Module 8 of 13 / National concepts

Real estate math

Build a repeatable calculation method for area, financing, income, commissions and closing statements.

Outline allocation: 7 of 80 scored questions. Reviewed October 15, 2026.

What you will learn

Choose the correct base and time unit.
Calculate prorations with stated assumptions.
Check whether an answer is economically plausible.

Start with units and the requested result

Write the unknown, the formula and units before entering numbers. Rectangle area is length × width; triangle area is one-half base × height. One acre is 43,560 square feet and one mile is 5,280 feet. Multiply before dividing when the formula calls for it, and keep intermediate precision until the final rounding. A price per square foot is not a total price; a monthly amount is not annual income. Source note: California DRE chapters support general concepts only; use the Pennsylvania modules and linked Pennsylvania authorities for state-specific rules.

Work through an example

A 150-by-290.4-foot rectangle is 43,560 square feet, or one acre.

Remember: Label feet, square feet, acres, months and years.

Percentages, loans and compensation

Part = whole × rate; whole = part ÷ rate. Commission calculations use the agreed price basis and negotiated rate. Apply a salesperson’s split to the brokerage’s allocated commission, not automatically to the whole sale price. LTV = loan ÷ value basis. One discount point is 1% of the loan amount. Simple interest = principal × annual rate × fraction of a year. PITI adds principal, interest, property taxes and insurance; do not add principal twice.

Work through an example

A $250,000 loan with two discount points has $5,000 in points, regardless of a higher sale price.

Remember: Identify the base before applying a percentage.

Income and investment calculations

Potential income less vacancy and collection loss, plus other income, gives effective gross income. Subtract operating expenses to obtain NOI before debt service and income taxes. Value = NOI ÷ cap rate; cap rate = NOI ÷ value. Equity is value less secured debt in a simplified problem. A cash-on-cash return uses stated annual cash flow divided by cash invested. Appreciation compounds when the problem specifies multiple periods; it is not always simple addition.

Work through an example

NOI of $48,000 divided by 0.08 indicates $600,000; subtracting mortgage payments before capitalizing would answer a different question.

Remember: Gross rent, NOI and cash flow are three different figures.

Prorations and closing statements

For every proration, identify whether the item is prepaid or accrued, who receives the closing day and whether the problem uses a 360- or 365-day year. An accrued seller obligation commonly creates a seller debit and buyer credit; a buyer reimbursing prepaid seller expenses commonly creates the reverse. Net to seller starts with price, then subtracts seller costs and payoffs and applies credits. Cash to close accounts for down payment, costs, deposits and credits without double-counting the loan.

Work through an example

On a 360-day basis, a $3,600 annual charge costs $10 per day; a stated 45-day seller allocation is $450.

Remember: Follow the question’s day-count instructions; do not import a local custom.

Check your understanding

Close your notes and explain the rule in your own words. Change one fact in an example: does the answer change? Use topic practice in the study room, then return to any rule you missed.

Practice in the study room →Next unit →

Sources and further reading

California DRE references support general national concepts only. Their California-specific rules are not Pennsylvania law; use the PA sources for state requirements.

Supplemental study only. State rules and transaction details matter; consult the linked official sources for the complete requirements. This lesson provides no prelicensing credit.