Real Estate Exam Math: 10 Formulas With Step-by-Step Examples

Formula: Sale Price × Commission Rate = Total Commission

Example A: A home sells for $325,000. The commission rate is 6%. Total commission = $325,000 × 0.06 = $19,500.

Example B: The total commission is $19,500. The listing broker gets 50%, and the listing agent gets 70% of the listing broker's share. Listing broker: $19,500 × 0.50 = $9,750. Listing agent: $9,750 × 0.70 = $6,825.

Common trap: forgetting to convert the percentage to a decimal. 6% = 0.06, not 6. If your answer is wildly large, you probably forgot this step.

Formula: Sale Price − Commission − Closing Costs = Net to Seller

Example A: Seller needs to net $280,000. Commission is 6%. Closing costs are $3,000. Sale Price = ($280,000 + $3,000) ÷ (1 − 0.06) = $283,000 ÷ 0.94 = $301,063.83.

Example B: A home sells for $400,000. Commission is 5%, closing costs are $4,500. Net to seller = $400,000 − ($400,000 × 0.05) − $4,500 = $400,000 − $20,000 − $4,500 = $375,500.

Common trap: when the problem gives you the desired net and asks for the sale price, do NOT just add the commission percentage. You must divide by (1 − rate) because the commission is based on the unknown sale price.

Formula: Cap Rate = NOI ÷ Property Value. Also: Value = NOI ÷ Cap Rate. Also: NOI = Value × Cap Rate.

Example A: A commercial property produces $72,000 in NOI and is valued at $900,000. Cap rate = $72,000 ÷ $900,000 = 0.08 = 8%.

Example B: An investor wants an 8% return. The property produces $56,000 in NOI. What should the investor pay? Value = $56,000 ÷ 0.08 = $700,000.

Common trap: confusing cap rate with interest rate. Cap rate is a measure of return based on net operating income, not a financing term. Also, remember NOI excludes mortgage payments — it is income after operating expenses but before debt service.

Formula: LTV = Loan Amount ÷ Appraised Value (or Purchase Price, whichever is lower)

Example A: A buyer purchases a $250,000 home with a $200,000 loan. LTV = $200,000 ÷ $250,000 = 0.80 = 80%.

Example B: A home appraises at $300,000 but the purchase price is $310,000. The buyer gets a $240,000 loan. LTV = $240,000 ÷ $300,000 (lower value) = 80%. PMI is typically required when LTV exceeds 80%.

Common trap: using the purchase price when the appraised value is lower. Lenders use the LOWER of the two.

Formula: Annual Amount ÷ 365 = Daily Rate. Daily Rate × Number of Days = Prorated Amount.

Example A: Annual property taxes are $5,475. Closing is April 10. Seller owns through the day of closing. January (31) + February (28) + March (31) + April 1–10 (10) = 100 days. Daily rate = $5,475 ÷ 365 = $15.00/day. Seller owes 100 × $15.00 = $1,500.00.

Example B: Annual HOA dues are $2,400. Seller prepaid for the full year. Closing is September 1. Buyer owes seller for September 1 through December 31 = 122 days. Daily rate = $2,400 ÷ 365 = $6.575/day. Buyer owes seller 122 × $6.575 = $802.19.

Common trap: getting the day count wrong. Carefully count the days in each month. Also, read whether the seller is responsible for the day of closing or not — it changes the count by one day.

Rectangle: Area = Length × Width. Triangle: Area = ½ × Base × Height. One acre = 43,560 square feet.

Example A: A rectangular lot is 200 feet × 300 feet. Area = 200 × 300 = 60,000 sq ft. In acres: 60,000 ÷ 43,560 = 1.38 acres.

Example B: An L-shaped lot can be divided into two rectangles: 100×200 and 50×150. Area = (100 × 200) + (50 × 150) = 20,000 + 7,500 = 27,500 sq ft.

Common trap: irregular shapes. Break them into rectangles and triangles, calculate each area, then add them together.

Formula: Assessed Value × Mill Rate ÷ 1,000 = Annual Tax. Or: Assessed Value × Tax Rate = Annual Tax.

Example A: A property has an assessed value of $180,000 and a mill rate of 25 mills. Tax = $180,000 × 25 ÷ 1,000 = $4,500/year.

Example B: A property is worth $300,000 but the assessment ratio is 60%. Assessed value = $300,000 × 0.60 = $180,000. Tax rate is 2.5%. Tax = $180,000 × 0.025 = $4,500/year.

Common trap: not applying the assessment ratio first. Many jurisdictions only tax a percentage of the market value, not the full value.

Formula: GRM = Sale Price ÷ Gross Annual Rent. Also: Value = GRM × Gross Annual Rent.

Example A: A property sold for $240,000 and generates $24,000/year in gross rent. GRM = $240,000 ÷ $24,000 = 10.

Example B: Similar properties have a GRM of 12. A rental property generates $30,000/year in gross rent. Estimated value = 12 × $30,000 = $360,000.

Common trap: using net income instead of gross rent. GRM uses GROSS rent — before expenses. If the problem gives you monthly rent, multiply by 12 first.

Appreciation: New Value = Original Value × (1 + Annual Rate). Depreciation: New Value = Original Value × (1 − Annual Rate).

Example A: A property worth $200,000 appreciates at 3% per year for one year. New value = $200,000 × 1.03 = $206,000.

Example B: A property worth $200,000 depreciates at 2% per year for one year. New value = $200,000 × 0.98 = $196,000. Straight-line depreciation for investment property: Cost ÷ Useful Life = Annual Depreciation. Residential rental: $200,000 ÷ 27.5 years = $7,272.73/year.

Common trap: multi-year appreciation. For 3% over 2 years, it is NOT $200,000 × 1.06. It is $200,000 × 1.03 × 1.03 = $212,180 (compound, not simple).

Formula: Market Value − Mortgage Balance = Equity.

Example A: A home is worth $350,000 and the remaining mortgage balance is $220,000. Equity = $350,000 − $220,000 = $130,000.

Example B: A buyer purchased for $300,000 with a $240,000 mortgage. After 5 years, the home is worth $340,000 and the mortgage balance is $215,000. Equity = $340,000 − $215,000 = $125,000. The equity grew from appreciation ($40,000) and principal paydown ($25,000).

Common trap: using the original purchase price instead of the current market value. Equity is based on what the property is worth NOW.