Math tricks that make calculations click

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.

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 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 ÷ 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.

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: cost of points ÷ monthly savings = months to break even. If you sell before break-even, points weren't worth it.

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.

Equity: the owner's financial interest. Property worth $400,000 with $250,000 remaining on mortgage = $150,000 equity. Equity grows two ways: appreciation (value rises) and amortization (loan balance falls). Negative equity ('underwater'): loan balance exceeds property value.

Selling price minus all costs = profit. Costs include: original purchase price, capital improvements (not repairs), selling costs (commission, closing costs, staging). Example: bought for $200,000, improvements $30,000, selling costs $24,000, sold for $350,000 → profit = $96,000.

Mill = 1/1000th of a dollar. Tax = Assessed value × Mill rate ÷ 1,000. Assessed value $200,000 × 25 mills ÷ 1,000 = $5,000 annual tax. Or: convert mill rate to decimal (25 mills = 0.025) × assessed value. Assessment ratio: if 80% ratio, market value $250,000 → assessed value $200,000.

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).

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.

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.

GRM = Sale Price ÷ Gross Annual Rent. Value = GRM × Annual Rent. Example: $24,000/yr rent × GRM of 10 = $240,000 value. GRM ignores expenses — quick estimate only.

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).

Tax = Assessed Value × Mill Rate ÷ 1,000. Example: $200,000 × 25 mills ÷ 1,000 = $5,000 tax. Shortcut: 25 mills = 0.025 × $200,000 = $5,000.

Profit % = Profit ÷ Original Cost × 100. Example: Bought $200,000, improved $20,000, sold $280,000. Profit = $60,000. Profit % = 27.3%. Watch for "percent of selling price" vs "percent of cost" trick questions.

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.

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.

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.

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.

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.

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).

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.

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.

Example: Buyer earns $6,000/month gross. Max front-end (28%): $6,000 × 0.28 = $1,680 max PITI. Taxes $200/month + insurance $100/month = $300. Max P&I = $1,680 - $300 = $1,380. If factor = $6.65 per $1,000 (7%, 30yr): max loan = ($1,380 ÷ $6.65) × $1,000 = $207,519. Back-end check (36%): $6,000 × 0.36 = $2,160 max all debt. Subtract car $400 + student loan $200 = $600 → max housing = $1,560 PITI. Use the MORE restrictive of front-end and back-end results.

Step 1: Potential Gross Income (PGI) = all units × monthly rent × 12. Step 2: EGI = PGI − vacancy and credit loss (typically 5-10%). Step 3: NOI = EGI − all operating expenses. Operating expenses INCLUDE: property taxes, insurance, management fees, maintenance, repairs, utilities, reserves for replacement. Operating expenses EXCLUDE: mortgage payments (debt service), income taxes, depreciation. Step 4: Value = NOI ÷ Cap Rate. Example: 8 units at $1,500/mo = $144,000 PGI. 5% vacancy = $7,200. EGI = $136,800. Expenses = $56,800. NOI = $80,000. Cap rate 8% → Value = $1,000,000.

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.