Real Estate Calculations
The broker exam includes math you must compute quickly and accurately, with extra emphasis on investment and closing-statement problems. This topic covers the core percentage formula, commissions, area and volume, and financial, investment, and proration calculations.
The Basic Percentage Formula
Most real estate math is a version of Part = Total x Rate. To find the part, multiply; to find the total or the rate, divide. A useful memory tool is the T-bar, with the part on top and the total and rate on the bottom. Commission problems apply this directly: Commission = Sale Price x Rate. For a net-to-seller problem, the commission is charged on the sale price, so Sale Price = Desired Net / (1 - commission rate); you cannot simply add the rate back to the net. Brokers must also split gross commission among the firm and its agents per the office plan.
Area, Volume, and Investment Measures
Area of a rectangle = length x width; area of a triangle = 1/2 x base x height; volume = length x width x height. Key conversions: 1 acre = 43,560 square feet, 1 mile = 5,280 feet, and 640 acres in a section (one square mile). For income property, Net Operating Income = effective gross income minus operating expenses, Value = NOI / capitalization rate, and the capitalization rate = NOI / value, so any two of those three values solve for the third. The gross rent multiplier = price / gross rent is a quicker screening tool that ignores expenses.
Finance and Proration Calculations
Interest for a period = Principal x Annual Rate x Time; for simple monthly interest, divide the annual interest by 12. Loan-to-value ratio = Loan Amount / Value, and the down payment is value minus loan. Property tax = Assessed Value x Tax Rate. Prorations at closing divide shared items (taxes, interest, rent) between buyer and seller by the number of days each owns the property, with the split depending on who is charged for the day of closing. On a settlement statement a prepaid item is credited to the seller, while an item the seller owes but has not paid is credited to the buyer.