Real Estate Math Formulas

Total Commission

Variables: Sale Price (in $), Commission Rate (as decimal, e.g., 6% = 0.06)

Example: $500,000 × 0.06 = $30,000

Agent Split

Variables: Total Commission (in $), Split % (as decimal)

Example: $30,000 × 0.70 = $21,000 (70/30 split)

Net to Seller

Variables: Sale Price, Commission, Closing Costs (all in $)

Example: $500,000 - $30,000 - $5,000 = $465,000

Loan-to-Value (LTV)

Variables: Loan Amount (in $), Property Value (in $)

Example: $240,000 ÷ $300,000 × 100 = 80% LTV

Tip: LTV > 80% typically requires PMI

Down Payment

Variables: Property Value (in $), Loan Amount (in $)

Example: $300,000 - $240,000 = $60,000 (20% down)

Monthly Payment (P&I)

Variables: P = Principal, r = Monthly rate (annual ÷ 12), n = Total payments

Tip: On the exam, you may be given a factor table instead

Total Interest

Variables: Monthly Payment (in $), Number of Payments, Principal (in $)

Example: ($1,610 × 360) - $240,000 = $339,600

Capitalization Rate (Cap Rate)

Variables: NOI = Net Operating Income, Property Value (in $)

Example: $24,000 ÷ $300,000 × 100 = 8% Cap Rate

Tip: Higher cap rate = higher risk/return

Net Operating Income (NOI)

Variables: Gross Income (in $), Operating Expenses (in $)

Example: $36,000 - $12,000 = $24,000 NOI

Tip: Do NOT include mortgage payments in operating expenses

Gross Rent Multiplier (GRM)

Variables: Property Price (in $), Annual Gross Rent (in $)

Example: $300,000 ÷ $36,000 = 8.33 GRM

Tip: Lower GRM generally indicates better value

Cash-on-Cash Return

Variables: Annual Cash Flow (in $), Total Cash Invested (in $)

Example: $6,000 ÷ $75,000 × 100 = 8% CoC Return

Daily Rate (365-day year)

Variables: Annual Amount (in $)

Example: $3,650 ÷ 365 = $10/day

Daily Rate (360-day/Banker's Year)

Variables: Annual Amount (in $)

Example: $3,600 ÷ 360 = $10/day

Tip: Check if exam specifies 360 or 365 day year

Proration Amount

Variables: Daily Rate (in $), Number of Days owed

Example: $10/day × 45 days = $450 credit/debit

Area of Rectangle

Variables: Length (in ft), Width (in ft)

Example: 100 ft × 50 ft = 5,000 sq ft

Area of Triangle

Variables: Base (in ft), Height (in ft)

Example: (100 ft × 40 ft) ÷ 2 = 2,000 sq ft

Acre Conversion

Variables: Square feet ÷ 43,560 = Acres

Example: 87,120 sq ft ÷ 43,560 = 2 acres

Price Per Square Foot

Variables: Sale Price (in $), Square Footage

Example: $300,000 ÷ 2,000 sq ft = $150/sq ft

Straight-Line Depreciation

Variables: Cost (in $), Salvage Value (in $), Useful Life (in years)

Example: ($100,000 - $10,000) ÷ 27.5 = $3,273/year

Tip: Residential = 27.5 years, Commercial = 39 years

Assessed Value

Variables: Market Value (in $), Assessment Rate (as decimal)

Example: $300,000 × 0.80 = $240,000 assessed

Property Tax

Variables: Assessed Value (in $), Mills (÷ 1000 for rate)

Example: $240,000 × (25 ÷ 1000) = $6,000 tax

Tip: 1 Mill = $1 tax per $1,000 of assessed value