Real Estate Exam Math Questions and Answers

Real estate exam math questions are rarely difficult because of advanced mathematics. They are challenging because they combine percentages, prorations, commissions, loan calculations, area measurements, and real estate vocabulary under time pressure.

The most effective approach is to identify the formula, write down the known numbers, convert percentages into decimals, and check whether the answer is reasonable before moving on.

Essential Real Estate Math Formulas

Percentage

[
\text{Part}=\text{Whole}\times\text{Rate}
]

To convert a percentage to a decimal, move the decimal point two places to the left:

• 5% = 0.05
• 6.5% = 0.065
• 12% = 0.12

Commission

[
\text{Commission}=\text{Sales Price}\times\text{Commission Rate}
]

If the commission is divided among multiple parties, calculate the total commission first, then apply each party’s share.

Loan-to-Value Ratio

[
\text{LTV}=\frac{\text{Loan Amount}}{\text{Property Value}}\times100
]

Equity

[
\text{Equity}=\text{Property Value}-\text{Loan Balance}
]

Simple Interest

[
\text{Interest}=\text{Principal}\times\text{Rate}\times\text{Time}
]

Time must be expressed in years. For example, six months equals 0.5 years.

Proration

[
\text{Daily Amount}=\frac{\text{Annual Amount}}{\text{Number of Days in the Proration Period}}
]

The exam may specify a 360-day financial year or a 365-day calendar year. Use the method stated in the question.

Area

For a rectangle:

[
\text{Area}=\text{Length}\times\text{Width}
]

For a triangle:

[
\text{Area}=\frac{\text{Base}\times\text{Height}}{2}
]

Because one acre contains 43,560 square feet:

[
\text{Acres}=\frac{\text{Square Feet}}{43,560}
]

Real Estate Exam Math Questions and Answers

Question 1: Commission on a Sale

A property sells for $425,000. The total commission is 6%. What is the total commission?

Solution:

[
\$425,000\times0.06=\$25,500
]

Answer: $25,500

If the commission is split equally between the listing brokerage and selling brokerage:

[
\$25,500\div2=\$12,750
]

Each brokerage receives $12,750 before any internal split with its affiliated licensee.

Question 2: Licensee’s Share of a Commission

A brokerage receives $18,000 from a transaction. The affiliated salesperson receives 70% of the brokerage’s share. How much does the salesperson receive?

Solution:

[
\$18,000\times0.70=\$12,600
]

Answer: $12,600

Do not apply the 70% split to the sales price. The split applies to the amount received by the brokerage.

Question 3: Finding the Sales Price from a Commission

A broker earns $21,000 from a 5% commission. What was the sales price?

Solution:

[
\text{Sales Price}=\frac{\$21,000}{0.05}
]

[
\text{Sales Price}=\$420,000
]

Answer: $420,000

When the commission amount is known but the sales price is missing, divide rather than multiply.

Question 4: Loan-to-Value Ratio

A buyer purchases a home for $360,000 and obtains a $288,000 mortgage. What is the loan-to-value ratio?

Solution:

[
\text{LTV}=\frac{\$288,000}{\$360,000}\times100
]

[
\text{LTV}=80\%
]

Answer: 80%

The down payment is:

[
\$360,000-\$288,000=\$72,000
]

The down payment percentage is 20%, which complements the 80% LTV.

Question 5: Calculating the Loan Amount

A lender offers an 80% loan-to-value mortgage on a property valued at $515,000. What is the loan amount?

Solution:

[
\$515,000\times0.80=\$412,000
]

Answer: $412,000

The buyer’s equity or down payment is:

[
\$515,000-\$412,000=\$103,000
]

Question 6: Equity

A property is worth $640,000. The owner owes $397,500 on the mortgage and $22,500 on a home equity loan. What is the owner’s equity?

Solution:

[
\text{Total Debt}=\$397,500+\$22,500=\$420,000
]

[
\text{Equity}=\$640,000-\$420,000=\$220,000
]

Answer: $220,000

Include all liens specified in the question. Equity is not calculated by subtracting only the first mortgage if other debts are secured by the property.

Question 7: Discount Points

A lender charges 2.25 discount points on a $280,000 loan. How much do the points cost?

One point equals 1% of the loan amount. Therefore:

[
\$280,000\times0.0225=\$6,300
]

Answer: $6,300

Points are calculated from the loan amount, not the property’s sales price. Mortgage points are a form of prepaid interest; tax treatment depends on the circumstances and applicable federal rules.

Question 8: Simple Interest

A buyer borrows $250,000 at 6% simple annual interest for nine months. How much interest accrues?

Convert nine months to years:

[
\frac{9}{12}=0.75
]

Then calculate:

[
\$250,000\times0.06\times0.75=\$11,250
]

Answer: $11,250

A common mistake is using 9 instead of 0.75 for the time period.

Question 9: Monthly Interest

A loan balance is $180,000, and the annual interest rate is 7%. What is one month’s interest?

First calculate annual interest:

[
\$180,000\times0.07=\$12,600
]

Then divide by 12:

[
\$12,600\div12=\$1,050
]

Answer: $1,050

This calculation gives the interest portion only. It does not include principal, taxes, insurance, mortgage insurance, or other loan charges.

Question 10: Property Tax Proration

Annual property taxes are $7,300. Closing occurs on April 1, and the seller is responsible for January 1 through March 31. Use a 365-day year. How much does the seller owe?

The seller’s period is 90 days:

[
\$7,300\div365=\$20\text{ per day}
]

[
\$20\times90=\$1,800
]

Answer: $1,800

If the seller has already paid the full year’s taxes, the buyer may credit the seller for the buyer’s future period. If taxes are unpaid, the seller may be debited for the seller’s share. Always determine who is being charged and whether the item is prepaid or unpaid.

Question 11: Rent Proration

Monthly rent is $2,400. Closing takes place on the 11th day of a 30-day month. The buyer is entitled to rent beginning on the day of closing. How much rent belongs to the buyer?

The buyer owns or receives the rent for 20 days, assuming the buyer’s period begins on day 11:

[
\$2,400\div30=\$80\text{ per day}
]

[
\$80\times20=\$1,600
]

Answer: $1,600

Proration questions may differ depending on whether the closing day belongs to the buyer or seller. Follow the convention provided in the question.

Question 12: Area of a Lot

A rectangular lot measures 150 feet by 200 feet. How many square feet does it contain?

[
150\times200=30,000\text{ square feet}
]

Answer: 30,000 square feet

To convert to acres:

[
30,000\div43,560\approx0.689\text{ acres}
]

Approximate answer: 0.69 acres

Question 13: Price per Square Foot

A 2,400-square-foot home sells for $456,000. What is the price per square foot?

[
\$456,000\div2,400=\$190
]

Answer: $190 per square foot

Do not confuse the home’s total square footage with the lot size. The question must identify which measurement is being used.

Question 14: Capitalization Rate

An investment property produces net operating income of $48,000 per year and is valued at $600,000. What is the capitalization rate?

[
\text{Cap Rate}=\frac{\text{NOI}}{\text{Value}}
]

[
\frac{\$48,000}{\$600,000}=0.08
]

[
0.08\times100=8\%
]

Answer: 8%

Net operating income generally excludes debt service and income taxes. Carefully distinguish NOI from cash flow before taxes.

Question 15: Value from NOI and Capitalization Rate

A property produces $72,000 in annual NOI, and comparable properties indicate a 9% capitalization rate. What is the estimated value?

[
\text{Value}=\frac{\text{NOI}}{\text{Cap Rate}}
]

[
\$72,000\div0.09=\$800,000
]

Answer: $800,000

Always convert the cap rate to a decimal before dividing.

Question 16: Gross Rent Multiplier

A property sells for $540,000 and produces $4,500 in monthly rent. What is the gross rent multiplier?

Using monthly gross rent:

[
\text{GRM}=\frac{\$540,000}{\$4,500}=120
]

Answer: 120

If the question gives annual rent, use annual rent consistently. Do not divide a sales price by monthly rent in one problem and compare the result with a multiplier based on annual rent.

Question 17: Transfer Tax

A state imposes a transfer tax of $1.10 per $500 of the sales price. The property sells for $350,000. What is the transfer tax?

Number of $500 units:

[
\$350,000\div\$500=700
]

Transfer tax:

[
700\times\$1.10=\$770
]

Answer: $770

When a tax is stated as a dollar amount per $500 or per $1,000, divide the transaction amount by that unit before multiplying by the tax rate.

Question 18: Seller’s Net Proceeds

A seller receives $525,000 for a property. The mortgage payoff is $284,000, the commission is 5.5%, and other seller expenses total $8,750. What are the seller’s net proceeds?

Commission:

[
\$525,000\times0.055=\$28,875
]

Total deductions:

[
\$284,000+\$28,875+\$8,750=\$321,625
]

Net proceeds:

[
\$525,000-\$321,625=\$203,375
]

Answer: $203,375

The mortgage payoff is a dollar amount, not a percentage. Read each expense carefully before calculating.

Question 19: Buyer’s Cash Required at Closing

A buyer purchases a $400,000 home with a 75% loan. The buyer must pay $6,000 in closing costs and has already deposited $8,000 in earnest money. How much additional cash is needed, assuming no other credits?

Down payment:

[
\$400,000\times0.25=\$100,000
]

Total buyer funds needed:

[
\$100,000+\$6,000=\$106,000
]

Subtract earnest money already deposited:

[
\$106,000-\$8,000=\$98,000
]

Answer: $98,000

The general structure is:

[
\text{Cash to Close}=\text{Down Payment}+\text{Buyer Costs}-\text{Deposits}-\text{Credits}
]

Actual settlement statements may include additional adjustments, prepaid items, lender credits, seller credits, and loan-related charges. The Consumer Financial Protection Bureau’s Loan Estimate and Closing Disclosure materials identify cash to close and itemized closing-cost categories.

Question 20: Depreciation Basis

An investor buys a rental property for $500,000. The land is valued at $125,000. What amount is generally used as the depreciable building basis before other adjustments?

[
\$500,000-\$125,000=\$375,000
]

Answer: $375,000

Land is not depreciable for federal income tax purposes. Certain acquisition costs may affect basis, while loan-related costs may receive different treatment; tax questions should be answered according to the rules and facts stated in the exam problem.

How to Solve Exam Math Problems Efficiently

1. Identify the question’s target

Determine whether the problem asks for:

• A percentage
• A dollar amount
• A loan amount
• A sales price
• A commission
• A proration
• A rate
• A value
• A square-foot measurement

Many wrong answers result from calculating the right numbers but answering a different question.

2. Write the formula before entering numbers

For example, if the problem asks for a cap rate, write:

[
\text{Cap Rate}=\frac{\text{NOI}}{\text{Value}}
]

This prevents reversing the numerator and denominator.

3. Convert percentages immediately

Write 6% as 0.06, 80% as 0.80, and 2.5% as 0.025. This simple habit prevents a large number of errors.

4. Track units

Label figures as:

• Dollars
• Months
• Days
• Years
• Square feet
• Acres
• Percentages

A calculation involving annual rent should not be mixed with a monthly multiplier unless the problem specifically requires a conversion.

5. Estimate before calculating

If a 6% commission applies to a $400,000 sale, the answer should be close to $24,000. An answer of $2,400 or $240,000 signals a decimal-place error.

6. Use the stated convention

Real estate exams may specify:

• 360-day year
• 365-day year
• 12 equal months
• Whether the closing day belongs to the buyer or seller
• Whether a month is treated as 30 days
• Whether the answer should be rounded

Never substitute a preferred convention for the one provided.

Common Real Estate Math Mistakes

Confusing sales price and loan amount

Commission is usually based on the sales price, while discount points are based on the loan amount. Read the wording carefully.

Forgetting to divide annual figures

To find monthly interest, monthly rent, or monthly taxes, annual figures generally must be divided by 12.

Misreading “per”

A tax of $2 per $1,000 is not 2%:

[
\$2\div\$1,000=0.002=0.2\%
]

Reversing prorations

First identify who owes the money and which days belong to that party. Then calculate the daily amount.

Adding debt instead of subtracting it

Debt reduces equity and seller proceeds:

[
\text{Equity}=\text{Value}-\text{Debt}
]

Rounding too early

Keep several decimal places during intermediate calculations. Round only when the final answer requires it.

Using the wrong basis for a percentage

A percentage may apply to the:

• Sales price
• Loan amount
• Assessed value
• Annual rent
• Brokerage commission
• Net operating income

The phrase immediately before the percentage often identifies the correct base.

Practical Study Strategy

Create a formula sheet containing the following:

• Commission
• LTV
• Equity
• Simple interest
• Prorations
• Area and acreage
• Cap rate
• Gross rent multiplier
• Loan points
• Seller net proceeds
• Buyer cash to close

Then practice each formula with several variations. Change the numbers, reverse the question, and practice identifying the unknown. For example, do not practice only calculating a commission; also practice finding the sales price when the commission is known.

Use a timed approach once the formulas become familiar. Complete straightforward percentage and commission questions first, mark lengthy problems for review, and return to them after answering the questions you can solve quickly.

LeapRealEstate.com can also be a helpful next step for structured real estate education, exam preparation, and additional practice as you build speed and confidence with calculation-based questions.

Final Exam-Day Checklist

Before submitting an answer, ask:

• Did I convert every percentage to a decimal?
• Did I use the correct base amount?
• Did I distinguish annual, monthly, and daily figures?
• Did I follow the stated proration convention?
• Did I include every lien or expense mentioned?
• Did I round only at the end?
• Does the answer make practical sense?
• Did I answer what the question actually asked?

Real estate exam math becomes manageable when each problem is reduced to a recognizable formula. Focus on identifying the correct base, maintaining consistent units, and checking the result for reasonableness.

Authoritative Sources

• [Internal Revenue Service — Real Estate Tax, Mortgage Interest, Points, and Other Property Expenses]
• [Consumer Financial Protection Bureau — Compare Loan Estimates]
• [Internal Revenue Service — Rental Expenses]
• [Consumer Financial Protection Bureau — TILA-RESPA Integrated Disclosure Guide]