A licensee sells 5/6 of an acre for $28,000, and receives a 6% commission. If she splits with her broker 50-50, what did she receive per square foot?

5/6ths of an acre = (5 x 43,560 SF) / 6, or 36,300 SF. Her commission was (.06 x $28,000) x .50, or $840. $840 / 36,300 SF = $.023 / SF. Convert acreage to square feet first: five-sixths of an acre is 43,560 times five divided by six, or 36,300 SF. Net commission is price times rate times the split. Rate per SF is net commission divided by area, rounded to three decimals.

A developer wants to develop a 16-acre subdivision. He figures that the streets and common area will take up about 30% of this overall area. If the minimum lot size is to be 12,000 SF, how many lots can the developer have on this property?

The total area available for lots is 11.2 acres (16 acres x 70% for houses), or 487,872 SF (11.2 x 43,560). Dividing this area by 12,000 SF / lot = 40.66. Thus he can have a 40-lot subdivision. Subtract the common-area percentage from gross acreage, convert acres to square feet (acres times 43,560), then divide buildable area by the minimum lot size. Always round the result down to whole lots, since a partial lot cannot be built upon.

Maria plans to mulch the flower area around her house. The house measures 40' x 30', and she figures she'll mulch an area 8' in width to form a big rectangle all around the perimeter. What is the square footage of the resulting mulched area?

First figure the area to be mulched. If the home is 40 x 30, the flower area adds 8' to each side of the house. Thus the outside perimeter of the flowered area is (40+8+8) by (30+8+8), or 46' by 56'. The area of the flowered area is (46' x 56') minus the house area of 1,200 SF. This is 1,376 SF. Border area equals the outer rectangle minus the house. Add the border width twice to each house dimension: (40 + 16) by (30 + 16) equals 46 by 56. Subtract the 1,200 SF house to get the mulched area.

Yard of Pizza has a percentage lease on its 1,800 SF space in Lincoln Shops. The terms are $1.40 / SF / month rent plus 1.75% of the store's gross income. If monthly sales averaged $41,500 last year, how much annual rent did Yard of Pizza pay last year?

Their fixed rent is (1,800 SF x $1.40/SF) x 12 months, or $30,240. The percentage rent is ($41,500 x .0175) x 12, or $8,715. Total rent is ($30,240 + 8,715), or $38,955. Percentage lease rent has two parts. Fixed rent is the rate per SF per month times SF times 12. Percentage rent is the sales rate times monthly gross times 12. Add both components to find annual rent, rounded to whole dollars.

Seller Frank receives an offer of $290,000 on a property he listed at $308,000. How much is the offer as a percent of the listing price?

To find the percent of listing price the offer is, divide the offer by the listing price. In this question the offer is $290,000 and the listing price is $308,000. Percent of listing price equals the offer divided by the listing price, then moved to a percent. The listing price is always the base, or denominator. Here $290,000 divided by $308,000 is about 0.94, or 94%.

If gross income on a property is $75,000, net income is $30,000 and the cap rate is 8%, the value of the property using the income capitalization method is

Value = Income / Cap rate. Thus, V= $30,000 / .08 = $375,000. The income capitalization formula is value equals net operating income divided by the cap rate. Use net income, not gross, and write the cap rate as a decimal. Here $30,000 divided by 0.08 equals $375,000.

A property is being appraised by the cost approach. The appraiser estimates that the land is worth $80,000 and the replacement cost of the improvements is $350,000. Total depreciation from all causes is $54,000. What is the indicated value of the property?

Cost Approach formula: Land + (Cost of Improvements + Capital Additions – Depreciation) = Value. Thus you have $80,000 + ($350,000 - 54,000), or $376,000. The cost approach values land plus depreciated improvements. Add the land value to the replacement cost of improvements, then subtract total accrued depreciation. Land itself is never depreciated, so only the structure cost is reduced.

An apartment building that recently sold for $400,000 had monthly gross rent receipts of $3,200. What is its monthly gross rent multiplier?

Use the formula: GRM = Price / Monthly Rent. Thus, $400,000 / $3,200 = 125. The gross rent multiplier is sale price divided by gross monthly rent. Price always goes on top; rent is the divisor. Use the same rent period (monthly or annual) for every comparable. $400,000 divided by $3,200 equals 125.

Emily has an interest-only home equity loan at an annual interest rate of 5.3%. If her monthly payment is $790, how much is the loan's principal balance (to the nearest $1,000)?

The equation for the loan amount is (annual interest divided by the interest rate) = loan amount. Thus, ($1,580 x 12) / .053 = $357,736 or $358,000 rounded. For an interest-only loan, annual interest equals the monthly payment times 12. Principal equals annual interest divided by the annual rate expressed as a decimal. Round the answer to the nearest $1,000 when the question requests it.

A lender offers the Greys two alternative loan packages for their $60,000 home equity application. One option is an interest-only loan for 5 years @ 6.5% interest with no points, and the second, a 6.25% interest-only loan for 5 years with 1 point to be paid at closing. Which loan will cost the Greys less total interest, and by how much?

The first option's interest total is (6.5% x $60,000) x 5 years, or $19,500. The second option will charge (6.25% x $60,000) x 5 years, plus $600, or a total of $19,350. The 2nd option is $150 cheaper. Compare total cost for each option: interest equals rate times principal times years, plus points, where one point is 1% of the loan amount. Subtract the two totals to find the difference and which loan costs less.

Both options charge the same amount of interest.

Mack is buying Roy's house for $500,000. Mack's loan amount is $325,000. He has agreed to pay 1.5 points at closing. How much will Mack pay for points?

$325,000 x .015 = $4,875. Remember, one point = 1% of the loan amount. Points are charged on the loan amount, not the sale price. One point equals 1% of the loan, so 1.5 points is 1.5% of the loan. Here $325,000 times 0.015 equals $4,875.

Loan applicant Taylor has an annual gross income of $76,000. How much will a lender allow Taylor to pay for monthly housing expense to qualify for a loan if the lender uses an income ratio of 30%?

Monthly income qualification is derived by multiplying monthly income by the income ratio. Thus (76,000 / 12) x .30 = $1,900. Remember to first derive the monthly income. Qualifying housing expense equals monthly gross income times the lender's income ratio. Convert the annual salary to monthly by dividing by 12 first. Here $76,000 divided by 12 is $6,333, times 0.30 equals about $1,900.

A homeowner sold her house and had net proceeds of $265,000. Her adjusted basis in the home was $231,000. She immediately bought another house for $301,000. What was her capital gain?

Capital gain = amount realized (net sales proceeds, $265,000) - adjusted basis ($231,000) = ($34,000). Capital gain equals the amount realized, meaning net sale proceeds, minus the adjusted basis in the property. The price paid for a replacement home is irrelevant. Here $265,000 minus $231,000 equals a $34,000 gain.

A certain investor wants an 11% return on investment from any real estate investment. A property priced at $360,000 has gross income of $60,000 and expenses of $22,000. Approximately how much too high or too low is the price of this property for the investor to obtain her desired return exactly?

Use the same formula V = I / R where V is the price and R is the rate of return. Then plug in the numbers to solve for V. The NOI of this property is ($60,000 - $22,000), or $38,000. The return is 11%. Therefore, the value to get this return must be $38,000 / .11, or $345,455. Since the price is $360,000, the price exceeds the amount needed for an 11% return by approximately $15,000 ($360,000 - $345,455 = $14,545). To find the price that yields a target return, divide net operating income by the desired rate. NOI is gross income minus operating expenses. Compare that value with the asking price to see how far over or under it is.

A property has a net income of $150,000, interest payments of $105,000, principal payments of $30,000, and annual cost recovery of $7,000. The property's tax rate is 28%. What is the property's annual tax on income?

The basic formula for tax liability is: Taxable Income x Tax Rate = Tax Liability. Taxable Income is Net Operating Income - Interest Expense - Cost Recovery Expense. Therefore, the annual tax is $150,000 (NOI) - $105,000 (Interest Expense) - $7,000 (Cost Recovery Expense) x 28% = $10,640. Note that the principal payment is not deductible in calculating taxable income. Taxable income equals net operating income minus interest expense minus cost recovery (depreciation). Principal payments are never deductible. Multiply taxable income by the tax rate to get the annual tax liability.

A school district's tax rate is 10 mills. The school district's required revenue from taxes is $10,000,000. What is the tax base of the area?

The mill rate = (tax requirement / the tax base). A mill is one one-thousandth of a dollar ($.001). To solve for the tax base, reconfigure this formula to be: Base = Tax Requirement / Mill Rate. Thus the Base = $10,000,000 / .010, or $1,000,000,000. One mill is one-thousandth of a dollar, or $0.001, so 10 mills is 0.010. The tax base equals the required revenue divided by the mill rate written as a decimal. Here $10,000,000 divided by 0.010 equals $1,000,000,000.

A property has sold for $508,000. The listing agreement calls for a commission of 7%. The listing broker and selling broker agree to share the commission equally. What will the listing agent receive if the agent is scheduled to get a 40% share from his broker?

First calculate the total commission, then the co-brokerage splits, then the agent-broker split. Thus: $508,000 x 7% = $35,560 total commission. ($35,560 x 50%) = $17,780 total listing broker share. $17,780 x 40% = $7,112 agent's share. Work through the splits in order. Multiply the sale price by the commission rate for the total. Halve that for the listing broker's share, then multiply by the agent's split of the broker's side.

Alexis is buying Jack's house. The closing date (day belongs to seller) of the sale transaction is September 1 (day 244 of the year). Her loan has a monthly payment of $577.84, with $525 going to interest in the first month. At closing, Alexis must pre-pay interest for the period of Sept. 2-Sept. 30. Use the 365-day method for prorating. What is her prepaid interest amount?

If the buyer pays $525 interest for 30 days, the daily expense is ($525 / 30), or $17.50. If there are 29 days of pre-paid expense, the buyer's charge is ($17.50 x 29), or $507.50. Find the daily interest by dividing monthly interest by the days in the month, here $525 by 30 equals $17.50. Multiply by the number of prepaid days, counting from the day after closing through month end. Use the 365-day method when directed.

A home sells for $322,600 in Primm County. Here, transfer taxes are set at $1.00 per $500 of the sale price. Title insurance runs $450, and the attorney costs $550. The agent's commission is 7%, and the mortgage balance is $210,000. Annual real estate taxes are estimated to be $4,000, half of which will have to be charged to the seller. If the seller pays all of these expenses, what will she net at closing?

First calculate the transfer tax: ($322,600 / 500) = 645.2 units of $500. Round this up to 646, then multiply times $1.00 to get $646 transfer tax cost. Next figure the commission @ ($322,600 x .07), or $22,582. Next, the seller's real estate tax proration charge will be $2,000. Then, add up the expenses: ($646 transfer tax + 450 title + 550 attorney + 22,582 commission + 210,000 loan payoff + 2,000 tax proration) = $236,228. Subtracting this from the sale price = $86,372. Net proceeds equal sale price minus every seller cost: commission, transfer tax (round units up per $500 of price), title, attorney, mortgage payoff, and the seller's share of tax proration. Add the charges, then subtract from price.

The Uptons carry a $280,000 property insurance policy which covers 75% of the replacement cost of their insurable property, valued at $380,000. They have an 80% co-insurance requirement in the policy. If the family incurs a $300,000 loss, what if any amount will the Uptons recover?

Use the formula: (Percent of insurable property value carried / 80% replacement cost) x claim = recovery. Thus, (75% / 80% x $300,000) = $281,250. However, the face value of the policy is the maximum they can receive, which is $280,000. Coinsurance recovery equals insurance carried divided by required coverage, times the loss. Required coverage is the coinsurance percentage times the property's replacement value. The payout can never exceed the policy's face value.

ApexAgent Practice Questions

Real Estate Math Practice Questions

Real estate math on the exam is a small set of formulas used over and over: commission, proration, loan to value, percentage change and area. The 20 problems below are worked through step by step, with the formula stated and each wrong answer traced back to the mistake that produces it. Practice the setups and the arithmetic stops costing you points.

20 practice questions with answers and explanations. Written and reviewed by the ApexAgent team against the national exam content outline, updated 2026-10-04.

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What this topic tests

Convert acres to square feet with 43,560, and round lot counts down.
In income problems, net operating income over cap rate gives value.
Commission splits multiply in sequence: total, broker share, agent share.
Points are 1% of the loan amount, never of the sale price.
Prorate interest and taxes using the stated daily or 365-day method.
Mill rate is dollars of tax per dollar of value; convert mills to decimals.

Jump to a question

1. A licensee sells 5/6 of an acre for $28,000,
2. A developer wants to develop a 16-acre subdivision. He
3. Maria plans to mulch the flower area around her
4. Yard of Pizza has a percentage lease on its
5. Seller Frank receives an offer of $290,000 on a
6. If gross income on a property is $75,000, net
7. A property is being appraised by the cost approach.
8. An apartment building that recently sold for $400,000 had
9. Emily has an interest-only home equity loan at an
10. A lender offers the Greys two alternative loan packages
11. Mack is buying Roy's house for $500,000. Mack's loan
12. Loan applicant Taylor has an annual gross income of
13. A homeowner sold her house and had net proceeds
14. A certain investor wants an 11% return on investment
15. A property has a net income of $150,000, interest
16. A school district's tax rate is 10 mills. The
17. A property has sold for $508,000. The listing agreement
18. Alexis is buying Jack's house. The closing date (day
19. A home sells for $322,600 in Primm County. Here,
20. The Uptons carry a $280,000 property insurance policy which

20 real estate exam questions on this topic

Question 1 of 20
A licensee sells 5/6 of an acre for $28,000, and receives a 6% commission. If she splits with her broker 50-50, what did she receive per square foot?
- $.023 / SFCorrect answer
- $.046 / SF
- $.037/ SF
- $.002 / SF
Correct answer: A. $.023 / SF
Why: 5/6ths of an acre = (5 x 43,560 SF) / 6, or 36,300 SF. Her commission was (.06 x $28,000) x .50, or $840. $840 / 36,300 SF = $.023 / SF.
The rule: Convert acreage to square feet first: five-sixths of an acre is 43,560 times five divided by six, or 36,300 SF. Net commission is price times rate times the split. Rate per SF is net commission divided by area, rounded to three decimals.
Why the other options are wrong
- Uses the full $1,680 commission without halving it for the 50-50 split, nearly doubling the rate.
- Mixes the un-split commission with a rounded 45,000 square foot area, an inconsistent setup.
- Divides the halved commission by 435,600 square feet, treating the lot as ten acres.
Question 2 of 20
A developer wants to develop a 16-acre subdivision. He figures that the streets and common area will take up about 30% of this overall area. If the minimum lot size is to be 12,000 SF, how many lots can the developer have on this property?
- 42
- 487
- 40Correct answer
- 57
Correct answer: C. 40
Why: The total area available for lots is 11.2 acres (16 acres x 70% for houses), or 487,872 SF (11.2 x 43,560). Dividing this area by 12,000 SF / lot = 40.66. Thus he can have a 40-lot subdivision.
The rule: Subtract the common-area percentage from gross acreage, convert acres to square feet (acres times 43,560), then divide buildable area by the minimum lot size. Always round the result down to whole lots, since a partial lot cannot be built upon.
Why the other options are wrong
- Applies a 28% street deduction instead of 30%, leaving slightly more buildable area.
- Converts 11.2 acres to 487,872 SF but forgets to divide by the 12,000 SF lot size.
- Deducts 30% of one acre rather than 30% of all 16 acres, leaving 684,000 SF.
Question 3 of 20
Maria plans to mulch the flower area around her house. The house measures 40' x 30', and she figures she'll mulch an area 8' in width to form a big rectangle all around the perimeter. What is the square footage of the resulting mulched area?
- 64 SF
- 2,576 SF
- 1,824 SF
- 1,376 SFCorrect answer
Correct answer: D. 1,376 SF
Why: First figure the area to be mulched. If the home is 40 x 30, the flower area adds 8' to each side of the house. Thus the outside perimeter of the flowered area is (40+8+8) by (30+8+8), or 46' by 56'. The area of the flowered area is (46' x 56') minus the house area of 1,200 SF. This is 1,376 SF.
The rule: Border area equals the outer rectangle minus the house. Add the border width twice to each house dimension: (40 + 16) by (30 + 16) equals 46 by 56. Subtract the 1,200 SF house to get the mulched area.
Why the other options are wrong
- Reports only the 8 by 8 corner square (64 SF), not the whole border area.
- Uses the outer rectangle (46 by 56) without subtracting the 1,200 SF house footprint.
- Adds the 8 foot border once per side (48 by 38) and omits the house subtraction.
Question 4 of 20
Yard of Pizza has a percentage lease on its 1,800 SF space in Lincoln Shops. The terms are $1.40 / SF / month rent plus 1.75% of the store's gross income. If monthly sales averaged $41,500 last year, how much annual rent did Yard of Pizza pay last year?
- $38,955Correct answer
- $43,420
- $30,240
- $21,525
Correct answer: A. $38,955
Why: Their fixed rent is (1,800 SF x $1.40/SF) x 12 months, or $30,240. The percentage rent is ($41,500 x .0175) x 12, or $8,715. Total rent is ($30,240 + 8,715), or $38,955.
The rule: Percentage lease rent has two parts. Fixed rent is the rate per SF per month times SF times 12. Percentage rent is the sales rate times monthly gross times 12. Add both components to find annual rent, rounded to whole dollars.
Why the other options are wrong
- Double counts part of the percentage rent, pushing the total about $4,500 above correct.
- Reports only the fixed base rent, omitting the 1.75% percentage rent entirely.
- Subtracts the percentage rent from the fixed rent instead of adding the two together.
Question 5 of 20
Seller Frank receives an offer of $290,000 on a property he listed at $308,000. How much is the offer as a percent of the listing price?
- 87%
- 91%
- 94%Correct answer
- 106%
Correct answer: C. 94%
Why: To find the percent of listing price the offer is, divide the offer by the listing price. In this question the offer is $290,000 and the listing price is $308,000.
The rule: Percent of listing price equals the offer divided by the listing price, then moved to a percent. The listing price is always the base, or denominator. Here $290,000 divided by $308,000 is about 0.94, or 94%.
Why the other options are wrong
- Understates the share, as if the offer were divided by a base near $333,000.
- Misreads or drops a digit so the offer becomes about $280,000, lowering the ratio.
- Inverts the ratio, dividing the listing price by the offer instead of offer by listing.
Question 6 of 20
If gross income on a property is $75,000, net income is $30,000 and the cap rate is 8%, the value of the property using the income capitalization method is
- $625,000
- $375,000Correct answer
- $3,750,000
- $937,500
Correct answer: B. $375,000
Why: Value = Income / Cap rate. Thus, V= $30,000 / .08 = $375,000.
The rule: The income capitalization formula is value equals net operating income divided by the cap rate. Use net income, not gross, and write the cap rate as a decimal. Here $30,000 divided by 0.08 equals $375,000.
Why the other options are wrong
- Uses gross income against a higher rate, dividing $75,000 by about 12%, not net by 8%.
- Slips a decimal in the cap rate, dividing net income by 0.008 instead of 0.08.
- Divides gross income, $75,000, by 8% instead of using the $30,000 net income.
Question 7 of 20
A property is being appraised by the cost approach. The appraiser estimates that the land is worth $80,000 and the replacement cost of the improvements is $350,000. Total depreciation from all causes is $54,000. What is the indicated value of the property?
- $296,000
- $456,000
- $324,000
- $376,000Correct answer
Correct answer: D. $376,000
Why: Cost Approach formula: Land + (Cost of Improvements + Capital Additions – Depreciation) = Value. Thus you have $80,000 + ($350,000 - 54,000), or $376,000.
The rule: The cost approach values land plus depreciated improvements. Add the land value to the replacement cost of improvements, then subtract total accrued depreciation. Land itself is never depreciated, so only the structure cost is reduced.
Why the other options are wrong
- Subtracts depreciation from improvements but forgets to add the $80,000 land value.
- Adds the $80,000 land value twice, once on each side of the calculation.
- Reverses both signs, subtracting land and adding depreciation back to the improvement cost.
Question 8 of 20
An apartment building that recently sold for $400,000 had monthly gross rent receipts of $3,200. What is its monthly gross rent multiplier?
- 80
- 0.01
- 110
- 125Correct answer
Correct answer: D. 125
Why: Use the formula: GRM = Price / Monthly Rent. Thus, $400,000 / $3,200 = 125.
The rule: The gross rent multiplier is sale price divided by gross monthly rent. Price always goes on top; rent is the divisor. Use the same rent period (monthly or annual) for every comparable. $400,000 divided by $3,200 equals 125.
Why the other options are wrong
- Uses the wrong divisor, roughly $5,000 per month, so the multiplier comes out far too low.
- Inverts the formula, dividing monthly rent by price instead of price by rent.
- Divides by a slightly higher rent near $3,600 rather than the $3,200 gross rent.
Question 9 of 20
Emily has an interest-only home equity loan at an annual interest rate of 5.3%. If her monthly payment is $790, how much is the loan's principal balance (to the nearest $1,000)?
- $444,000
- $358,000Correct answer
- $190,000
- $292,000
Correct answer: B. $358,000
Why: The equation for the loan amount is (annual interest divided by the interest rate) = loan amount. Thus, ($1,580 x 12) / .053 = $357,736 or $358,000 rounded.
The rule: For an interest-only loan, annual interest equals the monthly payment times 12. Principal equals annual interest divided by the annual rate expressed as a decimal. Round the answer to the nearest $1,000 when the question requests it.
Why the other options are wrong
- Uses a rate near 4.3% instead of 5.3%, inflating the computed principal balance.
- Treats $790 as the monthly interest with a rounded 5% rate, roughly halving the balance.
- Uses a 6.5% rate instead of 5.3%, which reduces the computed principal balance.
Question 10 of 20
A lender offers the Greys two alternative loan packages for their $60,000 home equity application. One option is an interest-only loan for 5 years @ 6.5% interest with no points, and the second, a 6.25% interest-only loan for 5 years with 1 point to be paid at closing. Which loan will cost the Greys less total interest, and by how much?
- The first option, by $150.
- The second option, by 150.Correct answer
- The second option, by $750.
- Both options charge the same amount of interest.
Correct answer: B. The second option, by 150.
Why: The first option's interest total is (6.5% x $60,000) x 5 years, or $19,500. The second option will charge (6.25% x $60,000) x 5 years, plus $600, or a total of $19,350. The 2nd option is $150 cheaper.
The rule: Compare total cost for each option: interest equals rate times principal times years, plus points, where one point is 1% of the loan amount. Subtract the two totals to find the difference and which loan costs less.
Why the other options are wrong
- Reverses which loan is cheaper; the second option wins once the point is counted.
- Counts only the rate savings (about $750) and ignores the $600 point paid at closing.
- Calls the totals equal, ignoring both the rate difference and the point charged.
Question 11 of 20
Mack is buying Roy's house for $500,000. Mack's loan amount is $325,000. He has agreed to pay 1.5 points at closing. How much will Mack pay for points?
- $450
- $4,500
- $4,875Correct answer
- $7,500
Correct answer: C. $4,875
Why: $325,000 x .015 = $4,875. Remember, one point = 1% of the loan amount.
The rule: Points are charged on the loan amount, not the sale price. One point equals 1% of the loan, so 1.5 points is 1.5% of the loan. Here $325,000 times 0.015 equals $4,875.
Why the other options are wrong
- Misplaces a decimal, applying 1.5% to about $30,000 rather than the $325,000 loan.
- Applies roughly 0.9% to the $500,000 price instead of 1.5% of the loan amount.
- Computes 1.5% of the $500,000 sale price instead of the $325,000 loan amount.
Question 12 of 20
Loan applicant Taylor has an annual gross income of $76,000. How much will a lender allow Taylor to pay for monthly housing expense to qualify for a loan if the lender uses an income ratio of 30%?
- $2,160
- $1,900Correct answer
- $1,215
- $4,433
Correct answer: B. $1,900
Why: Monthly income qualification is derived by multiplying monthly income by the income ratio. Thus (76,000 / 12) x .30 = $1,900. Remember to first derive the monthly income.
The rule: Qualifying housing expense equals monthly gross income times the lender's income ratio. Convert the annual salary to monthly by dividing by 12 first. Here $76,000 divided by 12 is $6,333, times 0.30 equals about $1,900.
Why the other options are wrong
- Applies a ratio above 30%, roughly 34%, to the monthly income figure.
- Applies 30% to income after subtracting about a third for assumed taxes.
- Uses the 70% complement of the 30% ratio, grossly overstating the allowance.
Question 13 of 20
A homeowner sold her house and had net proceeds of $265,000. Her adjusted basis in the home was $231,000. She immediately bought another house for $301,000. What was her capital gain?
- $265,000
- $36,000
- $34,000Correct answer
- None
Correct answer: C. $34,000
Why: Capital gain = amount realized (net sales proceeds, $265,000) - adjusted basis ($231,000) = ($34,000).
The rule: Capital gain equals the amount realized, meaning net sale proceeds, minus the adjusted basis in the property. The price paid for a replacement home is irrelevant. Here $265,000 minus $231,000 equals a $34,000 gain.
Why the other options are wrong
- Reports the net sale proceeds without subtracting the adjusted basis at all.
- Uses the difference between the new house price and proceeds (301,000 minus 265,000).
- Assumes buying a replacement home erases the gain, which the basis rule does not allow.
Question 14 of 20
A certain investor wants an 11% return on investment from any real estate investment. A property priced at $360,000 has gross income of $60,000 and expenses of $22,000. Approximately how much too high or too low is the price of this property for the investor to obtain her desired return exactly?
- $1,000 overpriced.
- $8,000 underpriced.
- $15,000 overpriced.Correct answer
- $16,000 underpriced.
Correct answer: C. $15,000 overpriced.
Why: Use the same formula V = I / R where V is the price and R is the rate of return. Then plug in the numbers to solve for V. The NOI of this property is ($60,000 - $22,000), or $38,000. The return is 11%. Therefore, the value to get this return must be $38,000 / .11, or $345,455. Since the price is $360,000, the price exceeds the amount needed for an 11% return by approximately $15,000 ($360,000 - $345,455 = $14,545).
The rule: To find the price that yields a target return, divide net operating income by the desired rate. NOI is gross income minus operating expenses. Compare that value with the asking price to see how far over or under it is.
Why the other options are wrong
- Rounds the small income shortfall (about $1,600) and reports it as a price gap.
- Reverses the direction and misstates the gap, calling the price below the required value.
- Flips the sign to underpriced and rounds the roughly $14,500 gap up to $16,000.
Question 15 of 20
A property has a net income of $150,000, interest payments of $105,000, principal payments of $30,000, and annual cost recovery of $7,000. The property's tax rate is 28%. What is the property's annual tax on income?
- $14,550
- $40,040
- $10,640Correct answer
- $2,240
Correct answer: C. $10,640
Why: The basic formula for tax liability is: Taxable Income x Tax Rate = Tax Liability. Taxable Income is Net Operating Income - Interest Expense - Cost Recovery Expense. Therefore, the annual tax is $150,000 (NOI) - $105,000 (Interest Expense) - $7,000 (Cost Recovery Expense) x 28% = $10,640. Note that the principal payment is not deductible in calculating taxable income.
The rule: Taxable income equals net operating income minus interest expense minus cost recovery (depreciation). Principal payments are never deductible. Multiply taxable income by the tax rate to get the annual tax liability.
Why the other options are wrong
- Adds the $7,000 cost recovery instead of subtracting it, raising taxable income to $52,000.
- Omits the interest deduction, taxing nearly the whole $150,000 net income at 28%.
- Deducts the $30,000 principal payment too, lowering taxable income to $8,000.
Question 16 of 20
A school district's tax rate is 10 mills. The school district's required revenue from taxes is $10,000,000. What is the tax base of the area?
- $10,000,000
- $100,000,000
- $1,000,000,000Correct answer
- $100,000,000,000
Correct answer: C. $1,000,000,000
Why: The mill rate = (tax requirement / the tax base). A mill is one one-thousandth of a dollar ($.001). To solve for the tax base, reconfigure this formula to be: Base = Tax Requirement / Mill Rate. Thus the Base = $10,000,000 / .010, or $1,000,000,000.
The rule: One mill is one-thousandth of a dollar, or $0.001, so 10 mills is 0.010. The tax base equals the required revenue divided by the mill rate written as a decimal. Here $10,000,000 divided by 0.010 equals $1,000,000,000.
Why the other options are wrong
- Reports the tax revenue itself as the base, skipping the division entirely.
- Treats 10 mills as 0.1 rather than 0.010, dividing by ten times too much.
- Shifts the mill conversion one place, using 0.0001 instead of 0.010.
Question 17 of 20
A property has sold for $508,000. The listing agreement calls for a commission of 7%. The listing broker and selling broker agree to share the commission equally. What will the listing agent receive if the agent is scheduled to get a 40% share from his broker?
- $17,780
- $14,224
- $10,668
- $7,112Correct answer
Correct answer: D. $7,112
Why: First calculate the total commission, then the co-brokerage splits, then the agent-broker split. Thus: $508,000 x 7% = $35,560 total commission. ($35,560 x 50%) = $17,780 total listing broker share. $17,780 x 40% = $7,112 agent's share.
The rule: Work through the splits in order. Multiply the sale price by the commission rate for the total. Halve that for the listing broker's share, then multiply by the agent's split of the broker's side.
Why the other options are wrong
- Stops at the listing broker's half of the commission, omitting the agent's 40% split.
- Applies the 40% agent split to the whole commission, skipping the 50-50 broker division.
- Uses a 30% agent split instead of 40%, lowering the listing agent's share.
Question 18 of 20
Alexis is buying Jack's house. The closing date (day belongs to seller) of the sale transaction is September 1 (day 244 of the year). Her loan has a monthly payment of $577.84, with $525 going to interest in the first month. At closing, Alexis must pre-pay interest for the period of Sept. 2-Sept. 30. Use the 365-day method for prorating. What is her prepaid interest amount?
- $507.50Correct answer
- $525.00
- $543.10
- $558.58
Correct answer: A. $507.50
Why: If the buyer pays $525 interest for 30 days, the daily expense is ($525 / 30), or $17.50. If there are 29 days of pre-paid expense, the buyer's charge is ($17.50 x 29), or $507.50.
The rule: Find the daily interest by dividing monthly interest by the days in the month, here $525 by 30 equals $17.50. Multiply by the number of prepaid days, counting from the day after closing through month end. Use the 365-day method when directed.
Why the other options are wrong
- Charges a whole month of interest rather than the 29 days actually prepaid.
- Inverts the proration, multiplying monthly interest by 30/29 instead of taking 29 of 30 days.
- Prorates the full $577.84 payment instead of the $525 interest portion.
Question 19 of 20
A home sells for $322,600 in Primm County. Here, transfer taxes are set at $1.00 per $500 of the sale price. Title insurance runs $450, and the attorney costs $550. The agent's commission is 7%, and the mortgage balance is $210,000. Annual real estate taxes are estimated to be $4,000, half of which will have to be charged to the seller. If the seller pays all of these expenses, what will she net at closing?
- $86,873
- $88,371
- $81,372
- $86,372Correct answer
Correct answer: D. $86,372
Why: First calculate the transfer tax: ($322,600 / 500) = 645.2 units of $500. Round this up to 646, then multiply times $1.00 to get $646 transfer tax cost. Next figure the commission @ ($322,600 x .07), or $22,582. Next, the seller's real estate tax proration charge will be $2,000. Then, add up the expenses: ($646 transfer tax + 450 title + 550 attorney + 22,582 commission + 210,000 loan payoff + 2,000 tax proration) = $236,228. Subtracting this from the sale price = $86,372.
The rule: Net proceeds equal sale price minus every seller cost: commission, transfer tax (round units up per $500 of price), title, attorney, mortgage payoff, and the seller's share of tax proration. Add the charges, then subtract from price.
Why the other options are wrong
- Charges the seller only $1,500 of the annual tax instead of half, lifting net by about $500.
- Drops the seller's $2,000 real estate tax proration, overstating the net by that amount.
- Deducts roughly $5,000 too much in seller charges, pushing the net proceeds too low.
Question 20 of 20
The Uptons carry a $280,000 property insurance policy which covers 75% of the replacement cost of their insurable property, valued at $380,000. They have an 80% co-insurance requirement in the policy. If the family incurs a $300,000 loss, what if any amount will the Uptons recover?
- $319,999
- $281,250
- $280,000Correct answer
- $375,000
Correct answer: C. $280,000
Why: Use the formula: (Percent of insurable property value carried / 80% replacement cost) x claim = recovery. Thus, (75% / 80% x $300,000) = $281,250. However, the face value of the policy is the maximum they can receive, which is $280,000.
The rule: Coinsurance recovery equals insurance carried divided by required coverage, times the loss. Required coverage is the coinsurance percentage times the property's replacement value. The payout can never exceed the policy's face value.
Why the other options are wrong
- Inverts the coinsurance fraction, using 80 over 75 instead of 75 over 80.
- Reports the coinsurance formula result but ignores the $280,000 policy face-value cap.
- Divides the loss by 80% instead of applying the coinsurance fraction to it.

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Real Estate Math: frequently asked

How do I convert mills to a dollar amount for tax problems?

A mill is one-thousandth of a dollar, or $0.001. So 10 mills equals $0.010, and 25 mills equals $0.025. Multiply the assessed value by the mill rate as a decimal to get the tax, and divide the required revenue by that rate to find the tax base.

What is the formula for finding a property's value by income capitalization?

Value equals net operating income divided by the capitalization rate. Use net income after operating expenses, never gross income, and write the rate as a decimal. Multiply value by the cap rate to check income, or divide income by the rate to get value.

How do I figure commission splits on the real estate exam?

Start with the sale price times the commission rate to get the total. Split that between the brokers as the agreement states, often 50-50. Then apply the individual agent's share of their broker's portion. Multiply each percentage in order, do not add them first.

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