The formula
How much down payment you need is three numbers, not one. Your down payment is the home price times the down-payment percentage divided by 100. Your loan is the home price minus the down payment. And your monthly payment is the loan at the monthly rate over the term — the loan times r times (1+r)^n divided by ((1+r)^n − 1), where r is the annual rate divided by 1200 and n is the term in years times 12. Whichever of the three you are solving for, the same three numbers decide it.
Step 1 — Work out the down payment
Start with the two numbers the calculation hangs on. In our worked example the home price is $400,000.00 and the down-payment percentage is 20%. The down payment is $400,000.00 × 20% = $80,000.00. Keep them fixed — every later step uses these two numbers, and changing one halfway through is how down-payment math goes wrong. The down payment calculator does this for you, and it finds the home price where a down payment is exactly $50,000.00.
Step 2 — Work out the loan
Your loan is the home price minus the down payment. At $400,000.00 with $80,000.00 down the loan is $400,000.00 − $80,000.00 = $320,000.00. That is the number the mortgage is actually written on — the down payment is cash you pay on day one, and the loan is what you borrow. At 25% down the loan is $300,000.00; at 10% down it is $360,000.00.
Step 3 — Work out the monthly payment
Your monthly payment is the loan at the monthly rate over the term. At a $320,000.00 loan, 6.5% and 30 years the monthly rate is 6.5% ÷ 1200 = 0.00541667 and the term is 360 months, so the payment is $2,022.62 a month. The total interest is $2,022.62 × 360 − $320,000.00 = $408,143.20. The payment is principal and interest only — it does not include property tax, homeowners insurance, PMI, or HOA dues. The mortgage payment calculator and the mortgage payment chart work this out for any loan.
The $400,000 example at 20%, 10% and 3% down
At 20% down the down payment is $80,000.00, the loan is $320,000.00, the payment is $2,022.62 a month, and the total interest is $408,143.20. At 10% down the down payment is $40,000.00, the loan is $360,000.00, the payment is $2,275.44 a month, and the total interest is $459,158.40 — $40,000.00 less cash on day one, $252.82 more a month, $51,015.20 more interest. At 3% down the down payment is $12,000.00, the loan is $388,000.00, the payment is $2,452.42 a month, and the total interest is $494,871.20. The pattern is the same every time: less cash today means a bigger loan, a bigger payment, and more interest.
The PMI line: why 20% matters
Twenty percent is the line because it usually avoids private mortgage insurance. Put down less than 20% on a conventional loan and the lender usually requires PMI, which adds to the monthly cost — so the 10% and 3% payments above are the principal-and-interest figures only, and the real monthly cost is higher. FHA loans allow as little as 3.5% down, which is how many first-time buyers get in with less cash. The PMI calculator works out what the insurance itself costs, and the big vs minimum down payment page compares the two sides directly.
The rate that gets you to $2,000 a month
If $2,000.00 a month is the line, the rate decides it. On a $320,000.00 loan over 30 years the exact rate for a $2,000.00 payment is 6.3922% — and 6.40% is the first 0.01pp step that actually reaches it, giving a payment of $2,001.62, $1.62 over the target. At 6.39% the payment is $1,999.52, $0.48 short. So the question “what rate do I need?” has a number attached: 6.40% is the line.
The price that gives you a $50,000 down payment
If $50,000.00 is the cash you have, the home price decides it. At 20% down a $50,000.00 down payment means a $250,000.00 home — the loan is $200,000.00, the payment is $1,264.14 a month, and the total interest is $255,090.40. And if the loan is the number you are watching, 25% down on a $400,000.00 home gives a $300,000.00 loan exactly.
How much house can you buy with $2,000 a month?
The smallest home price whose rounded payment reaches $2,000.00 at 20% down, 6.5% and 30 years is $395,526.06 — the down payment is $79,105.21, the loan is $316,420.85, and the total interest is $403,579.15. At $395,526.05 the payment is $1,999.99. And the term matters too: 19 years is the smallest whole-year term that gets a $320,000.00 loan to $2,500.00 a month or less — at 19 years the payment is $2,447.54, and at 18 years it is $2,517.00.