Real estate math
Commission splits, seller net, prorations, PITI, LTV, points, cap rates and the NJ transfer fee.
Real estate math in one paragraph
Key formulas and the trap in each
| Formula | Common trap | |
|---|---|---|
| Agent's commission | Price x rate x brokerage side x agent split | Applying the agent's split to the full commission |
| Price to net a set amount | (Net + costs) / (1 - commission rate) | Multiplying by 1 + the rate instead of dividing |
| Proration | Annual amount / 365 (or 360) x days | Crediting the wrong party, or counting the wrong days |
| LTV and points | Loan / lower of price or appraisal; points = % x loan | Using the higher value, or taking points on the price |
| Value from income | Value = NOI / cap rate | Using gross income instead of net operating income |
Real estate math: 4 rules to memorize
Split in order.
Total commission, then the side, then the agent.
Prorate per day.
Annual ÷ 365 (or 360) × days.
1 acre = 43,560 sq ft.
Convert before pricing.
IRV.
Income = Rate × Value.
Real estate math, explained
Every one is a short formula. The trap is almost always the order of steps or the base number, like taking points on the price instead of the loan. You cannot bring your own handheld calculator, so practice working the formulas cleanly on scratch paper.
Watch for the reverse problem. When a seller wants to net a set amount after commission, add the net and the costs, then divide by 1 minus the commission rate. Multiplying by 1 plus the rate looks close but is always wrong, because the commission is charged on the sale price, not the net.
For prorations, first decide who paid and who used. If the seller prepaid the year's taxes, the buyer owes the seller for the days the buyer will own the home: a credit to the seller, a debit to the buyer. If taxes are paid in arrears, the seller owes the buyer for the days the seller owned it.
The New Jersey Realty Transfer Fee is figured per $500 of consideration in brackets, and the seller pays it. There are two rate schedules: one when the total price is $350,000 or less, and a higher one above $350,000. A sale over $1 million also triggers a separate graduated fee of 1% to 3.5% for deeds recorded on or after July 10, 2025.
Open the math hub and calculatorsHow the exam tries to trip you up
- "The seller wants to net $280,000" questions invite you to add 5% to the net. Divide by 0.95 instead, after adding the seller's costs.
- Points and origination fees are percentages of the loan, not the price. Find the loan first, then add the percentages together and apply them once.
- A proration question tells you taxes were paid in advance. The seller gets a credit for the days after closing, so count the buyer's days, not the seller's.
- On the NJ transfer fee, the price decides which schedule applies. Above $350,000, every bracket uses the higher rates, not just the part over $350,000.
Real estate math practice questions
A $410,000 home sells at 5%. The listing brokerage keeps 60% and pays its salesperson 70% of that. What does the salesperson earn?
Real estate math flashcards
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All 7 terms at a glanceShowHide
- Cap rate
- Net operating income ÷ value.
- PITI
- Principal, interest, taxes and insurance: the full monthly payment.
- Acre
- 43,560 square feet.
- Equity
- Market value minus all loan balances owed on the property.
- Loan-to-value ratio
- Loan amount divided by the lower of the purchase price or appraised value.
- Required sale price
- (Desired net + seller costs) divided by (1 - commission rate).
- Origination fee
- Lender's fee for making the loan, stated as a percent of the loan amount, like points.
Real estate math: common questions
Sources and further reading
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