Study guide

Real Estate Math — Key Formulas

Math is the most-feared part of the exam, but it's also the most predictable: commissions, loan-to-value ratios, prorations, cap rates, and seller net sheets follow the same handful of formulas every time. About one question in ten is a calculation, and every one is points you can lock in with practice. Work through the formula reference, then drill until setting up the equation feels routine — the numbers change, the setups don't.

Core Formulas

Commission = price × rate.
Loan-to-value (LTV) = loan amount ÷ value (or price, whichever is lower).
Proration (arrears) = (annual amount ÷ 12) × months owned.
Discount points cost = loan amount × (points ÷ 100) — points are % of the LOAN, not the price.

Income Property Formulas

Cap rate = NOI ÷ value. Value = NOI ÷ cap rate.
GRM = price ÷ annual gross rent. Value = GRM × annual gross rent.
Straight-line depreciation = depreciable basis ÷ useful life (27.5 yrs residential, 39 yrs commercial). Land is NEVER depreciable.

Seller Net Sheet

Net to seller = sale price − commission − closing costs − loan payoff (and any concessions/credits).

Key vocabulary: Real Estate Math glossary (8 terms)

Practice Real Estate Math

Every Freehold question shows why the right answer is right — and cites its source.

A home sells for $350,000 with a 6% commission rate. What is the total commission?

$18,000
$19,500
$20,000
$21,000

Show answer & explanation

$21,000 — Multiply the sale price by the commission rate: $350,000 × 0.06 = $21,000. Commission is calculated on the full sale price unless the agreement states otherwise.

Source: PSI National Real Estate Exam Content Outline §11 Real Estate Calculations

A property sells for $400,000 with a 5% commission split equally between two brokerages. The selling agent receives 60% of their brokerage's share. How much does the selling agent earn?

$6,000
$8,000
$10,000
$12,000

Show answer & explanation

$6,000 — Total commission is $400,000 × 0.05 = $20,000. Each brokerage receives $10,000, and the agent's 60% share of $10,000 equals $6,000.

Source: PSI National Real Estate Exam Content Outline §11 Real Estate Calculations

A buyer purchases a home for $250,000 with an 80% loan-to-value mortgage. What is the loan amount?

$187,500
$200,000
$212,500
$225,000

Show answer & explanation

$200,000 — Multiply the price by the loan-to-value ratio: $250,000 × 0.80 = $200,000. The remaining $50,000 is the buyer's down payment.

Source: PSI National Real Estate Exam Content Outline §11 Real Estate Calculations

A $150,000 interest-only loan carries a 6% annual interest rate. What is the monthly interest payment?

$625
$700
$750
$900

Show answer & explanation

$750 — Annual interest is $150,000 × 0.06 = $9,000. Dividing by 12 months gives a monthly interest payment of $750.

Source: PSI National Real Estate Exam Content Outline §11 Real Estate Calculations

A rectangular lot measures 110 feet wide by 200 feet deep. What is its area in square feet?

20,000 sq ft
21,000 sq ft
21,500 sq ft
22,000 sq ft

Show answer & explanation

22,000 sq ft — Area of a rectangle equals width times depth: 110 ft × 200 ft = 22,000 square feet. To convert to acres, divide by 43,560 square feet per acre.

Source: PSI National Real Estate Exam Content Outline §11 Real Estate Calculations

Freehold is an independent study resource and is not affiliated with, endorsed by, or sponsored by PSI, Pearson VUE, or any state real estate licensing board or commission. Freehold does not guarantee passage of any licensing exam.