Math questions make up roughly 10-15% of the exam. They test commission splits, proration, mortgage calculations, property tax math, and capitalization rates.
Commission = sale price x commission rate. If the commission is split between listing and selling brokers, calculate the total commission first, then divide. If a salesperson receives a split from their broker, apply that percentage to the broker's share.
Proration divides expenses (taxes, insurance, HOA fees) between buyer and seller at closing based on the number of days each party owns the property. The seller is responsible through the day of closing. Use a 360-day year (30 days per month) unless told otherwise.
Cap rate = Net Operating Income / Property Value. This formula can be rearranged: Value = NOI / Cap Rate, or NOI = Value x Cap Rate. The cap rate helps investors compare the return on different investment properties.
NY charges a real estate transfer tax on all conveyances. The rate is $2 per $500 of consideration (or $4 per $1,000). NYC has an additional transfer tax. The mortgage recording tax varies by county. These calculations appear frequently on the exam.
1. A property sells for $750,000. The total commission is 5%. The listing broker and buyer's broker split the commission 50/50. The listing salesperson earns 40% of their broker's share. How much does the listing salesperson earn?
Total commission = $750,000 × 5% = $37,500. Listing broker's share (50%) = $18,750. Listing salesperson's share (40% of broker's share) = $18,750 × 40% = $7,500. Always apply splits sequentially — sale price → total commission → broker share → salesperson share.
2. Closing occurs on March 31. The annual property tax is $6,570 and has not yet been paid (taxes are paid in arrears). Using the 365-day method, what is the seller's share of the tax proration?
Daily tax rate = $6,570 ÷ 365 = $18/day. Seller owned Jan 1 through Mar 30 (buyer owns closing day) = 89 days. Seller's share = 89 × $18 = $1,602. Note: Jan = 31, Feb = 28, Mar = 30 (through Mar 30) = 89 days. Seller's proration = $18 × 89 = $1,602 ≈ $1,611 (closest answer using exact daily rate of $18.0). Taxes paid in arrears means the seller owes the buyer for the period they occupied. The buyer receives a credit at closing.
3. A buyer obtains a $280,000 mortgage at 7.5% annual interest. What is the interest portion of the FIRST monthly payment?
Monthly interest = Principal × Annual Rate ÷ 12 = $280,000 × 0.075 ÷ 12 = $280,000 × 0.00625 = $1,750. The first payment is almost entirely interest because the principal has not yet been reduced.
Acre
A unit of land measurement equal to 43,560 square feet.
Ad Valorem Tax
A property tax calculated as a percentage of the property's assessed value, literally 'according to value.'
Assessed Value
The value assigned to a property by a local tax assessor for the purpose of calculating property taxes.
Equalization Rate
The ratio of a municipality's total assessed value to its total market value, used to ensure equitable taxation across jurisdictions.
Mill Rate
A property tax rate expressed as the tax per $1,000 of assessed property value, one mill equals one-tenth of one cent.
Proration
The division of ongoing property expenses between buyer and seller based on the closing date.
Transfer Tax
A tax imposed on the transfer of real property ownership, paid at the time the deed is recorded.
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