 # Real Estate Math - Practice Questions, Exam Tips, and Formulas

by The CE Shop Team

## How Do Real Estate Agents Use Math?

If you want to become a real estate agent, you'll need to understand basic math concepts to successfully complete the real estate exam and calculate day-to-day transactions in real life. The following are instances in which real estate agents need to know math:

• Real estate exam
• Determining square footage
• Estimating lot size and property setbacks
• Calculating listing prices
• Figuring simple interest rates
• Evaluating loan-to-value ratios
• Computing commission

## How to Prepare for Math on the Real Estate Exam

While details vary by state, you can generally expect to encounter between 150 and 200 multiple choice questions on the real estate exam. Of those, roughly 10-15% involve math, which translates to between 15 and 30 questions per exam.

One of the best ways you can prepare for the real estate exam is to identify your areas of strength and those that require more intentional studying.

Although your immediate goal is to pass the real estate license exam, nailing each topic also creates a firm foundation on which you can build your new career as a real estate agent. A few sample math questions are provided below along with answers and explanations to give you an idea of what to expect.

### Real Estate Math Practice Questions

1. Solve for the annual Gross Rent Multiplier (GRM) for a four-unit apartment building in Indianapolis, IN, with an asking price of \$300,000 and gross annual rents of \$25,000, rounded to the nearest hundredth.
1. 12
2. 22
3. 20
4. 22

Explanation: Gross Rent Multiplier measures the value of an investment property. Using the formula: GRM = Property Price/Gross Annual Rental Income (where GRM is the ratio of the original real estate investment price to its yearly rental income). GRM doesn't include expenses, such as utilities, insurance, and property taxes. In this case, the equation is 300,000/25,000 = 12.

2. An agent represented both the seller and the buyer in a real estate transaction. Assuming there were no additional fees, find the sales price of the home if the commission was 6% and the agent received \$24,000.
1. \$14,400
2. \$144,000
3. \$1,440
4. \$400,000

Explanation: The formula for finding the commission on a property sale is Rate X Purchase Price = Total Commission. In this case, you have the rate and the commission, so you need to divide the Total Commission by the Rate to get the Purchase Price.

Once you convert 6% to a decimal (6% = 6/100 = .06), the formula looks like this:

24,000/.06=Purchase Price

Purchase Price =\$400,000.

3. A rental property has an income of \$1,500 per month. If the closing date is September 20th, how much rent is owed to the buyer? Use a 30-day calculation method.
1. \$50
2. \$200
3. \$500
4. \$4,500

Explanation: If the closing date is the 20th, that leaves 10 days' worth of rent owed to the buyer.

First, divide the total rent by the total number of days to find the daily rent, as follows:

1,500/30 days=\$50.

Simply multiply the daily rent by the 10 remaining days to arrive at the answer:

50 X 10=\$500.

Pro Tip: For more real estate math problems and non-math-related exam practice questions, check out The CE Shop's intuitive online real estate Exam Prep study program to help you ace your exam. Exam Prep Edge begins by allowing you to take an initial assessment. Once completed, you receive feedback on which topics you've mastered and the ones you should revisit.

## Common Real Estate Math Terms

The following are some of the terms you'll see regularly as a real estate agent.

### Amortization

In terms of loan repayment, amortization refers to spreading out fixed payments over a specific time period until the loan is paid off. While the monthly repayment amount remains the same, the ratio of principal (the original loan amount) and interest changes throughout the life of the loan. At the beginning of the loan term, most of the payment is applied to interest. As the loan's paid down, however, payments gradually shift to paying more on the principal than the interest.

### Assessed Value

The assessed value is the value of a property assigned to determine property taxes. A tax appraiser considers the area's comparable properties to calculate the fair market value for a property. The assessed value is then calculated as a percentage of the appraised value.

### Annual Interest

Also known as the annual percentage rate (APR), annual interest is the interest you pay on a loan over the course of a year. Written as a percentage, an APR includes costs and fees related to the loan. Home loans, for example, typically include processing, underwriting, appraisal, and origination fees.

### Capitalization Rate

Formula: Capitalization Rate = Net Operating Income / Cost of the Property (Current Asset Value of the Property)

Commercial investors use a capitalization rate ( or “cap rate”) to determine if a property is a good investment. The Net Operating Income (NOI) is the expected annual rental income minus all managing expenses, including taxes, property management, and lawn maintenance — though it doesn't include loan costs. Typically, lower cap rates represent high-value properties and lower risk.

Example:

A buyer paid \$1,300,000 cash for a property, and it generates \$150,000 annually in rent collection. Its taxes are \$20,000/year, leaving \$130,000 NOI.

\$130,000/\$1,300,000=10% cap rate

### Commission Rate

Typically calculated as 6% of the sales price, the commission is paid by the seller to the selling agent for services rendered. The selling agent then splits that 6% with the buying agent according to their agreement. Both agents also pay their Brokers as per their agreements.

### Decimal

The literal meaning of decimal is 'based on 10'. Used with a decimal point, it's any real number that's expressed in base 10. Where the decimal point is placed on the number changes its value significantly. For example, \$210.56 is quite different from \$21,056.00.

### Depreciation

The reduction in value of an asset over time.

### Discount Points

Fees the buyer pays directly to the lender at closing in exchange for a reduced interest rate. One point costs 1% of the total amount borrowed, or \$1,000 for every \$100,000 borrowed. Each discount point reduces the interest rate by approximately 1/8 of 1%.

### Down Payment

The amount of money paid up front on a loan. If a buyer wants to purchase a \$200,000 home and the lender requires a 20% down payment, the funds needed would be \$200,000 X 0.20 = \$40,000.

### Fraction

A number that represents a part of the whole. The top number is the numerator, and the bottom is called the denominator. Examples of fractions are ½, ¾, and 2/3.

### Gross Income

The amount of money earned before taxes and deductions are taken out.

### Gross Rent Multiplier (GRM)

GRM is a quick screening tool investors use to determine if the property offers a good return. Calculated using the formula GRM=Price/Gross Annual Rent, GRM doesn't include taxes or insurance.

Example:

A property that costs \$225,000 and generates \$26,400 in annual income has an 8.52 GRM.

\$225,000/\$26,400=8.52 GRM.

Using this formula tells the investor that it could take 8 ½ years to recoup the purchase price. Typically, the lower the number, the better the investment.

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

An assessment of risk that lenders evaluate before approving a mortgage. Individuals with low LTV ratios usually represent less risky borrowers, andqualify for lower interest rates as a result. They may have large down payments and more invested equity in the home. Borrowers with high LTV ratios are usually considered riskier investments, and they’ll probably pay higher interest rates and be required to buy mortgage insurance if they qualify for a loan.

### Market Value

This figure describes how much money the property would likely fetch in the current competitive market.

### Net Operating Income (NOI)

NOI is the profitability of a commercial property after the gross operating expenses are subtracted from the gross income. It represents the available cash flow generated by the property.

### Principal Amount

This term refers to the original face value of the money borrowed.

### Proration

Proration is the proportional distribution of property ownership expenses between all relevant parties. A closing statement proration could include interest, insurance, rent, taxes, and assessments.

### Sales Price

The sales price is the actual price the buyer paid for the property. It may or may not be the same as the asking or listed price.

## Real Estate Math Formulas Every Agent Needs to Know

The following are some common real estate math formulas that will be useful to you on the exam and in day-to-day operations as a real estate agent.

### Fractions, Decimals, and Percentages

Before launching into the formulas, take a little conversions refresher. We discuss fractions to decimals and percentages; decimals to percentages; and percentages to decimals below.

Converting decimals to percentages: The word percent means out of 100 (per = out of; cent = 100). For example, if you want to convert 0.2 to a percentage, move the decimal to the hundredths position, which is two places to the right.

0.20

0.20 X 100

20%

Convert percentages to decimals: Remove the % sign and divide the value by 100.

35%

35/100

.35

Alternately, you can simply remove the % sign and move the decimal over two places to the left:

63%

.63

Convert fractions to decimals: Divide the numerator (the number on top) by the denominator (the number on the bottom).

Simple fraction: Numerator/denominator = quotient (decimal)

Example: in the fraction 3/8, 3 is the numerator and 8 is the denominator.

3/8 = 0.375

Mixed fraction: In the mixed fraction example of 1¾, the initial 1 is the whole number, and the 3 in the fraction is the numerator while the 4 is the denominator.

First, change the mixed fraction to an improper fraction, so the numerator is greater than the denominator:

Multiply the whole number by the denominator: 1 X 4 = 4

Add the result of step 1 to the numerator: 4 + 3 = 7

Divide the result of step 2 by the denominator: 7/4 = 1.75

1¾ = 1.75

Convert fractions to percentages: To write a fraction as 'out of 100,' you first need to convert it to an equivalent fraction.

Multiply the numerator and denominator by the same number:

¾ X 25

3 X 25 = 75

4 X 25 = 100

75/100

Convert 75 out of 100 to a percentage = 75%

¾ = 75%

What if the denominator isn't a multiple of 100?

In the fraction 7/8, for example, 8 isn't a multiple of 100.

Simply revisit how to convert a simple fraction to a decimal: 7/8 = 0.875

Move the decimal two places to the right, where the hundredth column is, to arrive at 87.5%:

7/8 = 87.5%

## Common Formulas

### Simple Interest Formula

Simple Interest (SI) = Principal X Interest Rate X Time Period

Example:

\$10,000 borrowed at 5% interest for 5 years.

SI = 10,000 X .05 X 5; SI = \$2,500.

The total amount due in five years on a loan of \$10,000 at 5% interest is \$12,500.

### Gross Rent Multiplier Formula

Gross Rent Multiplier = Property Price / Gross Annual Rental Income

\$1,000,000/60,000 = 16.67

GRM = 16.67

### Loan-to-Value Ratio Formula

LTV Ratio = Mortgage Amount / Appraised Property Value

### Property Tax Formula

Taxes = Assessed Value X Tax Rate

While every jurisdiction is different, tax assessors generally use a tax rate calculated per \$1,000 of assessed value.

Example:

If a property's assessed value is \$345,000, and the tax rate is \$2.10 per \$100, you can find the tax amount as follows:

Taxes = \$345,000 X \$2.10/\$100

Taxes = \$345,000 X 0.021

Taxes = \$7,245

### Discount Points Formula

\$100,000 X .01 (1%) = \$1,000 for each discount point

## Is Becoming a Real Estate Agent the Right Career For You?

Whether you're looking to build your own massive real estate practice or you just want to help others find a new home, the benefits are the same for everyone. In real estate, you get to be your own boss, set your own schedule, work part-time if you choose, directly reap the rewards of your labor, and most importantly help people make their dream of homeownership come true — which, as it turns out, is also a very important and useful financial decision. As a real estate professional, you get to build your dreams and the dreams of others. Don’t wait, let’s get this party started — enroll in your first Pre-Licensing course today!