Calcs.finance

Formula and help

Down Payment Calculator Formula and Help

Learn how this calculator works, what formula it uses, and which assumptions sit behind the estimate.

Educational estimate, not financial advice.

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How it works

The Down Payment Calculator models three home-purchase cash questions. Home Price mode starts with upfront cash available and estimates the home price that fits the selected down payment and closing-cost assumption. Cash Needed mode starts with a known home price and down payment percentage. Down Payment Percentage mode starts with home price and upfront cash, subtracts selected closing costs, and estimates the remaining down payment percentage.

Use this calculator when you want to compare how upfront cash, home price, selected closing costs, down payment percentage, interest rate, and loan term interact before reviewing lender documents. Use Mortgage Payment for a focused principal-and-interest payment, Mortgage for broader housing-cost assumptions, House Affordability for income and debt constraints, and actual Loan Estimates, lender disclosures, local tax sources, insurer quotes, title or settlement statements, HOA documents, or assistance-program materials for official figures.

Formula notes

This formula page covers the app's Down Payment Calculator: three solve modes for estimated home price, cash needed, or implied down-payment percentage using entered upfront cash, selected closing-cost assumptions, and fixed principal-and-interest payment math. It does not calculate a Loan Estimate, Closing Disclosure, legal cash-to-close figure, PMI premium, assistance-program eligibility result, underwriting decision, approval, tax answer, or personalised mortgage advice.

H_percent = C / ((d + cc) / 100); H_fixed = d > 0 ? max(0, C - F) / (d / 100) : 0; ClosingCosts = mode == percent ? H * cc / 100 : F; DP = H * d / 100; CashNeeded = DP + ClosingCosts; DP_from_cash = max(0, C - ClosingCosts); DPct = H > 0 ? DP_from_cash / H * 100 : 0; Loan = max(0, H - DP); r = i / 100 / 12; n = years * 12; Pmt = r == 0 ? Loan / n : Loan * r / (1 - (1 + r)^(-n))

The calculator first chooses the selected solve mode, derives the home price, cash needed, or down-payment percentage from the entered assumptions, then estimates the remaining loan amount and a fixed principal-and-interest payment.
SymbolMeaningHow this page uses it
HHome priceThe entered or solved purchase price assumption used for down-payment and closing-cost math.
CUpfront cash availableThe entered cash amount used in home-price and down-payment-percentage solve modes.
dDown-payment percent inputThe entered target down-payment percentage used when solving home price or cash needed.
ccClosing-cost percent inputThe entered closing-cost percentage when closing costs are modeled as a percent of home price.
FFixed closing-cost inputThe entered closing-cost amount when fixed closing-cost mode is selected.
ClosingCostsModeled closing costsEither home price times the entered closing-cost percentage, or the entered fixed closing-cost amount.
DPDown-payment amountHome price times the target down-payment percentage in home-price and cash-needed solve modes.
DPctImplied down-payment percentageAvailable cash after modeled closing costs divided by home price when solving for down-payment percentage.
LoanLoan amountHome price minus down payment, floored at 0 so an oversized down payment cannot create a negative loan.
iAnnual interest-rate inputThe entered fixed-rate assumption. The app treats it as a simple annual rate for payment math, not as a legal APR.
rMonthly rateAnnual rate divided by 100 and by 12.
nPayment countLoan term years multiplied by 12 monthly payments.
PmtMonthly principal and interestThe fixed-rate principal-and-interest payment before taxes, homeowners insurance, PMI, HOA dues, escrow, fees, or other housing costs.
PMI noticeSimple below-20-percent noticeA plain notice when the calculated down-payment percentage is below 20 percent. It is not a PMI premium calculation or lender determination.

Step by step

  1. Read the selected solve mode: home price, cash needed, or down-payment percentage.
  2. When solving home price with percentage closing costs, divide upfront cash by the combined down-payment and closing-cost percentage.
  3. When solving home price with fixed closing costs, subtract the fixed closing-cost amount from upfront cash and divide by the down-payment ratio.
  4. If fixed closing costs are selected and the target down-payment ratio is 0 percent, return a 0 home-price estimate because the price is indeterminate without a down-payment ratio.
  5. Calculate closing costs from the selected mode: percentage of home price or the fixed closing-cost amount.
  6. For cash-needed mode, multiply home price by the target down-payment percentage and add modeled closing costs.
  7. For down-payment-percentage mode, subtract modeled closing costs from upfront cash, floor the remainder at 0, then divide by home price when home price is positive.
  8. Calculate loan amount as home price minus down payment, floored at 0.
  9. Convert the entered annual rate to a monthly decimal rate and convert term years to monthly payment count.
  10. Use the zero-rate payment branch when the monthly rate is 0; otherwise use the fixed-rate amortizing payment formula.
  11. Show the simplified PMI notice when the resulting down-payment percentage is below 20 percent.
  12. Round displayed currency outputs to two decimals after the full-precision calculation.
  13. Use CFPB Loan Estimate, private mortgage insurance, principal-and-interest versus total monthly payment, Regulation Z, lender, settlement, mortgage-insurance, tax, legal, or assistance-program sources before adding official disclosure, eligibility, cash-to-close, PMI, approval, or jurisdiction-specific claims.

Sources and validation

This calculator is an original implementation based on the app's documented down-payment solve modes, selected closing-cost assumptions, fixed principal-and-interest payment math, deterministic fixtures, edge cases, rounding policy tests, and internal validation. It is not copied from a single source.

Outputs are checked with deterministic fixtures for home-price, cash-needed, and implied down-payment-percentage solves, plus edge-case tests and internal validation artifacts. The result remains an educational estimate, not a Loan Estimate, not a Closing Disclosure, not a cash-to-close figure, not a PMI determination, not a lender quote, not an approval, not a tax answer, not a legal answer, not an assistance-program eligibility result, and not personalised mortgage advice.

  • CFPB Loan Estimate and compare Loan Estimates materials should be used before copy discusses official loan amount, projected payments, closing costs, estimated cash to close, lender credits, taxes, insurance, rate locks, lender forms, or mortgage-offer comparisons.
  • CFPB private mortgage insurance materials should be used before copy discusses conventional-loan PMI context, 20 percent down payment framing, PMI payment forms, PMI cost, or PMI alternatives.
  • CFPB principal-and-interest versus total monthly payment materials should be used before copy explains why the app's monthly payment output excludes taxes, homeowners insurance, mortgage insurance, escrow, HOA dues, or total monthly housing-payment items.
  • CFPB Regulation Z section 1026.37 plus lender disclosures should be used before copy discusses legal Loan Estimate disclosure fields, cash-to-close calculations, down payment and funds from borrower, closing-cost financing, disclosure timing, or disclosure accuracy.
  • FHA, VA, USDA, Fannie Mae, Freddie Mac, lender, mortgage-insurer, title or settlement, local tax authority, insurer, HOA, legal, and assistance-program sources are needed before copy makes product-specific, jurisdiction-specific, mortgage-insurance, tax, escrow, title, eligibility, underwriting, approval, or legal claims.

See the Calcs.finance methodology for the full review approach.

Assumptions

  • The selected solve mode determines which question is answered. Inputs that remain in the form state can still be present in server-rendered HTML, but the calculator uses the mode-specific formula branch for home price, cash needed, or down payment percentage. Closing costs are a simplified entered percentage of home price or a fixed entered amount; the estimate does not model lender credits, seller credits, earnest-money deposits, points, prepaid interest, escrow deposits, title fees, appraisal fees, recording fees, transfer taxes, program fees, or any other actual cash-to-close adjustment.
  • The monthly payment output is principal and interest only. It excludes property tax, homeowners insurance, mortgage insurance premiums, escrow, HOA dues, maintenance, utilities, assistance-program requirements, underwriting, rate locks, APR, lender approval, and official Loan Estimate or Closing Disclosure figures. The PMI notice uses a simple below-20-percent branch for educational context; real private mortgage insurance, FHA mortgage insurance premiums, VA funding fees, USDA guarantee fees, jumbo-loan overlays, lender-paid PMI, cancellation, and product eligibility depend on lender, agency, insurer, and program rules.
  • Package fixtures cover all three solve modes, and internal independent comparator checks may be used only as validation evidence. CFPB Loan Estimate materials are needed before copy discusses loan amount, closing costs, cash to close, projected payments, lender credits, taxes, or insurance; CFPB PMI materials are needed before discussing conventional-loan PMI context; CFPB principal-and-interest versus total monthly payment materials are needed before explaining monthly-payment boundaries; and Regulation Z section 1026.37 is needed before legal Loan Estimate disclosure claims. Results are educational estimates, not financial, tax, legal, lending, mortgage, consumer-rights, regulatory, or personalised advice.

Formula version 2026.05.22-generic-down-payment-modes

Common mistakes to avoid

  • Treating the down payment as the whole cash-to-close amount. The app adds only the selected closing-cost assumption, while real closing can include deposits, credits, prepaid items, escrow funding, title charges, taxes, insurance, and program fees.
  • Reading the monthly payment as a full housing payment. The output is a principal-and-interest estimate on the modeled loan amount, not a total monthly payment with tax, insurance, mortgage insurance, HOA dues, or escrow.
  • Treating the 20 percent PMI notice as a binding rule. It is a simplified conventional-loan signal, not a lender, insurer, FHA, VA, USDA, jumbo, cancellation, or assistance-program determination.

Worked example

Default fixtures: three down-payment questions

These examples use the app's package fixtures so the numbers match the production formula and rounding policy.

  1. Home-price fixture: $100,000 upfront cash, 20 percent target down payment, and 3 percent closing costs create a combined 23 percent cash requirement.
  2. $100,000 divided by 23 percent gives an estimated $434,782.61 home price.
  3. That implies an $86,956.52 down payment, $13,043.48 modeled closing costs, a $347,826.09 loan amount, and a $2,198.50 monthly principal-and-interest estimate at 6.5 percent for 30 years.
  4. Cash-needed fixture: a $500,000 home price with 20 percent down and 3 percent closing costs gives a $100,000.00 down payment plus $15,000.00 closing costs.
  5. The calculator reports $115,000.00 cash needed, a $400,000.00 loan amount, and a $2,528.27 monthly principal-and-interest estimate.
  6. Down-payment-percentage fixture: $100,000 upfront cash on a $500,000 home with 3 percent closing costs leaves $85,000.00 for down payment after $15,000.00 modeled closing costs.
  7. $85,000.00 divided by $500,000 gives 17.00 percent down, a $415,000.00 loan amount, and a $2,623.08 monthly principal-and-interest estimate.
  8. Because 17.00 percent is below 20 percent, the app shows the simple PMI or mortgage-insurance notice.

The fixtures illustrate the calculator's three mechanical solve modes. They do not show what a lender will disclose, approve, collect at closing, charge for PMI, require for reserves, or treat as verified funds.

What this formula does not include

  • The result is not a Loan Estimate, Closing Disclosure, legal cash-to-close figure, mortgage approval, underwriting result, lender quote, PMI premium, assistance-program eligibility result, tax answer, legal conclusion, or personalised mortgage advice.
  • Closing costs are simplified to either a single percentage of home price or a fixed amount. The calculator does not itemize origination charges, discount points, lender credits, seller credits, earnest money, prepaid interest, escrow reserves, title fees, appraisal fees, inspection costs, transfer taxes, recording fees, mortgage-insurance premiums, assistance funds, or cash-to-close adjustments.
  • The monthly payment output is principal and interest only. It excludes property taxes, homeowners insurance, PMI premiums, HOA dues, escrow deposits, utilities, repairs, maintenance, and other housing costs.
  • The PMI notice is a simplified below-20-percent branch. It is not a conventional PMI premium, FHA MIP, VA funding fee, USDA guarantee fee, jumbo-loan rule, lender overlay, cancellation schedule, or mortgage-insurance eligibility determination.
  • The annual interest-rate input is divided by 12 for payment math. It is not a legal APR, rate lock, finance-charge disclosure, or lender pricing offer.
  • When fixed closing costs are selected with 0 percent down in home-price mode, the app returns 0 because there is no positive down-payment ratio to solve a unique home price from cash.
  • Currency outputs are rounded for display after full-precision calculations, so hand calculations that round each intermediate step can differ by a few cents.
  • Scoped independent comparator checks and package fixtures cover the three solve modes. Named comparator evidence stays in internal validation artifacts and is not a public source for mortgage disclosures, product terms, PMI rules, or official closing figures.
  • The result is educational only and does not constitute financial, tax, legal, lending, mortgage, insurance, consumer-rights, regulatory, housing, or personalised advice.

Terms used in this calculator

Upfront cash available
The cash amount the app treats as available for down payment and selected closing costs. It is not the same as verified funds, reserves, or the official cash-to-close figure on a lender document.
Cash needed
The modeled down payment plus the selected closing-cost assumption. Real cash to close can include additional credits, deposits, prepaid items, escrow amounts, and settlement charges.
PMI notice
A simplified message based on whether the modeled down payment is below 20 percent. It is not a real mortgage-insurance quote, cancellation analysis, or loan-program eligibility decision.

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