Colorado Real Estate Exam Math: Commission, Proration & Cap Rate

Math appears throughout Colorado's 154-question exam. Here are the key formulas with worked examples.

Commission Calculations

Example: Property sells for $680,000. Commission 5.5%, split 50/50. Listing agent earns 55%. - Total: $680,000 × 0.055 = $37,400 - Listing side: $18,700 - Agent: $18,700 × 0.55 = $10,285

Proration (365-day year for Colorado)

Example: Annual taxes $7,300. Closing June 30. Taxes paid in arrears. - Daily: $7,300 ÷ 365 = $20/day - Seller's days (Jan 1 – June 30): 181 days - Seller's credit to buyer: 181 × $20 = $3,620

Cap Rate

Example: Denver duplex generates $4,200/month per unit. Annual expenses $14,400. Cap rate 5.5%. - Annual gross: $4,200 × 2 × 12 = $100,800 - NOI: $100,800 - $14,400 = $86,400 - Value = $86,400 ÷ 0.055 = $1,570,909

Net to Seller

Example: Seller wants $520,000 net after 5.5% commission. - Sale Price = $520,000 ÷ 0.945 = $550,264.55

LTV

Example: $750,000 home, 20% down. - Loan: $600,000 - LTV: $600,000 ÷ $750,000 = 80% → No PMI

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