Overview
The NY Real Estate Exam requires proficiency in several categories of math calculations, including commissions, property valuation, mortgage financing, taxes, measurements, and investment returns. Each category uses specific formulas that must be applied accurately under exam conditions. This guide breaks down every formula, common patterns, and pitfalls to help you maximize your score.
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Core Formula Reference Sheet
> Bookmark this section — these formulas appear across multiple question types.
| Formula | Equation |
|---|---|
| Commission | Sale Price × Commission Rate |
| Net Sale Price | Desired Net ÷ (1 − Commission Rate) |
| Value (Income Approach) | NOI ÷ Cap Rate |
| GRM Value | Monthly Rent × GRM |
| LTV Ratio | Loan Amount ÷ Sale Price |
| Monthly Interest | Loan Balance × Annual Rate ÷ 12 |
| DTI Max Payment | Gross Monthly Income × DTI % |
| Points Cost | Loan Amount × (Points × 0.01) |
| Property Tax | (Assessed Value ÷ 1,000) × Tax Rate |
| Mill Rate | Mills × $0.001 per dollar of assessed value |
| Triangle Area | (Base × Height) ÷ 2 |
| Rectangle Area | Length × Width |
| Section Acres | 640 ÷ number of fractional divisions |
| ROI | Net Profit ÷ Total Investment |
| Cap Rate | NOI ÷ Property Value |
| Percentage Change | (New − Old) ÷ Old × 100 |
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Commission Calculations
Overview
Commission problems test your ability to work through multi-step splits and work backwards from a known commission to find a sale price or rate.
Key Concepts
• Total Commission = Sale Price × Commission Rate
• Commission Splits are applied sequentially: broker split first, then salesperson split from the broker's portion
• Net to Seller / Working Backwards: When a seller wants a specific net amount after commission:
- Sale Price = Desired Net ÷ (1 − Commission Rate)
- Never add the commission percentage directly to the desired net
Step-by-Step: Multi-Tier Commission Split
1. Calculate the total commission (Sale Price × Rate)
2. Determine the listing broker's share (apply the broker split %)
3. Apply the salesperson's split to the listing broker's portion only
Example:
• Sale price: $450,000 | Rate: 6% | Broker split: 50/50 | Salesperson gets 60% of listing side
• Total commission = $450,000 × 0.06 = $27,000
• Listing broker's half = $27,000 × 0.50 = $13,500
• Salesperson's share = $13,500 × 0.60 = $8,100
Step-by-Step: Tiered Commission Rate
Some brokers charge different rates on portions of the sale price:
• Calculate commission on each tier separately
• Add together for the total
Example: 7% on first $100,000, 5% on remainder of $320,000 sale
• $100,000 × 0.07 = $7,000
• $220,000 × 0.05 = $11,000
• Total = $18,000
Key Terms
• Commission Rate – Percentage of sale price paid to broker(s)
• Split – Division of commission between parties (broker-to-broker or broker-to-salesperson)
• Net to Seller – Amount seller receives after paying commission
• Tiered Commission – Different rates applied to different portions of the sale price
Watch Out For
• ⚠️ When working backwards to find sale price: divide the net by (1 − rate), do not multiply the net by the rate and add it back
• ⚠️ In multi-tier splits, apply the salesperson percentage to their broker's portion only, not the total commission
• ⚠️ If a salesperson represents both sides of a transaction, their combined split percentages apply to the full commission — read the question carefully
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Property Valuation & Appraisal Math
Overview
Valuation math focuses on three approaches: income capitalization, gross rent multiplier (GRM), and assessed value/market value relationships.
Income Capitalization Approach
Value = NOI ÷ Cap Rate
Rearrangements:
• Cap Rate = NOI ÷ Value
• NOI = Value × Cap Rate
Example: NOI = $52,000 | Cap Rate = 6.5%
• Value = $52,000 ÷ 0.065 = $800,000
Gross Rent Multiplier (GRM)
Value = Monthly Rent × GRM
Rearrangements:
• GRM = Value ÷ Monthly Rent
• Monthly Rent = Value ÷ GRM
Example: Rent = $2,500/month | GRM = 120
• Value = $2,500 × 120 = $300,000
Assessed Value vs. Market Value
Market Value = Assessed Value ÷ Assessment Ratio
Example: Assessed value = $240,000 | Assessment ratio = 80%
• Market Value = $240,000 ÷ 0.80 = $300,000
Percentage Change in Value
% Change = (New Price − Old Price) ÷ Old Price × 100
Example: Bought for $300,000, sold for $375,000
• Change = $75,000 ÷ $300,000 = 0.25 = 25%
Key Terms
• Net Operating Income (NOI) – Gross income minus operating expenses (before debt service)
• Capitalization Rate (Cap Rate) – Rate of return used to estimate property value; reflects market risk
• Gross Rent Multiplier (GRM) – Sales price divided by monthly (or annual) gross rent
• Assessed Value – Value assigned by a taxing authority, often a percentage of market value
• Assessment Ratio – The percentage of market value used to set assessed value
Watch Out For
• ⚠️ Cap rate and GRM are estimation tools, not exact values — the exam expects you to use given figures without questioning them
• ⚠️ GRM typically uses monthly rent in NY exam problems; confirm which period is being used
• ⚠️ To find market value from assessed value, divide — do not multiply
• ⚠️ Percentage change always divides by the original (old) price, never the new price
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Mortgage & Financing Calculations
Overview
These calculations test your understanding of loan amounts, interest, qualifying ratios, and closing costs.
Loan-to-Value (LTV) Ratio
LTV = Loan Amount ÷ Purchase Price
• Down Payment = Purchase Price × Down Payment %
• Loan Amount = Purchase Price − Down Payment
Example: $400,000 home | 20% down
• Loan = $400,000 × 0.80 = $320,000
• LTV = $320,000 ÷ $400,000 = 80%
Monthly Interest (Simple Interest Method)
Monthly Interest = Loan Balance × (Annual Rate ÷ 12)
Example: $250,000 loan | 6% annual rate
• Monthly interest = $250,000 × (0.06 ÷ 12) = $1,250
Finding the Interest Rate
Annual Rate = (Monthly Interest ÷ Loan Balance) × 12
Example: Monthly interest = $900 | Balance = $180,000
• Monthly rate = $900 ÷ $180,000 = 0.005
• Annual rate = 0.005 × 12 = 6%
Debt-to-Income (DTI) Ratio
Max Payment = Gross Monthly Income × DTI %
Example: Income = $6,000/month | DTI = 28%
• Max payment = $6,000 × 0.28 = $1,680
Discount Points
Points Cost = Loan Amount × (Number of Points × 0.01)
• 1 point = 1% of the loan amount
• Points are paid at closing and typically lower the interest rate
Example: $300,000 loan | 2 points
• Cost = $300,000 × 0.02 = $6,000
Key Terms
• Loan-to-Value (LTV) – Ratio of loan amount to property value; higher LTV = higher lender risk
• Down Payment – Buyer's upfront cash contribution; reduces loan amount
• Discount Points – Prepaid interest paid at closing to reduce the mortgage rate; 1 point = 1% of loan
• Debt-to-Income (DTI) Ratio – Monthly debt obligations divided by gross monthly income
• Amortization – Gradual repayment of a loan through scheduled principal and interest payments
Watch Out For
• ⚠️ Monthly interest is calculated on the current loan balance — as the loan pays down, interest decreases
• ⚠️ DTI is based on gross (pre-tax) income, not net take-home pay
• ⚠️ Points are calculated on the loan amount, not the purchase price
• ⚠️ LTV and down payment are inverses: 20% down = 80% LTV
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Tax & Proration Calculations
Overview
Proration problems require you to determine how much of a prepaid or past-due expense is owed by each party at closing. Tax calculations test your ability to apply mill rates and tax rates correctly.
Proration Formula
Step 1: Find the daily rate = Annual amount ÷ 360 (or 365 if specified)
Step 2: Count the number of days the responsible party has used/will use the item
Step 3: Multiply daily rate × number of days
> NY Exam Convention: Use a 30-day month / 360-day year unless told otherwise.
#### Taxes Paid in Arrears (most common)
• Seller owes from January 1 through the day before closing
• Seller credits the buyer for unpaid taxes
Example: Annual taxes = $4,800 | Closing = September 1 | 360-day year
• Seller's days = Jan 1–Aug 31 = 8 months × 30 days = 240 days
• Daily rate = $4,800 ÷ 360 = $13.33
• Seller owes = 240 × $13.33 = $3,200
#### Prepaid Items (e.g., HOA dues, insurance)
• Seller has already paid for time the buyer will own the property
• Buyer credits the seller for the unused portion
Example: HOA dues = $2,400/year | Closing = April 1
• Remaining months = April–December = 9 months
• Buyer owes seller = $2,400 ÷ 12 × 9 = $1,800
Property Tax Calculation
Tax = (Assessed Value ÷ 1,000) × Tax Rate per $1,000
Example: Assessed value = $350,000 | Rate = $22 per $1,000
• Tax = (350,000 ÷ 1,000) × 22 = 350 × $22 = $7,700
Mill Rate
• 1 mill = $0.001 per dollar of assessed value = $1 per $1,000 of assessed value
• Tax = Assessed Value × (Mill Rate ÷ 1,000)
Example: 45 mills on $350,000 assessed value
• Tax = $350,000 × (45 ÷ 1,000) = $350,000 × 0.045 = $15,750
• Or: 45 mills = $45 per $1,000
Key Terms
• Proration – The fair division of income or expenses between buyer and seller at closing
• Paid in Arrears – Taxes owed for the past period, paid after the fact; seller typically owes at closing
• Prepaid Item – Expense paid in advance; seller receives credit from buyer for unused period
• Mill Rate – Tax rate expressed in thousandths; 1 mill = $1 per $1,000 of assessed value
• 360-Day Year (Banker's Year) – Standard assumption for NY exam proration problems (12 months × 30 days)
Watch Out For
• ⚠️ Always identify whether taxes are paid in arrears (seller credits buyer) or prepaid (buyer credits seller) — these are opposite directions
• ⚠️ Confirm the year basis: 360-day (banker's year) is standard for NY; some problems specify 365
• ⚠️ The closing day itself is typically assigned to the buyer — count up to but not including the closing date for the seller's portion
• ⚠️ To convert a mill rate: simply move the decimal three places left (45 mills = 0.045 = $45/$1,000)
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Area & Measurement Calculations
Overview
Area problems test your ability to calculate square footage of rectangles and triangles, convert to acres, and work with the Public Land Survey System (PLSS) for section/township descriptions.
Rectangle Area
Area = Length × Width
Triangle Area
Area = (Base × Height) ÷ 2
Example: Base = 400 ft | Height = 300 ft
• Area = (400 × 300) ÷ 2 = 60,000 sq ft
Converting Square Feet to Acres
Acres = Square Feet ÷ 43,560
Example: 150 ft × 200 ft = 30,000 sq ft
• 30,000 ÷ 43,560 = ≈ 0.69 acres
Public Land Survey System (PLSS) — Section Divisions
| Unit | Acres |
|---|---|
| 1 Township | 23,040 acres (36 sections) |
| 1 Section | 640 acres |
| 1/2 Section | 320 acres |
| 1/4 Section | 160 acres |
| 1/4 of 1/4 Section | 40 acres |
Method: Start with 640 acres and divide by each fraction in the legal description (right to left).
Example: NW ¼ of the SW ¼ of Section 12
• 640 ÷ 4 = 160 acres (SW ¼)
• 160 ÷ 4 = 40 acres (NW ¼ of the SW ¼)
Replacement Cost Calculation
Total Replacement Cost = Cost per Square Foot × Total Square Footage
Example: $180/sq ft × 2,400 sq ft = $432,000
Key Terms
• Square Footage – Area expressed in square feet (length × width for rectangles)
• Acre – Unit of land measurement equal to 43,560 square feet
• Section – One square mile = 640 acres in the PLSS
• Township – A 6-mile × 6-mile square containing 36 sections
• Replacement Cost – Cost to rebuild a structure at current labor and material prices
Watch Out For
• ⚠️ 1 acre = 43,560 sq ft — memorize this number; it appears frequently
• ⚠️ For PLSS section problems, read legal descriptions from right to left: start with the section, then apply each fraction
• ⚠️ Triangles — don't forget to divide by 2; this is the most common area calculation error
• ⚠️ Replacement cost uses building square footage only, not lot size
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Investment & Return Calculations
Overview
Investment math tests your ability to evaluate rental property performance through cap rate, NOI, and return on investment (ROI) calculations.
Net Operating Income (NOI)
NOI = Gross Rental Income − Operating Expenses
> NOI is calculated before mortgage payments (debt service) and income taxes.
Example: Gross rent = $42,000 | Expenses = $12,000
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