# Real Estate Math Questions & Cheat Sheet (May 2024) 50+

Math Practice Exam

1 / 50

Judy is considering buying a lakefront property. She learns that a property there just sold for \$550,000 and had frontage on the lake totaling 550 feet. About how much did the property sell per front foot?

2 / 50

A house was sold for \$355,000 which was 8% more than the original cost of the house. What was the original cost of the house? (Round to the nearest cent)

3 / 50

Mr. Wilson is looking for a new home. His gross income is \$7,000 a month and he has no idea what he can afford as he's just moved across the state. He finds four homes he likes, each varying in price. The first home he likes costs \$800 a month. The second, \$1,000 a month, the third \$2,225 a month, and the fourth \$2,500 a month. All of the home costs are total housing costs (PITI). Utilizing the 28/36 rule, which of the following houses would Mr. Wilson most likely be able to afford?

4 / 50

If a bank makes a 90% loan on a house valued at \$88,500, how much cash is required at closing in the form of a down deposit if the buyer has already paid \$4,000 in earnest money?

5 / 50

What is the annual interest rate on a \$10,000 loan that requires a semiannual interest payment of \$450?

6 / 50

What is the price per square front foot for a 50' wide x 100' long lot that sold for \$75,000?

7 / 50

A house sells for \$280,000 in West Philadelphia. The commission check is handed to the broker which is \$16,800. What was the percentage the broker received for this transaction?

8 / 50

An agent lists a seller's house for 6% commission. The final sales price for the home is \$555,000. How much commission did the seller actually pay?

9 / 50

Jean buys a property and closes on March 1st. The seller prepaid the properties semi-annual taxes of \$1,800. How much does Jean owe the seller in real estate taxes?

10 / 50

What is the interest rate on a \$200,000 loan that requires an annual interest payment of \$8,000?

11 / 50

Tina agrees to list her property on the condition that she will receive at least \$47,300 after paying a 5% broker's commission and paying \$1,150 in closing costs. At what price must the property sell for (round to nearest dollar if needed)?

12 / 50

What is the annual interest rate on a \$80,000 loan that requires a semiannual interest payment of \$1,000?

13 / 50

A house sells for \$330,000 in Albany New York. The commission check is handed to the broker which is \$17,325. What was the percentage the broker received for this transaction?

14 / 50

A property's market value is \$250,000. The assessment rate for the house is 15% with 27.50 mills. Find the annual property taxes.

15 / 50

Assuming there are no extra fees, and the broker is representing the buyer and the seller, what was the final sales price of a property if the commission rate was 6% and the broker received \$24,000.

16 / 50

A property's market value is \$450,000. The assessment rate for the house is 25% with 70.50 mills. Find the annual property taxes.

17 / 50

Jon buys a property and closes on March 1st. The seller prepaid the properties annual taxes of \$6,000 for the year. How much does Jon owe the seller in real estate taxes?

18 / 50

An agent is going to receive a 50% share of a 3% gross commission. The property sold for \$350,000. How much commission will the agent receive?

19 / 50

A lot purchased 25 years ago for \$40,000 has appreciated a total of 45% since its purchase. What is it worth today?

20 / 50

A lot purchased 10 years ago for \$55,000 has appreciated a total of 15% since its purchase. What is it worth today?

21 / 50

Gina buys a property in a suburb of Houston. The seller prepaid the properties quarterly taxes of \$750. How much does Gina owe the seller in real estate taxes if she closes on March 1st?

22 / 50

A house sells for \$2,500,000 in Morgantown, West Virginia. The commission check is handed to the broker which is \$137,500. What was the percentage the broker received for this transaction?

23 / 50

An agent lists a seller's house for 5% commission. The final sales price for the home is \$255,000. How much commission did the seller actually pay?

24 / 50

A home you listed sells for \$500,000. In the transaction your broker receives 3% of the sales price and you receive 75% of their check. How much commission do you receive in this transaction?

25 / 50

Find the annual GRM. A 9-unit building in Cleveland Ohio, with an asking price of \$2,000,000 and gross annual rents of \$105,000 (Round the nearest hundredth).

26 / 50

What is the price per square front foot for a 100' wide x 125' long lot that sold for \$125,000?

27 / 50

What is the annual interest rate on a \$300,000 loan that requires a monthly interest payment of \$500?

28 / 50

A property's market value is \$400,000. The assessment rate for the house is 25% with 22.75 mills and a \$30,000 property tax deduction. Find the annual property taxes.

29 / 50

A house was sold for \$275,000 which was 9% less than the original cost of the house. What was the original cost of the house? (Round to the nearest cent)

30 / 50

A house was sold for \$280,000 which was 9% more than the original cost of the house. What was the original cost of the house? (Round to the nearest cent)

31 / 50

Find the annual GRM. A 10-unit building in Dallas Texas, with an asking price of \$5,000,000 and gross annual rents of \$225,000 (Round the nearest hundredth).

32 / 50

Blake bought his home 5 years ago for \$115,000. He sold his home last month for \$145,000. What is the annual rate of appreciation?

33 / 50

The value of a property is \$180,000 today. What was the original cost of the property if it has lost 20% of its value over the past three years?

34 / 50

Melissa agrees to list her property on the condition that she will receive at least \$75,000 after paying a 6% broker's commission and paying \$2,000 in closing costs. At what price must the property sell for (round to nearest dollar if needed)?

35 / 50

A property's market value is \$500,000. The assessment rate for the house is 25% with 55.75 mills and a \$25,000 property tax deduction. Find the monthly property taxes.

36 / 50

The value of a property is \$91,000 today. What was the original cost of the property if it has lost 35% of its value over the past five years?

37 / 50

What is the interest rate on a \$150,000 loan that requires an annual interest payment of \$6,500?

38 / 50

A lot purchased 5 years ago for \$100,000 has appreciated a total of 10% since its purchase. How much per year did the property appreciate for?

39 / 50

A property's market value is \$2,250,000. The assessment rate for the house is 15% with 28.55 mills. Find the annual property taxes. (Round to the nearest cent)

40 / 50

A lot in a subdivision is being sold for \$5.00 per square foot. It is 100 feet wide and 120 feet deep. How much does the lot cost?

41 / 50

Roger bought his home 10 years ago for \$175,000. He sold his home last month for \$275,000. What is the annual rate of appreciation?

42 / 50

Cameron agrees to list his property on the condition that he will receive at least \$150,000 after paying a 6% broker's commission and paying \$2,500 in closing costs. At what price must the property sell for (round to nearest dollar if needed)?

43 / 50

Timothy agrees to list his property on the condition that he will receive at least \$100,000 after paying a 5% broker's commission and paying \$2,500 in closing costs. At what price must the property sell for (round to nearest dollar if needed)?

44 / 50

A lot in a subdivision costs \$300,000. It is 100 feet wide and 150 feet deep. How much is the price per square foot?

45 / 50

Newton buys a property and closes on September 1st. The seller prepaid the properties annual taxes of \$2,000 for the year. How much does Newton owe the seller in real estate taxes? (Round if necessary to the nearest cent)

46 / 50

A property's market value is \$750,000. The assessment rate for the house is 25% with 23.50 mills. Find the annual property taxes.

47 / 50

Masons gross income is \$10,250 a month. To qualify for most loans, what is the maximum monthly house payment Mason can make (using the 28/36 rule)?

48 / 50

Find the annual GRM. A 6-unit building in Buffalo New York, with an asking price of \$850,000 and gross annual rents of \$55,000 (Round the nearest hundredth).

49 / 50

Robin bought her home 5 years ago for \$190,000. She sold her home last month for \$199,000. How much did the house appreciate?

50 / 50

A home you listed sells for \$465,000. In the transaction your broker receives 6% of the sales price and you receive 55% of their check. How much commission do you receive in this transaction?

Real estate math is incredibly important not only for the real estate exam but for your real estate career. Understanding real estate math and doing real estate math problems can not only give you an advantage when you become an agent; but make the real estate exam much easier!

## How Much Math Is On The Real Estate Exam?

Regardless of what state you are taking your real estate exam in, there will be real estate math. It’s a fact; real estate math will show up. It’s hard to give you an exact number since every state varies. However, on average, our data suggest that anywhere between 5 to 20 math questions are on each state’s real estate exam

Since 5 to 20 questions can be a large margin, it’s best to be as prepared as possible, especially since every right question is as equally as important as the next on the real estate exam.

### How Much Math Will I Use As A Real Estate Agent?

Is there a lot of math in real estate? While you may not use real estate math every day as an agent, it’s essential to know what you are talking about. The worst thing an agent can do is come off as uneducated or underprepared. Things like knowing how many square feet are in an acre, or how to find annual GRM, is critical, and agents do need to know how to do that.

### Is Real Estate Math Difficult?

Real estate math is by no means difficult, but practice is needed to be able to apply the concepts correctly. Trust me, I understand. Math, in general, can be frightening, but real estate math is one of those things that, after a nice amount of practice, becomes much easier. And yes, you can use a calculator on the real estate exam in most states! So don’t worry too much about the arithmetic.

And…. of course, luckily for you, we put together this guide on real estate math to make your life much easier!

## Real Estate Math Definitions

The most important factor in understanding real estate math is to learn the words that go along with it. And guess what? By far, the most substantial chunk of the real estate exam is the vocabulary and definitions. By understanding both, you are already a step closer to acing the exam and understanding real estate math!

Here is a list of real estate math definitions that are essential for both obtaining your real estate license and taking the real estate exam.

• Amortization – Amortization is when payments divide into equal amounts for the duration of the loan.
• Ad valorem – The Latin phrase ad valorem means “according to value.”
• Appraisal – An appraisal is an estimate of approximate worth of something.
• Appreciation – Appreciation is any gain in the value of a property over time from any cause.
• Capitalization – Capitalization is the conversion of assets or income into capital.
• Capitalization rate – Cap rate is used to indicate the rate of return that is expected to be generated on a property.
• Cetris Paribus – A Latin phrase meaning “other things equal” or in plain terms all things remaining constant.
• Commission – A commission is a fee paid to an agent for performing a transaction.
• Debt – Something owed or promised.
• Depreciation – Depreciation is any loss in the value of a property over time from any cause.
• Discount points – Discount points also known as mortgage points are prepaid interest.
• Double net lease – “Double” means two additional costs will be added to your base rent. Usually, taxes and insurance costs are added to the monthly lease payment.
• Equity – Equity is the difference between the market value of your home and the amount you owe the lender who holds the mortgage.
• Escrow – Escrow is a way for money and property to be transferred from one party to another through the use of 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.
• Gross rent multiplier – 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. More specifically its a measure of the value of an investment property that is obtained by dividing the property’s sale price by its gross annual rental income.
• Interest – money paid or owed regularly at a particular rate.
• Investment – An investment is the legal purchase of something that is not consumed today but will be in the future to create profit.
• Market value or market price – The actual selling price of the property. So if your home sells for \$200,000. Its market value is \$200,000.
• Mill rate – The mill rate is the amount of tax payable per dollar of the assessed value of a property. Mill rate is also known as the millage rate.
• Net listing – A net listing is when an agent agrees to sell an owner’s property for a set minimum price. Anything over the minimum price belongs to the agent as commission.
• Net operating income – The total income of a property minus all operating expenses.
• Property tax – Property tax is a real estate ad-valorem tax, calculated by the local government, which is paid by the owner of the property. The tax is usually based on the value of the owned property.
• Principal – The amount borrowed (such as the face value of a debt security).
• Tax rate – The tax rate is the designated rate the government taxes a person, business, or entity.
• Triple net lease – “Triple” means three additional costs will be added to your base rent. Usually, taxes, insurance, and maintenance are all added to the monthly lease payment.

For a more extensive list, here is our full list of real estate terms & definitions.

Understanding real estate math formulas are as equally as important as learning your definitions. With many math formulas, it’s best to practice yourself, but we’ll get to that later— this a full list of real estate math formulas in their most basic form. For more on each one, keep scrolling down below.

## Real Estate Math Formulas

### Simple Interest Formula

Interest = (principal amount) x (rate of interest) (time)

### Commission Formula

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

### Gross Rent Multiplier Formulas

Gross Rent Multiplier = (property price) / (gross rental income)

Annual Gross Rental Income = (monthly rental income) x (12)

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

Housing costs to qualify for most loans= (gross monthly or annual income) x (.28 or .36)

### 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.

### Other Useful Real Estate Math Formulas

1 Acre = 43560 square feet

Area (ft2) = (length ft) x (width ft)

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

#### Commission

Most, if not all, real estate agents make money through commission. A commission is a fee paid to an agent for performing a transaction. A commission is usually a percentage of the property’s selling price, although sometimes it can be a flat fee.

As many of you know, agents are licensed salespersons who work under a broker. Agents cannot work independently, and therefore are prohibited from being paid a commission directly by consumers. Brokers, on the other hand, are able to work independently. So it’s worth noting, that all commission must be paid directly to the broker, then the broker splits the commission with his/her agents.

Normally real estate agents represent a buyer or a seller. So when it comes down to commission splits, it is split among all appropriate parties. Those parties include listing agents, their brokers, the buyer’s agent, and their broker too. But it all depends on the agreement the agent has with the broker.

For our sake (as well as what shows up on the real estate exam), we will be doing traditional commission splits. The formula for finding commission in a traditional commission split is pretty simple, just times whatever percentage you have by the total price of the house.

So for example: If you sell a house for \$200,000 with a commission of 5%, the total commission would be \$10,000. From there with that \$10,000, it is then divided accordingly. That part, as mentioned before, varies.

It’s also important to note that the fee comes out of the cost of the home; it is not an additional fee. So, for example, if you sell that house for \$200,000, the buyer still pays \$200,000, then the seller just subtracts the commission from the total. So the seller takes home \$190,000.

#### Gross Rent Multiplier

Gross Rent Multiplier 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. More specifically, its a measure of the value of an investment property that is obtained by dividing the property’s sale price by its gross annual rental income.

Gross rent multiplier is used in valuing commercial real estate. The issue with gross rent multiplier is it is a limited rough measure in that it does not consider the cost of factors such as utilities, taxes, maintenance, and vacancies. It is useful for comparing and selecting investment properties where depreciation and numbers are similar.

The gross rent multiplier calculation is easy. All you have to worry about is property price, gross rental income, and the GRM itself. The formula is Gross Rent Multiplier = Property Price / Gross Rental Income. Here is an example.

Let’s say you have the following information:

a 4-unit building with an asking price of \$200,000 and gross annual rents of \$24,000. Utilizing the formula, we can take the property price and divide it by the annual rental income.

So it would be: \$200,000/\$24,000 which = 8.33. So your GRM is 8.33

It’s also important to note the exam may try and throw you off and tell you the monthly gross rental income, rather than the annual. For that, just convert it (by multiplying by 12). So if the property had a monthly rental income of \$2,000, times that by 12, giving you an annual income of \$24,000. Then just treat the rest of the problem like before!

Lastly, if you haven’t figured it out already – Gross Rent Multiplier is the number of years the property would take to pay for itself in gross received rent. So in almost all cases, real estate investors want a lower Gross Rent Multiplier.

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

The 28/36 Rule states: that 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. Lenders typically want no more than 28% of your gross monthly income to go toward your housing expenses, including your mortgage payment, property taxes, and insurance. Once you add in monthly payments on other debt, the total shouldn’t exceed 36% of your gross income. If your debt-to-income ratio exceeds these limits on a house, you may not be able to get a loan, or you may have to pay a higher interest rate.

An example is if a woman wants to buy her first home. Her gross income is \$4500 a month or \$54,000 a year. According to the 28/36 rule, she would need to spend less than \$1260 in housing costs a month to qualify for most loans. All you do is multiply .28 by her monthly income. This is useful for agents to work with clients to determine what loans they can qualify. Remember 28/36.

#### Discount Points

Discount points, also known as mortgage points, are prepaid interest. If you (a borrower) want a lower monthly payment and have enough money to purchase some discount points, it’s not a bad idea.

Points can be expensive, and they are separate from a borrower’s down deposit. So if a borrower takes out a \$100,000 loan at 7% interest and puts \$15,000 down and buys two discount points. You would have to pay all that and an additional lump sum for the points.

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 level.

It’s usually a good rule of thumb to purchase discount points if the homeowner is going to own the house for more than ten years, as generally around that many years you break even.

Lastly, remember the percentage comes off the interest. So you’re not getting 0.25% off that \$100,000 you’re getting 0.25% off that 7%, which lowers your monthly payment.

#### Calculating Property Tax, Assessed Value, and Mill or Millage Rate

Property Tax, Assessed Value, and Millage Rate typically come hand and hand, and understanding each one is crucial to understanding all three. Property tax is one of the most common real estate math problems you’ll see on the real estate exam.

Property tax is a real estate ad-valorem tax, which is paid by the owner of the property. All ad valorem taxes are based on the determined value of the item being taxed. In order to find a property tax rate, you must multiply the assessed value with the mill rate.

The assessed value needs to be found before you can compute property tax. The assessed value is found by multiplying the assessment rate by the current market value.

The mill rate or millage rate is the amount of tax payable per dollar of the assessed value of a property. The term “millage” is derived from the Latin word “millesimum,” meaning “thousandth,” with 1 mill being equal to 1/1,000th of a currency unit. As used in relation to property tax, 1 mill is equal to \$1 in property tax.

So in order to find the property tax rate: you need the assessed value and the mill rate. In order to find assessed value: you need the assessment rate and market value. Lastly, and luckily with mill rates in most real estate math problems, you will almost always be given the rate. If not, all you have to do is convert, which is as simple as multiplying by a decimal.

Once you have all three, you can calculate your property tax! Here is an example:

So let’s say we own a house that has a market value of 100,000. Its assessment rate, which is established by the local government, is 10%. We would then take 10% of \$100,000, which is \$10,000; this is our assessed value. This means that \$10,000 is how much our property is worth (for taxation purposes).

Now let’s say our local tax rate is 50 mills, which means it’s \$50 per every \$1000 or .05 or 5%. As we established earlier, our property has a tax assessed value of \$10,000 in order to find out the final tax rate all you have to do is multiply your assessed value by .05. So 10,000\$ times .05 gives us 500\$. So our property taxes would be 500\$ a year.

#### Calculating Property Tax Deductions

States vary in property tax rates and deductions very as well. Widows, legally blind people, service members, and other particular groups get deductions; this aspect varies from state to state. For example, legally blind people get a \$1,000 deduction in Connecticut but only get a \$500 deduction in Florida. Although your state sets statewide property tax rules, your local government handles the administration and levying of the tax. So do your research or contact your local tax assessor for complete details on property tax exemptions.

Calculating property tax deductions is not too bad if you understand how to calculate regular property tax. All that is added is one more step! That one step is before you calculate your final tax rate, you have to subtract the deduction from the assessed value. Here is an example:

*For this example, we’ll be utilizing some generic numbers for the deductions to show you how the process works. These numbers are not accurate, so make sure to find out your state and local deduction numbers afterward.

A property’s market value is \$280,000. The assignment rate for the house is 30%, with 27.86 mills. The homeowner qualifies for the widow tax exemption (\$1,000). Find the annual property taxes.

\$1,312.38

\$2,312.38

\$2,340.24

\$2,540.24

First things first is our assessed value. Remember how to find that? Simple. \$280,000 times .3 which is \$84,000. Our new assessed value… Here is where those exemptions come in. Since the homeowner has the widow tax exemption we have to subtract \$1,000 from \$84,000. Which is \$83,000. Lastly, we have to convert our mills through division by 1000. Which gives us 0.02786. Finally, we can multiply our converted mill rate by the new (new) assessed value. So 0.02786 times \$84,000 which gives us \$2,312.38 as our final answer.

Remember find out your state rates for deductions and practice up and you’ll be a master at property tax problems.

#### Proration

Proration is the allocation or division of money items at the closing. Proration mainly comes into play when a seller prepays their home taxes for the year. Since they paid for the full year and are selling it, the buyer will then owe the seller the remaining months of taxes. The easiest way to break this down is by an example.

This is a common question you’ll see on the real estate exam.

Marissa buys a property and closes on July 1st. The seller prepaid the property’s annual taxes of \$2000 for the year. How much does Marrissa owe the seller in real estate taxes?

The first thing you want to look for is any terms specifying when, terms like annual, monthly, or quarterly. Since the seller paid the annual taxes, we know it’s based on the year. So the first thing we do is divide \$2000 by 12, which is \$166.67. Which is the seller’s monthly real estate tax. From there, we look at what month closing occurs in. They closed in July. This means Marissa owes the seller for the months of July, August, September, October, November, and December. Which is a total of 6 months. So from there, all we do is multiply \$166.67 by 6, which equals out nicely at \$1,000.

Meaning Marissa owes the seller \$1,000 in real estate taxes.

Now that we’ve covered pretty much everything you need to know you may be thinking what is the best place to get started?

### Real Estate Math Practice Questions

Well, luckily for you, you are already in the right place! We offer fully comprehensive real estate practice exams filled with real estate math problems.

We even have a section dedicated to real estate math located at the top of this guide.

### 35 Math Questions on the Real Estate Exam

We also have a detailed video questions review. Make sure to check that out here:

Oh and before you go! Here is our printable math cheat sheet. The cheat sheet has definitions and formulas so it’s perfect to study with:

Print that out and make sure to take it on the go, that way you can be as prepared as possible.

Practice your little heart out, and if for some reason you are still struggling, look into our real estate exam prep course down below, which comes with videos covering every aspect of the exam (including real estate math).

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