Chapter 11 Exam Fundamentals

Exam Weight and Scope: Real Estate Calculations account for approximately $10\%$ of the Salesperson Exam, which translates to roughly $8$ questions.
Core Competencies: The curriculum is designed to ensure real estate agents can: * Identify and apply essential math skills necessary to serve clients during transactions. * Determine loan qualification criteria and specific mortgage payment details. * Calculate property taxes, prorated closing costs, commissions, and the net amount a seller will receive at closing ( $\text{Net to Seller}$ ). * Analyze income-producing properties using specific investment metrics. * Evaluate property size (land and structures) and determined value based on size.

Basic Mathematical Concepts and Logical Frameworks

Operational Foundations: Calculations in real estate utilize the four basic arithmetic operations: addition, subtraction, multiplication, and division. These are applied through specific mathematical determinations, comparisons, and rules.
Key Definitions: * Calculation: A mathematical determination of the size or number of an object or value. * Equation: A statement that compares two things as equal, identified by the use of an equal sign ( $=$ ). * Formula: An established fact or rule expressed through mathematical symbols. An illustrated example is Newton's 2nd Law of Motion: $\text{Force} = \text{mass} \times \text{acceleration}$ ( $F = m \times a$ ).
The T-Bar Method: A visual tool used to represent the relationship between three components: the PART, the TOTAL, and the RATE. * The horizontal line in the "T" indicates division ( $\div$ ). * The vertical line in the "T" indicates multiplication ( $\times$ ). * Solving for Part: $\text{Part} = \text{Total} \times \text{Rate}$ . * Solving for Total: $\text{Total} = \frac{\text{Part}}{\text{Rate}}$ . * Solving for Rate: $\text{Rate} = \frac{\text{Part}}{\text{Total}}$ .
Applied T-Bar Examples (Commission Calculations): * Scenario 1 (Finding the Part): Sale price is $\$500,000$ and the commission rate is $2.5\%$ . * \500,000 \times 0.025 = \ $12,500$ (Commission Amount). * Scenario 2 (Finding the Total): Commission earned is $\$15,000$ at a rate of $2.5\%$ . * \15,000 \div 0.025 = \ $600,000$ (Sales Price). * Scenario 3 (Finding the Rate): Commission earned is $\$24,000$ on a sales price of $\$800,000$ . * \24,000 \div \ $800,000 = 0.03$ or $3\%$ (Commission Rate).

Conversions: Percentages, Decimals, and Fractions

Percentage to Decimal: Divide the percentage by $100$ or move the decimal point two places to the left. * $50\% \div 100 = 0.50$ * $2.5\% = 0.025$ * $0.25\% = 0.0025$
Decimal to Percentage: Multiply the decimal by $100$ or move the decimal point two places to the right. * $0.50 \times 100 = 50\%$ * $0.025 = 2.5\%$ * $0.0025 = 0.25\%$
Fraction to Decimal: Divide the numerator (top number) by the denominator (bottom number). * $\frac{1}{4} = 1 \div 4 = 0.25$ ( $25\%$ * $\frac{1}{2} = 1 \div 2 = 0.50$ ( $50\%$ * $\frac{3}{4} = 3 \div 4 = 0.75$ ( $75\%$

Standard Industry Ratios and Thresholds

Down Payments: Typically set at $20\%$ of the sales price (\300,000 \times 0.20 = \ $60,000$ ).
Loan-to-Value (LTV) Ratio: Generally targets $80\%$ of the appraised home value (\300,000 \times 0.80 = \ $240,000$ ).
Real Estate Commissions: Standard ranges are between $5\%$ and $6\%$ of the sale price (\300,000 \times 0.05 = \ $15,000$ ). These are often split between buyer and seller agents, commonly \2.5\% to $3\%$ each.
Discount Points: Each point costs $1\%$ of the total loan amount and typically lowers the APR by $0.25\%$ . * Example: \240,000 \times 0.01 = \ $2,400$ per point.
Debt-to-Income (DTI) Ratios: * Front-end: Max mortgage payment is often $28\%$ of gross monthly income (\10,000 \times 0.28 = \ $2,800$ ). * Back-end: Max for all monthly debts is often $36\%$ of gross monthly income (\10,000 \times 0.36 = \ $3,600$ ).
Capitalization Rate (Cap Rate): Considered "good" between $5\%$ and $10\%$ . * $\text{Net Operating Income} \div \text{Property Value} = \text{Cap Rate}$ . * \30,000 \div \ $300,000 = 10\%$ .

Mortgage Interest Calculations and Amortization

Timeframes: Interest is expressed as an Annual Percentage Rate (APR). Mortgage payments occur monthly. The interest charge for a specific payment is calculated on the remaining loan principal.
Amortization Table Usage: To find a monthly payment, divide the loan by $\$1,000$ and multiply by the relevant factor from an amortization chart. * Example: \600,000 \div \ $1,000 = 600$ . * $600 \times 4.28375 = \$2,570.25$ (Monthly Principal + Interest).
Total Interest Paid Over Loan Term: * $30\,\text{years} \times 12\,\text{months} = 360\,\text{payments}$ . * \2,570.25 \times 360 = \ $925,290$ (Total amount paid). * $\$925,290 - \$600,000 = \$325,290$ (Total interest paid).
Monthly Interest Step-by-Step Calculation: * Step 1 (Monthly Rate): $3.125\% \text{ APR} \div 12 = 0.00260417$ (Monthly Rate). * Step 2 (1st Month Interest): \600,000 \times 0.00260417 = \ $1,562.50$ . * Step 3 (1st Month Principal): $\$2,570.25 - \$1,562.50 = \$1,007.75$ . * Step 4 (New Principal Balance): $\$600,000 - \$1,007.75 = \$598,992.25$ . * Step 5 (2nd Month Interest): \598,992.25 \times 0.00260417 = \ $1,559.88$ .
Simple Interest Formula: Interest charged on the principal only, without compounding. * Formula: $A = P(1 + rt)$ * Variables: $A = \text{Total Accrued Amount (Principal + Interest)}$ , $P = \text{Principal}$ , $I = \text{Interest Amount}$ , $r = \text{Rate of interest per year}$ , $t = \text{Time period in months or years}$ .

Property, Transfer, and Recording Taxes

Annual Property Tax Factors: Requires Appraised Value, Assessment Ratio (varies by state), and Tax Rate. * Tax Rates: Can be per dollar (\5\text{ per }\ $100 = 0.05$ ) or in Mills (1/1000th of value). * Example: $20\text{ mills} = \frac{\$20}{\$1,000} = 0.02$ . * Calculation: \640,000 \text{ (Value)} \times 0.40 \text{ (Assessment Ratio)} = \ $256,000 \text{ (Assessed Value)}$ . * \256,000 \times 0.02 = \ $5,120 \text{ (Annual Tax)}$ .
Transfer Tax: Applied when property is sold. Usually a percentage of the sale price or a dollar amount per $\$1,000$ . * Scenario (Percentage): \450,000 \times 0.0005 \text{ (0.05\%)} = \ $225$ . * Scenario (Dollar Amount): $\frac{\$525,000}{\$1,000} = 525 \times \$1.50 = \$787.5$ .
Recording Tax (Deed or Mortgage): * Deed Tax: Based on Sales Price. * Mortgage Tax: Based on Loan Amount. * Example (Deed): $\frac{\$735,000}{\$1,000} = 735 \times \$3.00 = \$2,205$ . * Example (Mortgage): $\frac{\$580,000}{\$500} = 1160 \times \$1.75 = \$2,030$ .

Proration: Allocating Expenses Between Parties

Proration Types: * Prepaid Items: Already paid by the seller (e.g., fuel in tank, some taxes). * Accrued Items: Accumulated but not yet paid (e.g., interest on a loan, taxes paid in arrears).
Calculation Standards: * Statutory/Banker's Year: $360\,\text{days}$ ( $30\,\text{days/month}$ ). * Actual/Calendar Year: $365\,\text{days}$ ( $366$ in a leap year). * Closing Day Ownership: Typically belongs to the seller unless specified otherwise.
Property Tax in Arrears Example: Closing date $7/8/24$ . Total bill $\$3,484.32$ . Leap year ( $366\,\text{days}$ ). * Per Diem: \3,484.32 \div 366 = \ $9.52$ . * Seller Responsible: Jan 1 to July 8 = $177\,\text{days}$ . \177 \times \ $9.52 = \$1,685.04$ . * Buyer Responsible: July 9 to Dec 31 = $189\,\text{days}$ . \189 \times \ $9.52 = \$1,799.28$ .
Tenant Rent Proration Example: Closing April 4, 2024. Monthly rent $\$2,400$ . Landlord (Seller) gets closing day. * Daily Rent: \2,400 \div 30 = \ $80$ . * Landlord Days: $4$ . * Tenant Days: $26$ . \26 \times \ $80 = \$2,080$ (Prorated rent due for April).

Closing Costs and Net Proceeds

Buyer Funds (Cash to Close): $\text{(Down Payment + Closing Costs) - (Earnest Money + Other Credits)}$ . * Common Buyer Expenses: Lender fees, recording fees, and initial escrow for taxes/insurance. * Interim Interest: Buyers pay interest from the closing day through the end of the month because the first full mortgage payment covers the following month. * Scenario: Loan $\$540,000$ at $5\%$ , Bankers year, Close June 21. * Annual Interest: \540,000 \times 0.05 = \ $27,000$ . * Daily Interest: \27,000 \div 360 = \ $75$ . * Days Owed: $10$ (June 21 to 30). * Interest at Closing: \75 \times 10 = \ $750$ .
Seller Proceeds Calculation: $\text{Sales Price - (Commissions + Existing Loan Balance + Seller Credits/Closing Costs + Prorated Interests)}$ . * Example: Sales price $\$450,000$ , $5\%$ commission ( $95\%$ to seller), $\$120,000$ loan at $3.84\%$ , $\$5,000$ credit to buyer, close Nov 20. * Proceeds after commission: \450,000 \times 0.95 = \ $427,500$ . * Interim calc: $\$427,500 - \$120,000 - \$5,000 = \$302,500$ . * Monthly interest on loan: \120,000 \times 0.0032 \text{ (0.32\%)} = \ $384$ . * Daily interest: \384 \div 30 = \ $12.8$ . * 20 days of interest: \12.8 \times 20 = \ $256$ . * Final Net: $\$302,500 - \$256 = \$302,244$ .

Equity Calculations

Equity Definition: The difference between market value and debt ( $\text{Value - Debt = Equity}$ ).
Dynamics: * Increase: Paying down principal or property appreciation. * Decrease: Depreciation or additional lines of credit (Equity Loans). * Inverse Relationship: As equity increases, Loan-to-Value (LTV) decreases.
Example: Purchase price $\$500,000$ ( $10\text{ years ago}$ ). Current loan $\$400,000$ . Under contract for $\$750,000$ . * Equity: $\$750,000 - \$400,000 = \$350,000$ .

Investment Property Valuation: GRM and GIM

Gross Rent Multiplier (GRM): Used for residential rentals with $4$ or fewer units. Based on monthly income. * Step 1: $\text{Sale Price} \div \text{Gross Monthly Rent} = \text{GRM}$ . * Step 2: $\text{Subject Rental Income} \times \text{Avg GRM} = \text{Estimated Value}$ . * Example: Subject rent is $\$11,000$ . Three Comps: $79$ , $80$ , and $81\text{ GRMs}$ . Average GRM = $80$ . * Value: $80 \times \$11,000 = \$880,000$ .
Gross Income Multiplier (GIM): Used for properties with $5$ or more units. Based on annual income. * Step 1: $\text{Sale Price} \div \text{Gross Annual Income} = \text{GIM}$ . * Step 2: $\text{Subject Annual Income} \times \text{GIM} = \text{Estimated Value}$ . * Example: Sale $\$1,200,000$ with $\$240,000$ annual income = $5\text{ GIM}$ . * Value for income of $\$300,000$ : $5 \times \$300,000 = \$1,500,000$ .

Depreciation on Rental Properties

IRS Concept: Depreciation distributes the cost deduction across the useful life of the property.
Eligibility Rules: 1. Claimant must own the property. 2. Property must produce income. 3. Expected to last $>1\text{ year}$ . 4. Must have a determinable useful life (wears out/decays).
Land Limitation: Land cannot be depreciated as it does not wear down.
IRS Rates: Residential rental property is depreciated at $3.636\%$ annually over a $27.5\,\text{year}$ useful life.
Calculating Annual Depreciation: * Cost Basis: Includes purchase price + legal fees, recording fees, surveys, transfer taxes, title insurance. * Calculation: $\text{(Total Basis - Land Value)} \div 27.5 = \text{Annual Depreciation Amount}$ . * Tax Impact: $\text{Gross Income - Expenses - Depreciation = Taxable Income}$ .

Land Measurement and Conversions

Terminology: * Front foot (Frontage): Length along a street, highway, or waterway. * Perimeter: Sum of the lengths of all sides.
Critical Conversions for Exam: * $1\text{ Township} = 36\text{ Square Miles}$ . * $1\text{ Square Mile} = 640\text{ Acres}$ ( $1\text{ Section}$ * $1\text{ Acre} = 43,560\text{ Square Feet}$ . * $1\text{ Hectare} = 107,639\text{ Square Feet}$ ( $\approx 2.47\text{ acres}$ ). * $1\text{ Linear Mile} = 5,280\text{ Feet}$ .
Example (Acreage Calculation): Half-mile square subdivision. * Side: $5,280 \times 0.5 = 2,640\text{ ft}$ . * Area: $2,640 \times 2,640 = 6,969,600\text{ sq ft}$ . * Acres: $6,969,600 \div 43,560 = 160\text{ acres}$ .
Example (Land Worth): Three-quarters of a mile ( $3,960\text{ ft}$ ) by $3,190\text{ ft}$ . Price is $\$2,500\text{ per acre}$ . * Area: $12,632,400\text{ sq ft}$ . * Acres: $12,632,400 \div 43,560 = 290\text{ acres}$ . * Value: $290 \times \$2,500 = \$725,000$ .

Measuring Structures (ANSI Z765 Standards)

Measurement Guidelines: * Only contiguous (attached) finished spaces are included in total measurement. * Finished spaces must connect via stairways or hallways. * Rounding: Round to nearest inch or tenth of a foot, but report total square footage as a whole number. * Detached structures: Measured at floor level to exterior finished surfaces. * Included spaces: Stairwells and closets. * Vertical spaces: Treads/landings count toward the upper floor's square footage. * Ceiling Height: Must be $\ge 7\,\text{ft}$ . Beamed ceilings must be $\ge 6\,\text{ft } 4\,\text{in}$ under the beam. Slanted ceilings require $\ge 7\,\text{ft}$ height over at least $50\%$ of the floor area.
Geometric Area Formulas: * Square/Rectangle: $\text{Length} \times \text{Width}$ . * Triangle: $\frac{\text{Base} \times \text{Height}}{2}$ . * Circle: $\pi (3.14) \times \text{radius}^2$ .
Specific Area Types: * Gross Living Area (GLA): "Conditioned" (heated/cooled) spaces. Excludes unfinished basements, attics, and garages. * Usable Area: The specific space occupied by a tenant. * Rentable Area: The usable area PLUS the tenant's pro-rata share of common areas (pobbies, restrooms, hallways).