Sale price $400,000 × 6% commission = $24,000 total. Split 50/50 between listing and selling broker = $12,000 each. Each broker splits with their agent (e.g., 60/40): listing agent gets $7,200. Always work from the total commission down through each split.
T-Bar method: Part ÷ Whole = Rate. Part = Whole × Rate. Whole = Part ÷ Rate
T-Bar Formula
One formula that solves commission, tax, and percentage problems
Draw a T. Top = Part. Bottom left = Whole. Bottom right = Rate. Cover what you want to find. Top covered: Part = Whole × Rate. Bottom left covered: Whole = Part ÷ Rate. Bottom right covered: Rate = Part ÷ Whole. Works for commissions, tax rates, down payments, profit calculations.
Proration: divide annual cost by 365 (or 360 in banking) to get daily rate × days
Proration Calculations
How to split ongoing costs between buyer and seller at closing
Proration splits recurring costs (taxes, HOA dues, insurance, rent) proportionally between buyer and seller based on closing date. Step 1: annual amount ÷ 365 = daily rate. Step 2: daily rate × number of days = prorated amount. Closing day typically belongs to buyer. 30-day month method: annual ÷ 360.
LTV = Loan amount ÷ Appraised value × 100. 80% LTV = 20% down payment.
Loan-to-Value Ratio
LTV determines if PMI is required and affects interest rate
LTV = Loan amount ÷ Property value. $320,000 loan on $400,000 property = 80% LTV = 20% down. LTV above 80%: usually requires Private Mortgage Insurance (PMI). FHA loans: allow up to 96.5% LTV. VA loans: up to 100% LTV for qualifying veterans.
Area of rectangle = length × width. Triangle = ½ × base × height. Irregular: break into shapes.
Area Calculations
How to calculate square footage for exam problems
Rectangle/square: L × W. Triangle: ½ × base × height. Trapezoid: ½ × (base₁ + base₂) × height. Irregular lot: divide into rectangles and triangles, calculate each, add together. Convert to acres: square feet ÷ 43,560 = acres. 1 acre = 43,560 sq ft. 1 mile = 5,280 ft.
1 discount point = 1% of the loan amount. On a $300,000 loan, 1 point = $3,000. Points are prepaid interest paid at closing to get a lower interest rate. Break-even: monthly savings ÷ cost of points = months to break even. If you sell before break-even, points weren't worth it.
Depreciation (cost approach): (Cost - Land value) ÷ Economic life = Annual depreciation
Straight-Line Depreciation
How to calculate depreciation in the cost approach
Land never depreciates — only improvements. Building cost $200,000, economic life 40 years: annual depreciation = $5,000/year. After 10 years: $50,000 accumulated depreciation. Building value = $200,000 - $50,000 = $150,000. Add land value for total property value in cost approach.
Transfer tax/Documentary stamp tax: charged per $500 or $1,000 of sale price — varies by state
Transfer Tax
The tax charged when property changes hands
Varies by state. Common: $1.00 per $1,000 or $0.55 per $500 of sale price. $350,000 sale at $1/$1,000 = $350. Some states: buyer pays, some: seller pays, some: split. Know your state's rate. Round up to the next $500 or $1,000 increment (use the next higher bracket, not round down).
PITI: Principal, Interest, Taxes, Insurance — the four components of a monthly mortgage payment
PITI
The complete monthly mortgage payment broken into its four parts
Principal: reduces the loan balance. Interest: cost of borrowing. Taxes: property taxes collected monthly, held in escrow. Insurance: homeowner's insurance (and PMI if applicable) collected monthly, held in escrow. Lenders require PITI to calculate qualifying ratios.
One triangle solves almost every real estate math problem
PART on top. WHOLE bottom-left. RATE bottom-right. Cover what you want: PART = Whole × Rate. WHOLE = Part ÷ Rate. RATE = Part ÷ Whole. Works for commission, tax, interest, and more.
The income approach formula every investor and exam uses
Cap Rate = NOI ÷ Value. Value = NOI ÷ Cap Rate. Example: NOI $30,000, cap rate 6% → Value = $500,000. Lower cap rate = higher value (safer investment).
Proration splits ongoing costs between buyer and seller
Daily rate = Annual cost ÷ 365. Seller pays Jan 1 to closing. Buyer pays from closing onward. Taxes paid in arrears → seller owes buyer. Paid in advance → buyer owes seller.
PAID through the day of closing by the SELLER — buyer owns day of closing forward
How prepaid and accrued expenses are divided between buyer and seller at closing
Prorations split recurring costs fairly — the seller pays for their portion, buyer pays for theirs
Items prorated at closing: property taxes, HOA dues, rent (on investment property), interest (on assumed loans), utilities. Steps: (1) Find annual amount. (2) Divide by 360 (banker's year) or 365 to get daily rate. (3) Count days seller owned in that period. (4) Multiply daily rate × seller's days. Taxes in arrears (paid after): seller owes buyer (debit seller, credit buyer). Taxes in advance (prepaid): buyer owes seller (credit seller, debit buyer). Exam tip: most states use 360-day banker's year and 30-day months.
In arrears
Seller owes buyer — debit seller, credit buyer
In advance
Buyer owes seller — credit seller, debit buyer
Banker's year
360 days, 30-day months — used on most state exams
Transfer tax = Sales price ÷ $500 × tax rate per $500 (or per $1,000)
Documentary transfer tax — varies by state and county
Transfer taxes are calculated per unit of value — know the formula and your state's rate
Formula: (Sales price ÷ unit amount) × tax rate per unit. Common rates: $1.10 per $1,000 (California state), plus county additions. Example: $350,000 sale at $1.10 per $1,000: ($350,000 ÷ $1,000) × $1.10 = 350 × $1.10 = $385. Some states base it on $500 units: $350,000 ÷ $500 = 700 units × rate. Some states exempt the loan balance (only tax equity). Typically paid by seller. Exam always states the rate — just apply the formula correctly.
Step 1
Divide sale price by $500 or $1,000 (round up)
Step 2
Multiply by the tax rate given in the problem
Equity only
Some states tax only equity — subtract existing loan first
Quick valuation method for income properties using rent as the input
GRM gives a fast estimate — unlike cap rate, it ignores expenses
GRM (Gross Rent Multiplier) = Sale Price ÷ Gross Annual Rent. Example: Property sells for $480,000, annual rent $48,000 → GRM = 10. To estimate value: GRM × Gross Annual Rent. Example: GRM of 9 in the market, property rents for $3,000/month ($36,000/year) → estimated value = 9 × $36,000 = $324,000. Monthly GRM: divide by monthly rent instead. GRM is simpler than cap rate but ignores expenses — useful only for quick comparisons of similar properties in the same market.
GRM formula
Sale Price ÷ Gross Annual Rent = multiplier
Estimate value
Market GRM × subject property's annual rent
Limitation
Ignores vacancies and operating expenses — use with cap rate
Residential: 27.5 years. Commercial: 39 years. Land is never depreciated.
IRS straight-line depreciation rules for investment real property
Depreciation is a paper loss that reduces taxable income — one of real estate investing's key tax benefits
Only the building (improvement) depreciates — not the land. Annual depreciation = Building Value ÷ Recovery Period. Residential rental: 27.5 years. Commercial: 39 years. Example: $275,000 building value ÷ 27.5 = $10,000 annual depreciation deduction. This reduces taxable income without a cash outlay. Depreciation recapture: when you sell, IRS taxes the accumulated depreciation at 25%. Cost segregation: accelerates depreciation by classifying components as personal property (5-7 year life) — used by investors to front-load deductions.
Part ÷ Whole = Rate. Part = Whole × Rate. Whole = Part ÷ Rate.
The T-bar formula applied to appreciation, depreciation, and value change problems
Every real estate math problem with a percent uses the same three-part formula
T-Bar: Part / Whole × Rate — cover the unknown. Part = Whole × Rate. Whole = Part ÷ Rate. Rate = Part ÷ Whole. Appreciation: property bought for $200,000, appreciated 15% → $200,000 × 0.15 = $30,000 gain → current value $230,000. Depreciation problem: property is worth $180,000 after losing 10% → $180,000 is 90% of original → $180,000 ÷ 0.90 = $200,000 original value. Key: when property has ALREADY changed in value and you need the original — divide the current value by (1 ± rate).
Part
The dollar amount of change or portion
Whole
The original or total value — what you divide into
Already changed?
Divide current value by (1 ± rate) to find original
The rectangular survey system — how to calculate acreage from legal descriptions
Read section descriptions right to left — each fraction cuts the previous parcel in half
Township: 6 miles × 6 miles = 36 square miles = 36 sections. Section: 1 mile × 1 mile = 640 acres. Subdivisions: ½ section = 320 acres. ¼ section = 160 acres. ½ of ¼ = 80 acres. ¼ of ¼ = 40 acres. Reading: "NW ¼ of the SW ¼ of Section 5" — start from the right: start with 640 acres, take the SW ¼ = 160 acres, then the NW ¼ of that = 40 acres. Price per acre: total price ÷ number of acres. Example: $48,000 for the NE ¼ of the SE ¼ of a section (40 acres) → $48,000 ÷ 40 = $1,200 per acre.
Break-even months = Point cost ÷ Monthly savings. Stay longer = points worth it.
How to calculate whether paying points makes financial sense
If you plan to sell or refinance before break-even, don't pay points
Step 1: Calculate cost of points. 1 point = 1% of loan amount. Example: 2 points on $250,000 loan = $5,000. Step 2: Calculate monthly savings from reduced rate. 0.5% rate reduction on $250,000 ≈ $80/month savings (use factor tables on exam). Step 3: Break-even = $5,000 ÷ $80 = 62.5 months ≈ 63 months (5.25 years). Decision: if staying more than 63 months → pay points. If selling sooner → don't pay. Exam tip: the problem will give you all numbers — just divide cost by savings to get months.
Remaining balance = you've paid X months — use amortization schedule logic
How to calculate the outstanding loan balance at any point in the loan term
On the exam: remaining balance = original loan minus total principal paid (not total payments)
Simple approach for exam: Interest for period = Remaining balance × monthly rate. Principal paid = Payment − Interest. Repeat for each payment. Example: $100,000 loan at 6% (0.5%/month), payment $600. Month 1: Interest = $100,000 × 0.005 = $500. Principal = $600 - $500 = $100. New balance = $99,900. Month 2: Interest = $99,900 × 0.005 = $499.50. Principal = $100.50. New balance = $99,799.50. Exam shortcut: if given a factor table and asked for balance after N payments — look up remaining term factor and multiply by original loan amount.
Q: How do you calculate commission and net proceeds to the seller?
A: Commission = Sale Price × Commission Rate. Example: $400,000 sale at 5% → $400,000 × 0.05 = $20,000 commission. Net proceeds to seller: Sale Price - Commission - Existing Mortgage Payoff - Other Closing Costs (transfer tax, repairs, prorations). Example: $400,000 sale, 5% commission ($20,000), $180,000 mortgage payoff, $3,000 other costs → Net = $400,000 - $20,000 - $180,000 - $3,000 = $197,000. Reverse commission problems: if seller wants to net $300,000 after 6% commission: Net = Sale Price × (1 - 0.06) → $300,000 = Sale Price × 0.94 → Sale Price = $300,000 ÷ 0.94 = $319,149 (round up to ensure seller nets at least $300,000).
Q: How do you calculate the monthly mortgage payment using given factors?
A: Mortgage payments are calculated using amortization factors. Exam will typically give you a factor table or the payment per $1,000 borrowed. Formula: Monthly Payment = (Loan Amount ÷ 1,000) × Factor. Example: $200,000 loan at 7% for 30 years, factor = $6.65 per $1,000 → Payment = 200 × $6.65 = $1,330/month. PITI: add property taxes and insurance to get total monthly housing payment. From payment: $1,200/month total, $200 taxes, $100 insurance → P&I = $900. If factor is $5.37 per $1,000, loan amount = ($900 ÷ $5.37) × 1,000 = $167,597. Always read carefully — does the problem ask for P&I only or full PITI?
Q: How do you calculate property tax and tax prorations?
A: Property tax = Assessed Value × Tax Rate (mill rate). Mill rate: 1 mill = $1 per $1,000 of assessed value. Example: $300,000 assessed value, 20 mills → $300,000 × 0.020 = $6,000 annual tax. Some states use assessed value as a percentage of market value: if assessment ratio is 80%, a $400,000 home is assessed at $320,000. Proration: taxes paid in arrears (most common). Annual tax = $6,000. Close on April 30, seller owned 120 days. Daily rate (banker's year): $6,000 ÷ 360 = $16.67/day. Seller owes: 120 × $16.67 = $2,000 → debit seller, credit buyer. On the closing statement: seller is debited $2,000, buyer is credited $2,000.
Q: How do you calculate profit or loss and capital gains tax on a property sale?
A: Adjusted Basis = Purchase Price + Capital Improvements (added value, not repairs) + Acquisition Costs. Capital Gain = Sale Price - Selling Costs - Adjusted Basis. Example: Bought for $200,000, added $30,000 kitchen remodel, paid $10,000 in acquisition costs → Adjusted Basis = $240,000. Sold for $350,000, paid $21,000 commission + $5,000 other costs → Net Sale = $324,000. Capital Gain = $324,000 - $240,000 = $84,000. Primary residence exclusion: $250,000 gain excluded ($500,000 married) if lived there 2 of last 5 years. 1031 exchange: defer capital gains by reinvesting in like-kind property — must identify replacement within 45 days, close within 180 days.
Q: How do you calculate net operating income and the value of an income property?
A: Step 1: Potential Gross Income (PGI) = Total rent if 100% occupied. Step 2: Effective Gross Income (EGI) = PGI - Vacancy & Credit Loss. Step 3: NOI = EGI - Operating Expenses (taxes, insurance, maintenance, management, reserves — NOT mortgage or depreciation). Step 4: Value = NOI ÷ Cap Rate. Example: 10 units at $1,200/month = $144,000 PGI. 5% vacancy = $7,200 → EGI = $136,800. Operating expenses = $56,800 → NOI = $80,000. Cap rate in market = 8% → Value = $80,000 ÷ 0.08 = $1,000,000. Cash-on-cash return = Annual Cash Flow (NOI - Debt Service) ÷ Equity Invested. This is different from cap rate — cap rate ignores financing, cash-on-cash includes it.