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## The most basic mathematics

In the world of U.S. real estate, it is critical to understand basic mathematical concepts that are regularly applied in various real estate transactions and calculations. Below, we will explore these essential mathematical concepts:

**Fractions**

**Addition and Subtraction with the Same Denominator:**

Formula:

a / c + b / c = (a + b) ÷ c

Example:

1/2 + 1/2 = (1 + 1) / 2 = 2/2 = 1

**Addition and Subtraction with Different Denominators:**

Formula:

a / c + b / d = (ad + bc) / cd

Example:

1/2 + 1/3 = (3 + 2) / 6 = 5/6

**Multiplication:**

Formula:

(a / c) x (b / d) = ab / cd

Example:

(2/5) x (4/6) = 8/30 = 4/15

**Decimals and Percents (Decimals and Percents)**

**Conversion of Decimals to Percentages:**

Formula:

Decimal Number x 100 = Number in Percentage

Example:

0.022 x 100 = 2.2%

**Conversion of Percentages to Decimals:**

Formula:

Number in Percentage ÷ 100 = Decimal Number

Example:

2.2 ÷ 100 = 0.022

**Multiplication of Percentages:**

Formula:

Percent Number ÷ 100 = Decimal Number Initial Number x Decimal Number = Land

Example:

The 75% of 256 (75% x 256) = ?

75 ÷ 100 = 0.75 256 x 0.75 = 192

**Percentage Division:**

Formula:

Number in Percentage ÷ 100 = Decimal Number Initial Number ÷ Decimal = Dividend

Example:

240 ÷ 75% = ?

75% ÷ 100 = 0.75 240 ÷ 0.75 = 320

**Decimals, Fractions, and Percentages (Decimals, Fractions, and Percentages)**

**Conversion of Fractions to Percentages:**

Formula:

a / b or a ÷ b = a divided by b = decimal number decimal number x 100 = number in percent

Example:

2 / 5 = 2 divided by 5 = 0.4 0.4 x 100 = 40%

**Conversion of a Percentage to a Fraction and Simplification:**

Formula:

X% = X ÷ 100 or X / 100 X ÷ a, where "a" is the largest number that evenly divides 100 ÷ a in the numerator and denominator.

Example:

40% = 40 ÷ 100, or 40 / 100 40 ÷ 20 = 2 100 ÷ 20 = 5

**Conversion of Fractions to Decimals and Percentages:**

Formula:

Decimal x 100 = Number in Percentage

Example:

0.75 x 100 = 75%

**Equations**

**Addition and Subtraction:**

Formula:

If a = b + c

Then b = a - c (subtracting c from both sides)

Y c = a - b (subtracting b from both sides)

Example:

10 = 6 + 4

6 = 10 – 4

4 = 10 – 6

**Multiplication and Division:**

Formula:

If a = b x c

Then b = a / c (dividing both sides by c)

Y c = a / b (dividing both sides by b)

Example:

10 = 2 x 5

2 = 10 ÷ 5

5 = 10 ÷ 2

**Linear and Perimeter Measurement**

**Linear Measurement of Rectangles:**

Formula:

Side A = Area ÷ Side B

Example:

A rectangular house has one side 40 feet long and an area of 1,200 sq. ft. What is the length of the other side?

Side A = (1,200 ft. ÷ 40 ft.) = 30 ft.

**Perimeter measurement:**

Formula:

Perimeter = Sum of all sides of an object

Example:

A five-sided lot has the following dimensions:

Side A = 50 ft. Side B = 60 ft. Side C = 70 ft. Side D = 100 ft. Side E = 30 ft.

What is the perimeter of the lot?

P = 50 feet + 60 feet + 70 feet + 100 feet + 30 feet = 310 feet

**Area Measurement**

**Square and Rectangle:**

Formula:

Area = Width x Depth (Horizontal) or Width x Height (Vertical)

Width = Depth (Height) ÷ Area

Depth (Height) = Width ÷ Area

Example:

A house is 40 feet deep and 30 feet wide. what is its area?

Area = 40 ft x 30 ft = 1,200 sq ft (SF)

**Triangle:**

Formula:

Area = (Height x Base) ÷ 2

Note: Sometimes, the Base is also called "width".

Example:

An A-shaped house has a front facade 30 ft. wide and 20 ft. high. What is the area of the facade?

Area = (30 ft x 20 ft) ÷ 2 = 300 square feet (SF)

**Conversion of Square Feet to Acres:**

Formula:

Acres = Area in Square Feet ÷ 43,560 Square Feet

Example:

How many acres is 196,020 square feet?

196,020 sq. ft. ÷ 43,560 sq. ft. = 4.5 acres

**Conversion of Acres to Square Feet:**

Formula:

Square Feet = Number of Acres x 43,560 Square Feet

Example:

How many square feet is 0.75 acres?

0.75 acres x 43,560 sq. ft. = 32,670 sq. ft.

**Linear and Area Conversion Chart (Linear and Area Conversion Chart)**

**Linear and Area Conversion Chart**

**Linear measures**

**Metric conversions**

**Calculating Area from the Legal Description (Calculating Area from the Legal Description)**

Formula:

First, multiply all the denominators of the fractions in the legal description. Then, divide 640 by the resulting product.

Examples:

How many acres are in the north half of the southwest quarter of Section 6?

640 / (2 x 4) = 640 / 8 = 80 acres

How many acres are in the west half of the northwest quarter of the northeast quarter of Section 8?

640 / (2 x 4 x 4) = 640 / 32 = 20 acres

**Volume Measurement**

Formula:

Volume = Width x Height x Depth (for objects with 90 degree angles)

Base = (Height x Depth) ÷ Volume

Height = (Base x Depth) ÷ Volume

Depth = (Base x Height) ÷ Volume

Example:

What is the volume of a 40 ft x 30 ft x 20 ft house?

40 ft x 30 ft x 20 ft = 24,000 cu. ft.

**Leases**

**Percentage Lease Rent Calculation**

In the U.S. real estate industry, commercial leases often involve a rental component based on a percentage of a business' sales. This concept is known as "Monthly percentage rent".

**Formula:**

The calculation of the monthly percentage rent is made by multiplying the monthly sales of the business by the percentage rent agreed in the contract.

**Example:**

Imagine a store that generates $50,000 per month in sales. The lease stipulates a percentage rent of 1.5%. To calculate the monthly amount of the percentage rent, we apply the formula as follows:

**($50,000 x 0.015) = $750 per month**

In this case, the monthly percentage rent would be $750. This means that, in addition to the base rent, the tenant must pay $750 per month as a percentage of its sales. This approach is common in commercial leases and allows the owners to share in the success of the leased business.

**Contracts for Sale (Contracts for Sale)**

**Percentage of Listing Price Calculation (Percentage of Listing Price Calculation)**

In real estate transactions, it is common to calculate the percentage of offer relative to the listing price of a property. This calculation is used to determine how much is being offered in relation to the initial sales price.

**Formula:**

The calculation of the percentage of the listing price is made by dividing the offer made by the listing price of the property.

**Example:**

Suppose a property is listed at a price of $150,000 and receives a purchase offer for $120,000. To calculate the percentage of the offer with respect to the listing price, we apply the formula as follows:

**($120,000 ÷ $150,000) = 80%**

In this case, the offer represents 80% of the listing price. This calculation is useful for both buyers and sellers, as it provides a clear measure of the relationship between the offer and the initial selling price.

**Earnest Money Deposit Calculation**

When purchasing a property, it is common to make an earnest money deposit, also known as a "earnest money deposit," as a token of interest and commitment in the transaction. The amount of this deposit can be calculated using the following formula.

**Formula:**

The deposit is calculated by multiplying the bid price by the percentage required or accepted in the market.

**Example:**

Let's imagine that a seller requires a deposit of 2% on a property that is listed for $320,000. To calculate the required deposit (assuming a full price offer), we apply the formula as follows:

**($320,000 x 2%) = $6,400**

In this case, the required deposit would be $6,400. This money is held in escrow until the transaction closes and is generally credited towards the final purchase price of the property. Escrowing money is a common practice in real estate negotiations to protect both parties involved.

**Appraisal & Value**

**Adjusting Comparables (Adjusting Comparables)**

In property valuation, it is common to adjust the value of comparables to determine the appraised value of a particular property. Here are the rules and examples for making these adjustments correctly.

**Rules:**

- Never adjust the value of the subject.
- If the comparable is superior to the subject, it detracts from the comparable.
- If the comparable is less than the subject, it adds value to the comparable.

**Example:**

Suppose the subject has a pool for $10,000 and no porch. A comparable that sold for $250,000 has a porch ($5,000), an additional bathroom ($6,000) and no pool.

Adjustments to comparable: $250,000 (+10,000 - 5,000 - 6,000) = $249,000, indicated value of the subject.

**Gross Rent Multiplier (Gross Rent Multiplier)**

The Gross Rental Multiplier is a tool used to estimate the value of a rental property as a function of its monthly rental income and is commonly abbreviated as GRM. Here are the formulas and examples for calculating it.

**Formulas:**

- Sales price = Monthly rental income x GRM
- Monthly rental income = Sales Price / Gross Rental Multiplier

**Examples:**

What is the value of a four-unit building with a monthly rent of $2,800 and a GRM of 112?

$2,800 rental x 112 GRM = $313,600

What is the GRM of a four-unit building with a monthly rent of $2,800 and a value of $313,600?

$313,600 price ÷ $2,800 rent = 112 GRM

**Gross Income Multiplier (Gross Income Multiplier)**

The Gross Income Multiplier is used to estimate the value of a commercial property as a function of its annual income and is commonly abbreviated as GIM. Below are the formulas and examples for calculating it.

**Formulas:**

- Gross Revenue Multiplier = Selling price ÷ Annual revenue
- Selling Price = Annual Revenue x Gross Revenue Multiplier
- Annual revenue = Selling price ÷ Gross Revenue Multiplier

**Examples:**

What is the value of a commercial property with an annual income of $33,600 and a GIM of 9.3?

$33,600 of income x 9.3 GIM = $312,480

What is the GIM of a commercial property with an annual income of $33,600 and a value of $312,480?

$313,600 of price ÷ $33,600 of income = 9.3 GIM

**Cost Approach (Cost Approach)**

**Cost Approach Formula**

The Cost Approach is a methodology used in the valuation of properties to estimate their value based on the replacement cost of improvements and other factors. The formula used in this approach is presented here.

**Formula:**

The value is calculated by adding the value of the land to the cost of the improvements, taking into account capital additions and subtracting depreciation.

**Example:**

Assume the land value is $50,000 and the replacement cost of a house is $150,000. A new garage was added for $30,000 and the total depreciation is $10,000.

Value = $50,000 (land value) + ($150,000 + $30,000 - $10,000) = $220,000

**Depreciation**

Depreciation is the decrease in value of a property over time due to various factors. Here are the formulas and an example for calculating depreciation.

**Formulas:**

- Annual depreciation = Initial depreciation base ÷ depreciation period
- Depreciation base = (Initial value of the property + Capital improvements - Land value)
- Depreciation term is expressed in number of years.

**Example:**

Assume that the value of the property is $500,000, the value of the land is $110,000 and the depreciation term is 39 years.

Step 1: ($500,000 - $110,000) = $390,000 depreciation base.

Step 2: ($390,000 ÷ 39 years) = $10,000 annual depreciation.

**Income Capitalization Formula**

The income capitalization formula is used to estimate the value of a property based on its annual net income and a capitalization rate. Here are the formulas and examples for calculating it.

**Formulas:**

- Value = Annual net operating income ÷ Capitalization rate
- Capitalization rate = Annual net operating income ÷ Value
- Annual net operating income = Value x Capitalization rate

**Examples:**

A property generates $490,000 of net income and is sold at a capitalization rate of 7%. What is its value?

$490,000 ÷ 7% = $7,000,000,000 of value

A property has a net income of $490,000 and is sold for $7,000,000. What is its capitalization rate?

$490,000 ÷ $7,000,000 = 0.07, or 7%

The value of a property is $7,000,000 and the capitalization rate is 7%. What is the annual net operating income of the property?

$7,000,000 x 0.07 = $490,000

**Net Operating Income (NOI, Net Income)**

Net Operating Income, often abbreviated as NOI, is a key metric in the valuation of commercial and investment properties. Here is the formula and an example for calculating NOI.

**Formula:**

NOI is calculated by subtracting vacancy losses and operating expenses from potential income, and then adding other income.

**Note:** NOI does not include debt payments.

**Example:**

A building has 10 office suites that generate a potential annual rent of $10,000 each. The vacancy rate is 10% and annual expenses are $35,000. The vending machines generate $5,000 in additional revenue. What is the NOI?

$100,000 (rent) - $10,000 (vacancy) + $5,000 (other income) - $35,000 (expenses) = $60,000 of NOI

**Finance**

Understanding a variety of financial concepts is crucial to making informed decisions about loans, interest rates and other aspects of real estate transactions. Here, we will explore some of these key concepts in English, as they are commonly used in the real estate industry. **U.S. real estate**:

**Points**

**Definition:**

A **point** equals 1% of the loan amount or 0.01 multiplied by the loan amount.

**Formulas:**

Points = Fee Paid ÷ Loan Amount

Fee Paid = Loan Amount x Points

Loan Amount = Fee Paid ÷ Points

**Examples:**

A borrower pays $500 for a loan of $10,000. **points** are paid?

$500 ÷ 10,000 = 0.05 = 5 **points**

A borrower pays 5 **points** on a $10,000 loan. What is the rate paid?

$10,000 x 0.05 = $500

A borrower repays $500 as 5 **points** What is the amount of the loan?

$500 ÷ 0.05 = $10,000

**General rules:**

- 1 point charged increases the lender's yield by 0.125%
- 8 points charged increase the lender's yield by 1%

**Example:** A lender wishes to obtain a yield of 7% on a loan at 6.5%. How many **points** should be charged?

(7% – 6.5%) = 0.5%

0.5% ÷ 0.125% = 4 **points**

**Interest Rate, Principal and Payment**

**Notice:**

Interest rates on mortgage financing apply to annual interest payments and exclude principal payments. Remember to convert annual payments to monthly, or vice versa, as the question requires, and exclude principal payments from your calculations.

**Formulas:**

Payment = Principal x Rate

Principal = Payment ÷ Rate

Rate = Payment ÷ Principal

**Examples:**

A borrower has a loan of $100,000 at 6% interest. What are the annual and monthly payments?

Annual payment = $100,000 x 0.06 = $6,000

Monthly payment = $6,000 ÷ 12 = $500

A borrower has a monthly payment of $500 on a loan at 6%. What is the principal amount of the loan?

Principal = ($500 x 12) ÷ 6% = ($6,000 ÷ 0.06) = $100,000

A borrower has a monthly payment of $500 on a loan of $100,000. What is the interest rate on the loan?

Rate = ($500 x 12) ÷ $100,000 = ($6,000 ÷ 100,000) = 0.06 = 6%

**Total Interest, Interest Rate, and Loan Term**

**Formulas:**

Interest-only loan: Total interest = Loan amount x Rate x Term in years

Amortized Loan: Total interest = (Monthly payment x 12 x term) - Loan amount

**Examples:**

A borrower obtains a 10-year interest-only loan of $50,000 at 6%. How much interest will he pay?

($50,000 x 0.06 x 10) = $30,000

A borrower obtains a 10-year amortized loan of $50,000 at 6% with monthly payments of $555.10. How much interest will he pay?

($555.10 x 12 x 10) - $50,000 = $16,612

**Amortization Calculation**

**Formulas:**

Month 1: Principal Paid = Monthly Payment - (Loan Amount x Rate ÷ 12)

Month 2: New loan amount = (Paid-in capital of the previous month - Paid-in capital)

Principal paid = Monthly payment - (New loan amount x Rate ÷ 12)

**Example:**

A borrower obtains a 30-year amortized loan of $100,000 at 7% with a monthly payment of $665.31. What is the principal paid in the second month?

Month 1: Principal paid = $665.31 - ($100,000 x 7% ÷ 12) = $665.31 - ($583.33 interest paid) = $81.98

Month 2: New loan amount = $100,000 previous month's loan amount - $81.98 paid-in capital = $99,918.02

Paid-in capital = $665.31 - ($99,918.02 x 7% ÷ 12) = $665.31 - ($582.86 interest paid) = $82.45

**Loan Constants (Loan Constants)**

**Formulas:**

Monthly payment = (Loan amount x Loan constant) / 1000

Loan Amount = (Monthly Payment ÷ Loan Constant) x 1000

Loan constant = (Monthly payment ÷ Loan amount) x 1000

**Examples:**

A borrower obtains a loan of $100,000 with a constant 6.3207. What is the monthly payment?

Monthly payment = ($100,000 ÷ 1,000) x 6.3207 = $632.07

A borrower has a monthly payment of $632.07 on a loan with a monthly constant of 6.3207. What is the loan amount?

Loan amount = ($632.07 ÷ 6.3207) x 1000 = $100,000

A borrower obtains a loan of $100,000 with a monthly payment of $632.07. What is the loan constant?

Borrowing constant = ($632.07 ÷ $100,000) x 1,000 = 6.3207

**Loan-to-Value Ratio (LTV)**

**Formulas:**

LTV Ratio = Loan ÷ Price (Value)

Loan = LTV Ratio x Price (Value)

Price (Value) = Loan ÷ LTV Ratio

**Examples:**

A borrower can obtain a loan of $265,600 for a house of $332,000. What is his LTV ratio?

LTV ratio = $265,600 ÷ 332,000 = 80%

A borrower can obtain an 80% loan for a $332,000 home. What is the loan amount?

Loan = $332,000 x 0.80 = $265,600

A borrower obtained an 80% loan for $265,600. What was the price of the house?

Price (Value) = $265,600 ÷ 0.80 = $332,000

**Financial Qualification**

**Income Ratio Qualification (Income Ratio Qualification)**

Formula: Monthly principal and interest payment (PI) = Income Ratio x Gross monthly income

**Example:**

A lender uses an income ratio of 28% for the monthly principal and interest (PI) payment. A borrower earns $30,000 per year. What is the monthly PI payment the borrower can afford?

Monthly PI payment = ($30,000 ÷ 12) x 0.28 = $700

How much can the borrower borrow if the loan constant is 6.3207 (See also: loan constant)?

Loan amount = ($700 ÷ 6.3207) x 1,000 = $110,747.22

**Debt Ratio Qualification (Debt Ratio Qualification)**

Formulas:

Debt ratio = (Housing Expense + Other debt payments) ÷ Gross monthly income

Housing Expense = (Gross Monthly Income x Debt Ratio) - Other Debt Payments

**Example:**

A lender uses a debt ratio of 36%. A borrower earns $30,000 per year and has monthly non-housing debt payments of $500. What is the housing payment he can afford?

Housing expense = ($30,000 ÷ 12 x 0.36) - 500 = ($900 - 500) = $400

**Investment**

Knowledge of financial concepts is essential to making informed decisions about investment, appreciation, income and more. Here are some of these key concepts in English, as they are commonly used in the **U.S. real estate**:

**Appreciation Calculations**

**Simple Appreciation**

**Formulas:**

Total appreciation = Present value - Original price

Total appreciation rate = Total appreciation ÷ Original price

Average annual appreciation rate = total appreciation rate ÷ number of years

One-year appreciation rate = (Annual appreciation amount) ÷ (Value at the beginning of the year)

**Examples:**

A home purchased for $200,000 five years ago is now worth $300,000. What is the total amount of appreciation, the total appreciation rate and the average appreciation rate?

Total appreciation = ($300,000 - 200,000), or $100,000

Total appreciation rate = ($100,000 ÷ 200,000), or 50%

Average annual appreciation rate = 50% ÷ 5 years = 10%

A house that cost $250,000 is worth $268,000 one year later. What is the one-year appreciation rate?

One year appreciation rate = ($18,000 ÷ 250,000) = 7.2%

**Compounded Appreciation**

**Formula:**

Appreciated value = Initial value x (1+ annual rate) x (1+ annual rate) ... for the relevant number of years

**Example:**

A $100,000 property is expected to appreciate by 5% each year for the next 3 years. What will its appreciated value be at the end of this period?

Appreciated value = $100,000 x 1.05 x 1.05 x 1.05 = $115,762.50

**Rate of Return, Investment Value, Income**

**Formulas:**

Where Revenue = net operating income (NOI); Rate = rate of return, capitalization rate or percentage return; and Value = value, price or amount of investment:

Rate = Revenue ÷ Value

Value = Revenue ÷ Rate

Revenue = Value x Rate

**Examples:**

An office building has a net income of $200,000 and was sold for $3,200,000. What was the rate of return?

Rate = ($200,000 NOI ÷ $3,200,000 price) = 6.25%

An office building has a net income of $200,000 and a capitalization rate of 6.25%. What is its value?

Value = ($200,000 ÷ 6.25%) = $3,200,000

An office building is sold for $3,200,000 with a capitalization rate of 6.25%. What is its NOI?

Revenue = $3,200,000 x 6.25% = $200,000

**Basis, Adjusted Basis, and Capital Gain**

**Formulas:**

Capital gain = Realized amount - Adjusted basis, where

Realized amount = Selling price - Cost of sales

Adjusted Basis = Initial Basis + Capital Improvements - Total Depreciation

Total depreciation = (Initial depreciated base ÷ Depreciation period in years) x Depreciation years

Depreciated basis = Value of initial property + Capital improvements - Value of land

**Example:**

Tip: work the example backwards from the last formula to the first.

An apartment building was purchased for $500,000, with the land value estimated at $100,000. The owner added a parking lot for $100,000. The property depreciated over a 40-year period (for current purposes!). Three years later, the property was sold for $700,000, and the selling costs were $50,000. What was the capital gain?

Depreciated basis = $500,000 purchase price + $100,000 parking - $100,000 land = $500,000 Total depreciation = ($500,000 ÷ 40 years) x 3 years = $37,500 Adjusted basis = $500,000 purchase price + $100,000 parking lot - $37,500 Total depreciation = $562,500 Amount realized = $700,000 selling price - $50,000 cost of sales = $650,000 Capital gain = $650,000 amount realized - $562,500 adjusted basis = $87,500

**Depreciation**

**Formulas:**

Annual depreciation = (Initial depreciated base) ÷ (Depreciation period in number of years)

Depreciated basis = (Initial property value + Capital improvements - Land value)

**Example:**

Value of property = $500,000; value of land = $110,000; depreciation term = 39 years

($500,000 - 110,000) = $390,000 depreciated basis ($390,000 ÷ 39 years) = $10,000 depreciation per annum

**Equity**

**Formula:**

Equity = Current market value - Current balance of loan(s)

**Example:**

A home that was purchased for $150,000 with a loan of $100,000 is now worth $300,000. The current loan balance is $80,000. What is the owner's equity?

Equity = $300,000 value - $80,000 debt = $220,000

**Net Income**

**Formula:**

NOI = Potential rent - Vacancy loss + Other income - Operating expenses

Note: NOI does not include debt payments!

**Example:**

A building has 10 office suites that generate a potential annual rent of $10,000 each. Vacancies = 10% and annual expenses are $35,000. The vending machines generate $5,000. What is the NOI?

$100,000 rent - $10,000 vacancies + $5,000 other income - $35,000 expenses = $60,000 NOI

**Cash Flow (Cash Flow)**

**Formula:**

Cash Flow = (Net Operating Income - Debt Service) where debt service is the payment of IP.

**Example:**

A building generates NOI of $100,000 after expenses and has a debt payment of $40,000. What is its cash flow?

Cash flow = $100,000 - $40,000 = $60,000

**Investment Property Income Tax Liability (Investment Property Income Tax Liability)**

**Formula:**

Tax Liability = (NOI + Reserves - Interest Expense - Depreciation) x Tax Rate

**Example:**

An office building has an NOI of $200,000, an annual reserve expense of $20,000, interest expense of $130,000 and annual depreciation of $50,000. Assuming a tax rate of 28%, what is its income tax liability?

Fiscal responsibility = ($200,000 + $20,000 - $130,000 - $50,000) x 28% = $11,200

**Return on Investment (ROI)**

**Formula:**

ROI = NOI ÷ Price

**Example:**

An investment property generates a cash flow of $100,000 and is appraised at $1,500,000. What is the owner's return on investment?

ROI = $100,000 ÷ $1,500,000 = 6.67%

**Return on Equity (Return on Equity)**

**Formula:**

ROE = Cash flow ÷ Equity

**Example:**

An investment property generates a cash flow of $100,000. The owner has equity of $500,000 in the property. What is the owner's return on equity?

ROE = $100,000 ÷ $500,000 = 20%

**Taxation**

Understanding tax issues is critical for any investor or property owner. Here are some key concepts in English commonly used in the real estate industry. **U.S. real estate**:

**Converting Mill Rates (Converting Mill Rates)**

**Definition:**

1 mill = $0.001; a mill rate of 1 mill for every $1,000 = 0.1%; a tax rate of 1% = 10 mills

**Formula:**

Tax = (Taxable value ÷ 1000) x Mill rate

**Example:**

A tax rate on a house with a taxable value of $200,000 is 7 mills per thousand dollars of valuation. What is the tax?

Tax = ($200,000 ÷ 1,000) x 7 mills = $1,400

**Tax Base**

**Formula:**

Taxable income = Assessed valuations - Exemptions

**Example:**

A town has a total assessed valuation of $20,000,000 and exemptions totaling $4,000,000. What is the tax base?

$20,000,000 – $4,000,000 = $16,000,000

**Tax Rate, Base, and Requirement**

**Formulas:**

Tax rate = Tax requirement ÷ Taxable base

Taxable base = Tax requirement ÷ Tax rate

Tax requirement = Taxable income x Tax rate

**Example:**

A town has a tax base of $160,000,000 and a budget of $8,000,000. What is the tax rate?

Tax rate = ($8,000,000 ÷ $160,000,000 ) = 0.05, or 5%, or 50 mils

**Special Assessments**

**Formula:**

Special Assessment = Total Cost of Special Assessment x Owner's Share

**Example:**

A homeowner owns 100 feet of an 800-foot breakwater that needs to be repaired. The total cost of the assessment will be $80,000. What is the owner's assessment?

Owner's share = 100 ft ÷ 800 ft = 0.125, or 12.5% Special assessment = $80,000 x 12.5% = $10,000

Tax concepts are fundamental to understanding the financial implications of real estate properties and real estate investments. These English terms are widely used in the U.S. real estate industry.

**Commissions**

In the **U.S. real estate**Commissions are a fundamental aspect of real estate transactions. Here are some key concepts related to commissions that are widely used:

**Commission Splits (Commission Splits)**

**Formulas:**

Total commission = Selling price x Commission rate

Co-brokerage split = Total commission x Percentage of co-brokerage

Agent split = Co-brokerage split x Percentage of the agent

Broker Division = Co-brokerage Division - Agent Division

**Example:**

A $300,000 property is sold with a 7% commission, with a 50-50 co-brokerage split and a 60% split for the agent with his broker. What are the total commissions, co-brokerage, agent and broker?

Total Commission = $300,000 x 0.07 = $21,000

Co-brokerage split = $300,000 x 0.07 x 0.50 = $10,500

Division of the agent = $10,500 x 0.60 = $6,300

Broker's broker split = $10,500 - $6,300 = $4,200

**Seller's Net**

**Formula:**

Seller's net = Selling price - (selling price x commission) - Other closing costs - Loan balance

**Example:**

A house sells for $260,000 and has a loan balance of $200,000 at closing. The commission is 7% and other closing costs are $2,000. What is the seller's net?

Net from seller = ($260,000 - ($260,000 x 0.07) - $2,000 - $200,000) = $39,800

**Price to Net an Amount (Price to Net an Amount)**

**Formula:**

Sales price = (Desired amount + Closing costs + Loan payment) / (1 - Commission rate)

**Example:**

A home seller wants to net $50,000. The commission is 7%, the loan payment is $150,000 and the closing costs are $4,000. What should the sales price be?

Selling price = ($50,000 + $4,000 + $150,000) / 0.93 = $219,355

Understanding how commissions are calculated and divided is essential for anyone involved in real estate transactions in the United States. These terms are common in the real estate industry and facilitate communication between agents, brokers and sellers.

**Closing Costs & Prorations (Closing Costs & Prorations)**

Closing costs and appraisals are essential elements in any real estate transaction. Here are some key concepts in English related to closing costs and appraisals that are widely used:

**30-Day/12-Month Method (30-Day 12-Month Method)**

**Formulas:**

Monthly amount = Annual amount / 12

Daily amount = Monthly amount / 30

Proration = (Monthly amount multiplied by the number of months) + (Daily amount multiplied by the number of days)

**Example:**

An annual tax bill is $1,800. The closing is on April 10. What is the seller's share of the taxes?

Monthly amount = ($1,800 ÷ 12) = $150; number of months = 3 Daily amount = ($150 ÷ 30) = $5.00; number of days = 10 Proration = ($150 x 3 ) + ($5 x 10) = ($450 + $50) = $500, seller's portion **365-Day Method (365-Day Method)**

**Formula:**

Daily amount = (Annual amount ÷ 365) or (Monthly amount ÷ Length of month)

Proration = Daily amount multiplied by the number of days

**Example:**

An annual tax bill is $1,800. The closing is on April 10. What is the seller's share of the taxes?

Daily amount = ($1,800 ÷ 365) = $4.93

January 1 to April 10 = (31 + 28 + 31 + 31 + 10) days, or 100 days

Prorate = $4.93 x 100 days = $493, seller's share

**Income Received in Advance (Rent)**

**Logic:**

Credit the buyer and debit the seller on the buyer's behalf

**Example:**

Seller receives $1,000 rent. Month is 3/4 of the way there.

Buyer's share is ($1,000 x 25%) = $250

Credit to buyer / debit to seller $250. **Expenses paid in Arrears (Tax) (Expenses paid in Arrears)**

**Logic:**

Credit the buyer and debit the seller on the seller's behalf

**Example:**

Buyer will pay $1,000 tax. The year is 3/4 of the way.

Buyer's share is ($1,000 x 25%) = $250

Credit to buyer / debit to seller $750.

Understanding how closing costs and pro rata closing costs and proceeds are calculated and apportioned is critical in real estate transactions in the United States. These English terms are essential to facilitate effective communication between buyers, sellers and real estate professionals.

**Insurance Coverage**

**Recovery with Co-Insurance Clauses (Recovery with Co-Insurance Clauses)**

Understanding coinsurance clauses in insurance policies is essential to protect yourself in the event of a loss. Here is a key concept related to insurance coverage and coinsurance clauses that are widely used:

**Formula:**

Recovery = (Damage claim) x (Covered replacement cost percentage ÷ Minimum coverage requirement)

**Example:**

A homeowner insures his home for $100,000. The replacement cost is $150,000. A coinsurance clause requires coverage of 80% of the replacement cost to avoid penalties. A fire destroys the house. How much can the homeowner recover from the insurer?

Claim recovery = $150,000 x (67% of covered cost ÷ 80% required) = $125,625

Understanding coinsurance clauses is critical to ensuring that insurance coverage is adequate and effective in the event of a claim. These English terms are essential for clear and accurate communication with insurance companies and other real estate professionals.