Freehold

Formula reference

Real Estate Math Formulas

Every formula the exam tests, with variables explained and a fully worked example for each - commissions, prorations, LTV, points, cap rate, GRM, depreciation, and seller's net.

Commissions

Full page for each: Commission · Commission Split

Commission

commission = sale price × commission rate
  • sale price — The final agreed sale price of the property
  • commission rate — The agreed commission percentage, as a decimal

Worked example: A home sells for $420,000 at a 5.5% commission rate.

  1. $420,000 × 0.055 = $23,100

$23,100 total commission

Commission Split

agent share = sale price × total rate × listing/selling split × agent's split with their broker
  • total rate — The full commission rate on the sale
  • listing/selling split — Share the agent's side of the transaction receives, e.g. 50%
  • agent's split — The agent's percentage of their brokerage's share

Worked example: Sale price $380,000, 6% total commission, split 50/50 between brokerages, agent keeps 70% of their side.

  1. $380,000 × 0.06 = $22,800 total
  2. $22,800 × 0.50 = $11,400 to the agent's brokerage
  3. $11,400 × 0.70 = $7,980 to the agent

$7,980 to the agent

Prorations

Full page for each: Annual Expense Proration

Annual Expense Proration

seller's share = (annual amount ÷ 12) × months owned
  • annual amount — The full-year cost being prorated, e.g. property tax
  • months owned — Number of months the seller owned the property that year

Worked example: Annual property tax is $3,600. Seller owned the home for 5 months before closing.

  1. $3,600 ÷ 12 = $300 per month
  2. $300 × 5 = $1,500

$1,500 seller's share, credited to the buyer

Loans & LTV

Full page for each: Loan-to-Value Ratio · Down Payment from LTV

Loan-to-Value Ratio

LTV = loan amount ÷ appraised value (or price, whichever is lower)
  • loan amount — The amount being borrowed
  • appraised value — The lender's basis for the ratio

Worked example: A buyer borrows $255,000 on a home appraised at $300,000.

  1. $255,000 ÷ $300,000 = 0.85

85% LTV

Down Payment from LTV

down payment = price × (1 − LTV)
  • price — Purchase price
  • LTV — Loan-to-value ratio as a decimal

Worked example: Price is $340,000 with a 90% LTV loan.

  1. 1 − 0.90 = 0.10
  2. $340,000 × 0.10 = $34,000

$34,000 down payment

Points & Interest

Full page for each: Discount Points · Monthly Interest (Interest-Only)

Discount Points

cost of points = loan amount × (points ÷ 100)
  • loan amount — The amount being borrowed, not the purchase price
  • points — Number of discount points, each equal to 1% of the loan

Worked example: A $280,000 loan with 2 discount points.

  1. 2 ÷ 100 = 0.02
  2. $280,000 × 0.02 = $5,600

$5,600 to buy down the rate

Monthly Interest (Interest-Only)

monthly interest = (principal × annual rate) ÷ 12
  • principal — Outstanding loan balance
  • annual rate — The stated annual interest rate, as a decimal

Worked example: $200,000 principal at 6% annual interest.

  1. $200,000 × 0.06 = $12,000 annual interest
  2. $12,000 ÷ 12 = $1,000

$1,000 monthly interest

Area & Acreage

Full page for each: Rectangular Area · Square Feet to Acres

Rectangular Area

area = width × depth
  • width — Lot or room width
  • depth — Lot or room depth

Worked example: A lot is 90 feet wide and 150 feet deep.

  1. 90 × 150 = 13,500 sq ft

13,500 square feet

Square Feet to Acres

acres = square feet ÷ 43,560
  • square feet — Total lot area in square feet

Worked example: A parcel measures 87,120 square feet.

  1. 87,120 ÷ 43,560 = 2

2 acres

Transfer Tax

Full page for each: Transfer Tax

Transfer Tax

transfer tax = sale price × tax rate (often per $1,000 or $500 of price)
  • sale price — The property's sale price
  • tax rate — The jurisdiction's transfer tax rate

Worked example: Sale price $500,000, transfer tax of $2 per $1,000.

  1. $500,000 ÷ $1,000 = 500 units
  2. 500 × $2 = $1,000

$1,000 transfer tax

Cap Rate & GRM

Full page for each: Capitalization Rate · Gross Rent Multiplier

Capitalization Rate

cap rate = net operating income ÷ property value
  • net operating income — Annual income after operating expenses, before debt service
  • property value — Current market value or purchase price

Worked example: A property has $48,000 NOI and is valued at $600,000.

  1. $48,000 ÷ $600,000 = 0.08

8% cap rate

Gross Rent Multiplier

GRM = property price ÷ annual gross rent
  • property price — Purchase price or value
  • annual gross rent — Total rent collected in one year before expenses

Worked example: Price is $360,000, annual gross rent is $30,000.

  1. $360,000 ÷ $30,000 = 12

GRM of 12

Depreciation

Full page for each: Straight-Line Depreciation

Straight-Line Depreciation

annual depreciation = depreciable basis ÷ useful life (years)
  • depreciable basis — Improvement value, excluding land
  • useful life — 27.5 years residential, 39 years commercial under IRS rules

Worked example: A rental building's depreciable basis is $275,000 (residential).

  1. $275,000 ÷ 27.5 = $10,000

$10,000 annual depreciation

Seller's Net

Full page for each: Seller's Net Proceeds

Seller's Net Proceeds

net to seller = sale price − commission − closing costs − loan payoff
  • sale price — The final sale price
  • commission — Total commission paid by the seller
  • closing costs — Seller-paid closing costs
  • loan payoff — Remaining mortgage balance paid off at closing

Worked example: Sale price $450,000, commission $27,000, closing costs $4,000, loan payoff $210,000.

  1. $450,000 − $27,000 = $423,000
  2. $423,000 − $4,000 = $419,000
  3. $419,000 − $210,000 = $209,000

$209,000 net to the seller

Worked answers to common math questions

How do you calculate commission for the real estate exam?

commission = sale price × commission rate. Example: A home sells for $420,000 at a 5.5% commission rate. $420,000 × 0.055 = $23,100 = $23,100 total commission.

How do you calculate commission split for the real estate exam?

agent share = sale price × total rate × listing/selling split × agent's split with their broker. Example: Sale price $380,000, 6% total commission, split 50/50 between brokerages, agent keeps 70% of their side. $380,000 × 0.06 = $22,800 total $22,800 × 0.50 = $11,400 to the agent's brokerage $11,400 × 0.70 = $7,980 to the agent = $7,980 to the agent.

How do you calculate annual expense proration for the real estate exam?

seller's share = (annual amount ÷ 12) × months owned. Example: Annual property tax is $3,600. Seller owned the home for 5 months before closing. $3,600 ÷ 12 = $300 per month $300 × 5 = $1,500 = $1,500 seller's share, credited to the buyer.

How do you calculate loan-to-value ratio for the real estate exam?

LTV = loan amount ÷ appraised value (or price, whichever is lower). Example: A buyer borrows $255,000 on a home appraised at $300,000. $255,000 ÷ $300,000 = 0.85 = 85% LTV.

The Math Trainer drills all of this

Every question sourced and explained. Guided Study Path, on-device coach, real exam settings for your state. No ads, no subscriptions, ever.

Get Freehold free
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.