Real Estate Math

Math questions are guaranteed on the exam. The good news: a handful of formulas cover almost all of them. Practice until they're automatic.

Must-know formulas

• Commission = Sale Price × Commission Rate.
• Area of a rectangle = Length × Width (then ÷ 43,560 for acres).
• Percentage: Part = Whole × Rate (the 'T-bar' relationship).
• Loan-to-value (LTV) = Loan Amount ÷ Value.
• Simple interest = Principal × Rate × Time.

Worked example — commission

A home sells for $420,000 with a 6% total commission, split 50/50 between two brokerages. Total commission = $420,000 × 0.06 = $25,200. Each brokerage receives $12,600 before any agent split.

Worked example — proration

Annual taxes are $3,650. Daily rate = $3,650 ÷ 365 = $10/day. If the seller owned the property for 120 days of the year before closing, the seller owes 120 × $10 = $1,200, shown as a debit to the seller and credit to the buyer (if taxes are paid in arrears).

Worked example — LTV and down payment

Price $380,000, loan $304,000. LTV = 304,000 ÷ 380,000 = 0.80 (80%). Down payment = $380,000 − $304,000 = $76,000, or 20%. If the appraisal is $370,000 and the lender uses the lesser of price or value, LTV = 304,000 ÷ 370,000 ≈ 82.2%.

Worked example — cap rate and GRM (broker depth)

NOI $42,000, cap rate 7%. Value = 42,000 ÷ 0.07 = $600,000. If monthly rent is $4,000 and GRM is 150, indicated value ≈ 4,000 × 150 = $600,000. Broker items often ask you to solve for NOI (value × cap) or to reject a GRM that mixed monthly rent with an annual multiplier.

Worked example — net to seller

Seller wants $282,000 net and will pay a 6% commission (no other costs in the stem). Sale price = 282,000 ÷ (1 − 0.06) = 282,000 ÷ 0.94 = $300,000. Check: $300,000 × 0.06 = $18,000; $300,000 − $18,000 = $282,000.

Worked example — transfer / recordation tax

Many stems tax each $100 (or fraction) of price. On a $250,100 sale at $0.50 per $100: taxable units = 2,501 (round up the extra $100); tax = 2,501 × $0.50 = $1,250.50. Read whether buyer, seller, or both pay, and whether the rate is per $100 or per $1,000.