# Real Estate Math

If you’re a student embarking on your real estate career, you are probably doing a course for your real estate license and wondering how much math is involved in the real estate exam.

Fortunately, there’s definitely no need for you to know all the math concepts and formulas for the profession.

However, you still need to understand a number of math concepts to become a professional real estate agent. Let’s discuss and figure out what you need to know.

## What Is Real Estate Math?

For those of you intimidated by real estate math, don’t worry.

Usually, there are only a minimal number of math questions on any real estate exam. A great bulk of the real estate exam relies on vocabulary and concepts.

Math’s difficulty level on a real estate exam is based on the information you probably learned in high school. These include employing basic number multiplication, fractions, decimals, and percentages.

It’s important to know real estate math basics such as understanding units and how to reason and apply simple math formulas to solve a real estate issue, whether in your real estate exam or real life.

Complicated real estate problems are straightforward; use logic and careful step-by-step methods to solve these problems, such as those involving appraisals and depreciation.

Again, it’s not hard math. All you need to do is break the problems down and solve them one step at a time.

### What Are the Types of Math Problems That You Should Absolutely Know How to Do?

- Measurement conversions, including area measurements, linear measurements, and volume measurements
- Converting percentages, fractions, and decimals, which means understanding the T method
- Understanding Discounts vs Profit
- Math questions involving a number of real estate math formulas that involve Gross Rent Multiplier (GRM), commission, simple interest, the loan to value (LTV) ratio, and more.

## Real Estate Math Definitions

If you are studying for the real estate exam, you need to master basic real estate law, the ins and outs of mortgages and liens, zoning regulations, sales techniques, public relations, advertising, and a whole new vocabulary to cover these areas.

Here are a number of common real estate math definitions to get started on your exam prep:

(You can access some more real estate math definitions, including the ultimate glossary of all real estate terms, here)

### 28/36 Rule or “*The Mortgage Rule of Thumb*”

According to this rule, a household should spend a maximum of 28% of its gross monthly income on total housing expenses and no more than 36% on total debt service, including housing and other debt such as car loans and credit cards.

### Ad Valorem Tax

The Latin phrase *ad valorem* means “according to value.” An ad valorem tax is a form of taxation based on the value of a transaction or a property, either real estate or personal property.

### Amortization

It is the schedule of your monthly loan payments. Amortization is a method of equalizing the monthly payment over the life of the loan.

It can also be defined as the recovery of financial capital over time, for which the concept can apply to lending or capital investment.

Schedules prepared by lenders will also show tax and insurance payments if made by the lender and the tax/insurance escrow account balance.

### Appraisal

An appraisal is a numerical estimate of approximate worth for something.

### Appreciation

Appreciation is any gain in the value of a property over time from any cause.

### Board Foot

A number unit of cubic measure for lumber equal to a 1-foot square by 1 inch thick.

### Capitalization

Capitalization is the conversion of assets or income into capital.

The capitalization rate is used to indicate the rate of return that is expected to be generated on a property.

### Commission

A commission is a fee paid to an agent or broker for performing a transaction.

### Depreciation

Depreciation is any loss in the value of a property over time from any cause.

### Discount Points

Discount points, or mortgage points, are prepaid interest payments that borrowers can choose to pay to lower the interest on future payments.

Discount points are a one-time fee, paid upfront at either the time a mortgage is first arranged or during a refinance.

Points don’t always have to be paid out of pocket; they can sometimes be rolled into the loan’s balance.

The purchase of each point generally lowers the interest rate on the mortgage by up to 0.25%. Typically, one discount point covers a 0.25% percent change in the loan rate. However, lenders are free to set discount points at any number.

### Double Net Lease

A double net lease is a rental agreement whereby the tenant agrees to cover the costs of two of the three primary categories of property expenses: taxes, utilities, or insurance premiums.

The term “Double” means that two additional costs will be added to the number of your base rent.

### Equity

Equity is the number difference between your home’s market value and the amount you owe the lender who holds the mortgage payment.

In other words, it’s the amount of money you’d receive after a complete mortgage payment if you were to sell the home.

### Escrow

Escrow is a way for money and property to be transferred from one party to another by using a neutral, third-party agent also known as an escrow agent.

Escrow makes it a lot safer for both buyers and sellers to close the sale without worrying about getting snubbed or cheated.

### Front Foot

In real estate, a front foot is defined as a property measurement of the front footage of a parcel of property adjoining the street.

### Gross Rent Multiplier

The gross rent multiplier (GRM) is the ratio of the price of a real estate investment to its annual rental income before accounting for expenses such as property taxes, insurance, and utilities.

GRM is the number of years the property would take to pay for itself in gross received rent. It is a measure of a property’s value, obtained by dividing the property’s selling price by its gross annual rental income.

The gross rent multiplier is a simplified way to analyze a rental property’s value using the income approach.

### Interest

The term “interest” can be defined as the cost of borrowing money and is usually expressed as a yearly percentage paid as part of your monthly loan payment.

### Investment

The legal purchase of something that is not consumed today but will be in the future to create profit.

### Linear Foot

A linear foot is exactly what it sounds like: a 12-inch measurement (approximately 1-foot long) that extends in a straight (or linear) line. If something has a number of 12 lineal feet long, it is 12 feet long.

Fun fact: Pricing for a freight moving company is often based on the number of linear feet your household goods take up in the trailer.

### Market Value

Market value is an opinion of what a property would sell for in a competitive market based on the features and benefits of that property (the value), the overall real estate market, supply and demand, and a comparison between a number of other similar properties have sold for in the same condition.

For example, if your home sells for $100,000, then its market value is $100,000.

### Mill Rate

“Millage,” or “mill rate,” is a term some states and localities use to calculate property tax liability.

The mill rate is the amount of tax payable per dollar of the assessed value of a property.

The mill rate is based on the term “mills.” It is a number that represents the amount per $1,000 of the assessed value of the property.

### Net Listing

A net listing is when an agent agrees to sell an owner’s property for a set minimum property price. Any number over the minimum price belongs to the agent as commission.

### Net Operating Income

This term is a number that refers to the total income of a property minus all operating expenses.

### Principal

The total value of money borrowed (such as the face value of a debt security).

### Property Taxes

Property taxes (the same as real estate taxes) are ad valorem taxes assessed on real estate by a local government and paid by the property owner.

Real estate or property tax in dollar terms is calculated by multiplying the assessed property value and the mill rate and dividing by 1,000.

### Proration

Proration is the allocation or dividing of certain money items done by an attorney or real estate broker at the closing.

There are actually 4 categories of proration: proration for property tax, insurance, homeowner’s association fees, and utilities.

Seller and buyer prorations are credits and debits designed to ensure that both parties pay their fair share of the costs associated with the home.

### Running Foot

A number measurement of the length of a piece of wood refers to a single-dimensional measurement of length, without regard to its thickness or width.

### Selling Price

The final amount of money that a buyer and seller have agreed upon when a property sells. It differs from the list price or asking price because negotiations can take place between both the seller and buyer to arrive at the sales price.

### Township

A township is a public land surveying unit with a number of 36 sections or 36 square miles.

### Triple Net Lease

With a triple net lease (triple-net or NNN), the tenant agrees to pay the property expenses such as real estate taxes, building insurance, and maintenance in addition to rent and utilities.

## Real Estate Math Formulas

### T Method

Out of all of the real estate math formulas, the most basic one is the T-Method. In fact, once you understand this, you’ll realize many real estate math problems apply this math concept.

The relationship between Total, Part, and Rate and is visualized by drawing a T.

The top of T (Part) acts as the numerator, one of the bottom elements of the T (Total or Rate) acts as the denominator, and the remaining is what the quotient is equal to.

If the problem is looking for Part, the equation involves multiplying the numbers given as total and rate at the bottom.

Basically, we can get the 3 following math formulas based on the T-Method:

Part / Total = Rate

Part / Rate = Total

Total x Rate = Part

Examples of applications of the real estate math formula include calculating the **sales price, commission rate, and commission.** For instance, in the case of commission:

#### Commission Formulas

**Commission **= (house selling price) x (commission percentage)

**Rate of Commission **= Commission / Sales Price

**Sales Price** = Commission / Rate of commission

### Simple Interest Formula

Just like the T method! The horizontal line of the pyramid means division, and the vertical lines also mean multiplication. Hence, Interest or I = P x R x T (part x rate in decimal x time)

If you’re looking for how much an interest rate has grown, the formula that accounts for principal + interest is:

**A = P(1 + rt)**

Where: A = Total Accrued Amount

P = Principal Amount Invested

I = Interest

r = Interest rate per year **in decimal**; r = R/100

t = Time Period involved in months or years

### Loan to Value (LTV) Ratio

**LTV Ratio = APV ÷ MA**

Where APV is the Appraised Property Value, and MA stands for Mortgage Amount.

### Gross Rent Multiplier

**Gross Rent Multiplier = Property Price ÷ Gross Annual Rental Income**

Annual Gross Rental Income = Monthly Rental Income × 12

### Gross Scheduled Income

This real estate formula lets you know how much income your property will generate if all units within it are rented and if there are no defaults in rent payments.

This can be a useful measure to compare with your actual income.

**Gross Scheduled Income = Rental Income + Lost Rental Income from Vacant Units**

**Gross Operating Income**

This figure reflects the gross operating income in addition to all other sources of income from your rental property. This can include revenue from parking spaces, public vending machines, or others.

**Gross Operating Income = (GSI – Lost Rental Income from Vacant Units) + Other Income**

**Capitalization Rate**

The cap rate is among the most important formulas.

The cap rate formula compares an investment property’s net operating income with its market value, allowing investors to quickly compare properties to see which is the most worth it.

**Cap Rate = ****Net Operating Income**** / Market Value of Property**

### Discount Points Formulas

Discount Points = Prepaid Interest

Break-Even Point = Points Cost ÷ Monthly Payment Savings

### Property Tax Formulas

Property Tax Rate = (assessed value) x (mill rate)

Assessed Value = (assessment rate) x (market value)

1 mill = equal to 1/1,000th of a dollar or $1 in property tax.

### 28/36 Rule Formula

Housing costs or property price to qualify for most loans = (gross monthly or annual income) x (0.28 or 0.36)

### Net Operating Income

The first thing you need to do is figure out your gross operating income to use the net operating income formula.

Once you have that figure, you subtract your operating expenses: things like insurance and maintenance costs.

However, you should note that things like property depreciation and interest payments do not factor into operating costs.

**Net Operating Income = Gross Operating Income – Total Operating Expenses**

### Return of Investment (ROI)

This formula allows you to see how much of your initial investment you can recoup annually.

**ROI = Annual Returns / Cost of Investment**

**Occupancy Rate**

This figure reflects the time that a property is rented out over a period of time. The occupancy rate is an important indicator of success. A low occupancy rate can let you know that action is needed from the end of the seller.

**Occupancy Rate = Number of Days Occupied / Total Number of Days in 1 Year**

**Break-Even Ratio**

This figure is often used to evaluate risk when making real estate investments. When using this formula, a figure that’s too high can indicate that it will be an uphill battle to break even with property and recoup debts.

**Break Even Ratio = (Debt Servicing Costs + Operating Expenses) / Gross Operating Income**

### Other Useful Real Estate Math Formulas

1 Acre = 43560 square feet

1 yard = 3 feet

Area of a rectangle or square (in square units, such as feet or acres) = (length) x (width)

Area of a triangle = (Base X Height) / 2

Area of a Trapezoid = ( First Base Length + Second Base Length ) x Height / 2

Perimeter = (side) + (side) + (side) + (side)

## Exam Practice Math Problems

The licensing exam may have a number of questions similar to the following examples below:

**Example Number 1: Calculating Transfer Taxes**

Sally plans to purchase Bob’s house for $320,000 in Sweetwater County. The County charges a recordation tax of $0.15 per $100 to a buyer and a grantor’s tax of $1.25 per $100 to a seller.

Calculate the transfer taxes for Sally and Bob.

** Answer:**

To solve items like this, we can first convert each rate to a decimal.

**Recordation Tax Rate = $.15/$100 = 0.0015**

**Grantor’s Tax Rate = $1.25/$100 = 0.0125**

Then, we multiply each number by the sales price:

**Recordation Tax = $320,000 x 0.0015 = $480**

**Grantor’s Tax = $320,000 x 0.0125 = $4,000**

Therefore, Sally pays $480 in taxes, and Bob pays $4,000 in taxes.

### Example Number 2: Listing Price and Commission

A client tells you he is willing to pay you a 5% commission as long as she nets $250,000 on her property sale. To comply with her request, what would be the minimum listing price?

**Answer:** $263,157.89

Solution: x = total value of property

x – 5%(x) = $250,000

100%(x) -5%(x) = $250,000

95%(x) = $250,000

0.95(x)= $250,000

0.95x÷0.95=$250,000÷0.95

x=$263,157.89

### Example Number 3: Net Proceeds

The sales price of a home was $180,000. The seller paid a 4% commission to a broker, then paid 1% of the sales price for fees and another $500 in miscellaneous fees. What were the net proceeds to the seller?

**Answer: **$170,500

**Solution**: Add up all expenses to get net costs

$180,000(4%)=$180,000(0.04)=$7,200

$180,000(1%)=$180,000(0.01)=$1,800

$7,200+$1,800+$500=$9,500 total seller costs

$180,000 – $9,500 = $170,500

### Example Number 4: Gross Rent Multiplier

Calculate the Gross Rent Multiplier given a $500,000 Property Price and $42,000 Gross Annual Rents.

**Answer:** GRM = 11.9

**Solution**: $500,000 / $42,000

## FAQs About Real Estate Math:

### Is There a Lot of Math Involved in Real Estate?

While you may not use real estate math in every single work day, it’s still crucial to show that you know what you are talking about when it comes down to the numbers, or else no one will think you’re a knowledgeable agent.

Knowing the terminologies are essential if you want to leave a good impression for your client.

A real estate agent has to make calculations often in a number of different areas – like knowing how to convert square feet are in an acre or how to find the annual gross rent multiplier. Real estate agents need to know how to do that.

### Is Real Estate Math Difficult?

Real estate agents would say that real estate math is by no means difficult, so it shouldn’t daunt you.

The key to conquering real estate math is to practice well enough to apply concepts to real estate situations correctly.

The more practice and time spent on understanding the challenging real estate math problems, the better you will excel not only in your exam but throughout your whole real estate career.

Being proficient at math and doing real estate math problems can help you stand out in your field and market, and ultimately a better agent.

### Can You Use a Calculator for the Real Estate Exam?

Of course. Financial and real estate calculators are allowed in most states, but they must be handheld, solar or battery-powered, and silent. Be sure to follow the guidelines for acceptable calculators.

Depending on where you are in the United States, whether or not you can bring your own calculator or if it will be provided by the examiner varies.

## Conclusion

Remember, nothing is tricky when it comes to real estate math; just practice, practice, practice. There’s no other way other than hard work and repetition.

By understanding both the real estate math formulas and concepts, you are already a step closer to getting every number correct and acing the real estate exam!

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