJ 2% vs HI 0.35% is a 6-figure swing on identical incomes).
The trap to avoid. Real estate agents and lenders will often quote you the 43% QM ceiling because it makes bigger commission. On $100k, that pushes you to a $390,000 house — about $70k more than the 33% number, and $70k of extra stress every month. The 28/36 rule is conservative on purpose.