Real Estate Math Practice Test

25 practice questions

Choose an answer, then check it under Show answer.

1. Question 1 of 25Medium

   A seller agrees to sell a property for $320,000. The listing agreement specifies a 5% commission to the broker, and the seller must pay $8,000 in additional closing costs. What is the net amount the seller will receive after all deductions?

   1. AA. $304,000
   2. BB. $296,000
   3. CC. $312,000
   4. DD. $288,000
   Show answer to question 1

   Answer: B. $296,000

   First, subtract the commission: 5% of $320,000 = $16,000, so $320,000 − $16,000 = $304,000. Then subtract closing costs: $304,000 − $8,000 = $296,000 net to seller.

   Why the other options are wrong

   • A$304,000 is the amount after commission but before deducting closing costs.
   • C$312,000 results from subtracting only the $8,000 closing costs and omitting the commission.
   • D$288,000 results from incorrectly deducting a 10% commission ($32,000) and omitting the $8,000 closing costs.

2. Question 2 of 25Medium

   Maya bought a condominium for $240,000 and later sold it for $276,000. After paying $9,600 in selling costs, what was Maya's percentage of profit on her original cost?

   1. AA. A 12.0% profit
   2. BB. A 15.0% profit
   3. CC. An 11.0% profit
   4. DD. A 10.0% profit
   Show answer to question 2

   Answer: C. An 11.0% profit

   Selling proceeds after costs are $276,000 − $9,600 = $266,400. The net profit is $26,400, and $26,400 ÷ $240,000 = 0.11, or 11.0%.

   Why the other options are wrong

   • AA 12.0% profit would require a $28,800 net gain.
   • BA 15.0% profit is the result before deducting the $9,600 selling costs.
   • DA 10.0% profit would be only $24,000, not the $26,400 net gain.

3. Question 3 of 25Easy

   A real estate agent measures a rectangular room that is 15 feet long and 12 feet wide. The area of the room is calculated by:

   1. AA. multiplying the length by the width and dividing by 2
   2. BB. dividing the length by the width
   3. CC. multiplying the length by the width
   4. DD. adding the length and width, then multiplying by 2
   Show answer to question 3

   Answer: C. multiplying the length by the width

   Area of a rectangle is found by multiplying its length by its width. For a 15 ft by 12 ft room, area = 15 × 12 = 180 square feet.

   Why the other options are wrong

   • AMultiplying length by width and dividing by 2 gives the area of a triangle, not a rectangle.
   • BDivision of length by width gives a ratio, not the area.
   • DThis formula gives the perimeter, not the area.

4. Question 4 of 25Medium

   A seller wants to net $185,000 from the sale of their home. The existing mortgage payoff is $112,500, closing costs are estimated at $3,500, and the listing broker charges a 6% commission. What is the minimum sale price required to achieve this net amount, rounded to the nearest whole dollar?

   1. AA. $320,213
   2. BB. $316,489
   3. CC. $322,070
   4. DD. $319,060
   Show answer to question 4

   Answer: A. $320,213

   To calculate the required sales price, add the desired net proceeds, mortgage payoff, and closing costs ($185,000 + $112,500 + $3,500 = $301,000), then divide by the complement of the commission rate (100% − 6% = 94%, or 0.94), yielding $320,213. Multiplying $301,000 by 1.06 produces $319,060, which is incorrect because the commission is calculated as a percentage of the total final sale price, not the subtotal of the expenses.

   Why the other options are wrong

   • BOmitting closing costs gives ($185,000 + $112,500) ÷ 0.94 = $316,489.36, rounded to $316,489. This leaves the seller short of the desired net after paying the $3,500 closing costs.
   • CThis price exceeds the minimum: $322,070 × 0.94 − $112,500 − $3,500 = $186,745.80 in net proceeds. It provides $1,745.80 more than required, rather than finding the minimum sale price.
   • DAdding 6% to the subtotal gives $301,000 × 1.06 = $319,060. This incorrectly bases the commission on the subtotal instead of the final sale price.

5. Question 5 of 25Hard

   An apartment building has $6,500 in monthly gross potential rent, an 8% vacancy and collection loss rate, and operating expenses equal to 35% of effective gross income. The property just sold for $800,000. Using annual gross potential rent, what are its gross rent multiplier (GRM) and capitalization rate? Round both answers to two decimal places.

   1. AA. GRM 12.31, cap rate 6.10%
   2. BB. GRM 9.80, cap rate 5.50%
   3. CC. GRM 10.26, cap rate 5.83%
   4. DD. GRM 10.67, cap rate 6.25%
   Show answer to question 5

   Answer: C. GRM 10.26, cap rate 5.83%

   Annual gross potential rent = $6,500 × 12 = $78,000. Annual GRM = sale price ÷ annual gross potential rent = $800,000 ÷ $78,000 ≈ 10.26. Effective gross income = $78,000 × (1 − 0.08) = $71,760. Operating expenses = $71,760 × 0.35 = $25,116. Net operating income (NOI) = $71,760 − $25,116 = $46,644. Capitalization rate = NOI ÷ sale price = $46,644 ÷ $800,000 = 0.058305 = 5.8305%, rounded to 5.83%.

   Why the other options are wrong

   • AThe annual GRM rounds to 10.26, not 12.31. The capitalization rate based on $46,644 NOI and the $800,000 sale price rounds to 5.83%, not 6.10%.
   • BThe annual GRM rounds to 10.26, not 9.80. The capitalization rate based on $46,644 NOI and the $800,000 sale price rounds to 5.83%, not 5.50%.
   • DThe annual GRM rounds to 10.26, not 10.67. The capitalization rate based on $46,644 NOI and the $800,000 sale price rounds to 5.83%, not 6.25%.

6. Question 6 of 25Medium

   A commercial property is purchased for $1,170,000. The land value is estimated at 20% of the purchase price. Using straight-line depreciation over 39 years, what is the accumulated depreciation after 7 years?

   1. AA. $120,000
   2. BB. $168,000
   3. CC. $240,000
   4. DD. $210,000
   Show answer to question 6

   Answer: B. $168,000

   Only the building can be depreciated; land is not depreciable. Building value is $1,170,000 × 80% = $936,000. Annual depreciation is $936,000 ÷ 39 = $24,000. After 7 years, accumulated depreciation is $24,000 × 7 = $168,000.

   Why the other options are wrong

   • AThis corresponds to only 5 years of correct depreciation, possibly from using the wrong number of years.
   • CThis corresponds to 10 years of correct depreciation, an overestimate of the time period.
   • DThis results from depreciating the entire purchase price ($1,170,000) over 39 years, ignoring that land is not depreciable.

7. Question 7 of 25Easy

   A real estate agent sells a house for $320,000. The agreed commission rate is 6% of the sale price. What is the total commission earned?

   1. AA. $192,000
   2. BB. $1,920
   3. CC. $19,200
   4. DD. $19,000
   Show answer to question 7

   Answer: C. $19,200

   Commission is calculated as sale price multiplied by the commission rate: $320,000 × 0.06 = $19,200. This is a straightforward application of the commission formula.

   Why the other options are wrong

   • AThis results from using a rate of 60% instead of 6%.
   • BThis results from using a rate of 0.6% (misplacing the decimal) instead of 6%.
   • D$19,000 incorrectly rounds the commission to the nearest $1,000. No rounding is requested; the exact commission is $19,200.

8. Question 8 of 25Hard

   A buyer contracts to purchase a residential property for $400,000 with a 75% loan-to-value mortgage and puts down $15,000 in earnest money. The lender assesses a 1% loan origination fee, and title and settlement fees total $3,800. The buyer must prepay a 1-year hazard insurance policy of $1,400 and fund a 3-month property tax escrow at $350 per month. The buyer must also reimburse the seller $200 for prepaid homeowners association dues. The seller agreed in the contract to provide a $2,500 credit toward buyer closing fees. How much cash must the buyer present at closing?

   1. AA. $92,950
   2. BB. $94,450
   3. CC. $91,950
   4. DD. $91,550
   Show answer to question 8

   Answer: C. $91,950

   The buyer must bring $91,950 to closing. The buyer's total obligations consist of the $100,000 down payment, $3,000 origination fee (1% of the $300,000 loan), $3,800 settlement fees, $1,400 hazard insurance, $1,050 tax escrow reserve ($350 × 3), and $200 HOA dues reimbursement, which sum to $109,450. Subtracting the credits of $15,000 in earnest money and $2,500 in seller credit leaves $91,950. The amount of $92,950 results from improperly computing the origination fee on the total sales price instead of the loan amount.

   Why the other options are wrong

   • ACalculating origination on the purchase price gives $400,000 × 1% = $4,000 instead of $3,000, producing $91,950 + $1,000 = $92,950. The fee applies to the $300,000 loan.
   • BOmitting the seller's $2,500 credit gives $109,450 − $15,000 = $94,450. Both the earnest money and seller credit must reduce the buyer's cash due.
   • DTreating the $200 HOA reimbursement as a buyer credit instead of a charge gives $91,950 − $200 − $200 = $91,550. The buyer owes this reimbursement to the seller.

9. Question 9 of 25Medium

   A borrower obtains a $200,000 loan at 5% annual interest, amortized over 30 years with monthly payments of $1,073.64. What is the amount of principal paid in the first monthly payment?

   1. AA. $240.31
   2. BB. $266.67
   3. CC. $1,073.64
   4. DD. $833.33
   Show answer to question 9

   Answer: A. $240.31

   The first monthly payment includes interest on the principal. Interest for the first month is $200,000 × (0.05/12) = $833.33. The principal paid is the payment minus interest: $1,073.64 − $833.33 = $240.31.

   Why the other options are wrong

   • B$266.67 might result from incorrectly dividing the annual interest rate by 12 on a different principal amount or from miscalculating the interest portion.
   • C$1,073.64 is the total monthly payment, not the principal paid in the first month.
   • D$833.33 is the interest portion of the payment, not the principal reduction.

10. Question 10 of 25Medium

    Elena and Marco sold their house for $486,000. The transfer tax is $1.25 for each $500 of the sale price. They also paid $2,875 in title charges, $640 in recording fees, and $315 in escrow fees, and their mortgage payoff was $318,400. What amount did the sellers receive after these deductions?

    1. AA. $163,770
    2. BB. $161,340
    3. CC. $162,555
    4. DD. $162,312
    Show answer to question 10

    Answer: C. $162,555

    Divide the sale price by the tax interval, then multiply by the per-unit tax: $486,000 ÷ $500 = 972 units, and 972 × $1.25 = $1,215. Add the other closing costs and mortgage payoff to the tax, then subtract the total from the sale price: $486,000 − $1,215 − $3,830 − $318,400 = $162,555.

    Why the other options are wrong

    • AThis omits the $1,215 transfer tax, leaving $163,770.
    • BThis doubles the transfer tax to $2,430, producing $161,340.
    • DThis uses a transfer tax of $1,458 based on $1.50 per $500, producing $162,312.

11. Question 11 of 25Medium

    A homeowner purchased a property for $250,000. The home has since appreciated by 20% in market value. The owner currently owes $195,000 on the first mortgage and $30,000 on a home equity loan. What percentage of the current market value is the owner's equity?

    1. AA. 35%
    2. BB. 25%
    3. CC. 30%
    4. DD. 75%
    Show answer to question 11

    Answer: B. 25%

    With 20% appreciation, the current market value is $300,000 ($250,000 multiplied by 1.20). Total remaining encumbrances equal $225,000 ($195,000 + $30,000), yielding $75,000 in equity ($300,000 − $225,000). Dividing the $75,000 equity by the $300,000 market value produces an equity percentage of 25%. The figure of 30% is incorrect because it divides the equity by the original purchase price ($250,000) rather than the current market value.

    Why the other options are wrong

    • AIgnoring the home equity loan gives ($300,000 minus $195,000) ÷ $300,000 = 35%, overstating equity by excluding $30,000 of debt.
    • CDividing $75,000 in equity by the original $250,000 purchase price gives 30%, but the question requires dividing by the current $300,000 market value.
    • DDividing total debt of $225,000 by the current $300,000 market value gives 75%, which is the debt percentage, not the owner's equity percentage.

12. Question 12 of 25Hard

    An investor purchased two contiguous commercial lots together for $300,000. The investor later sold the first lot for $180,000, realizing a 20% profit on its individual cost. If the second lot subsequently sold for $110,000, what was the percentage loss on the second lot?

    1. AA. 36.4% loss
    2. BB. 26.7% loss
    3. CC. 3.3% loss
    4. DD. 29.5% loss
    Show answer to question 12

    Answer: B. 26.7% loss

    Because the first lot sold for $180,000 at a 20% profit, its individual purchase cost was $150,000 ($180,000 ÷ 1.20). Subtracting $150,000 from the $300,000 aggregate purchase price leaves an original cost basis of $150,000 for the second lot. Selling the second lot for $110,000 produced a $40,000 loss, which corresponds to a 26.7% loss ($40,000 ÷ $150,000). The option showing a 3.3% loss represents the net loss across the entire two-lot investment portfolio rather than the specific loss on the second lot.

    Why the other options are wrong

    • ADividing the $40,000 loss by the $110,000 selling price gives 36.4%, but percentage loss must use the second lot's $150,000 original cost as the denominator.
    • CCalculating ($300,000 − $180,000 − $110,000) ÷ $300,000 gives 3.3%, but that measures the combined investment's loss, not the second lot's loss.
    • DIncorrectly subtracting 20% from the first lot's selling price gives $180,000 × 0.80 = $144,000, leaving $156,000 for the second lot; ($156,000 − $110,000) ÷ $156,000 = 29.5%. Profit is based on cost, not selling price.

13. Question 13 of 25Medium

    A homebuyer purchases a property for $340,000 with a 10% down payment. To obtain a lower interest rate, the buyer agrees to pay 2.5 discount points to the lender. What is the total cost of these discount points?

    1. AA. $7,650
    2. BB. $9,180
    3. CC. $8,500
    4. DD. $6,120
    Show answer to question 13

    Answer: A. $7,650

    Discount points are assessed on the principal loan balance rather than the sale price. A 10% down payment on a $340,000 purchase leaves a loan balance of $306,000. Multiplying $306,000 by 2.5% (0.025) yields $7,650. The amount of $8,500 incorrectly computes the points based on the full purchase price.

    Why the other options are wrong

    • BUsing 3% instead of 2.5% gives $306,000 × 0.03 = $9,180, incorrectly charging three discount points rather than the agreed 2.5 points.
    • CApplying 2.5% to the purchase price gives $340,000 × 0.025 = $8,500, but discount points are calculated on the $306,000 loan amount.
    • DUsing 2% instead of 2.5% gives $306,000 × 0.02 = $6,120, incorrectly charging two discount points rather than the agreed 2.5 points.

14. Question 14 of 25Medium

    A property has an assessed value of $185,000 and the local tax rate is 1.25% of assessed value. What is the monthly property tax amount?

    1. AA. $2,312.50
    2. BB. $231.25
    3. CC. $185.00
    4. DD. $192.71
    Show answer to question 14

    Answer: D. $192.71

    The annual tax is $185,000 × 0.0125 = $2,312.50. The monthly tax is $2,312.50 ÷ 12 ≈ $192.71.

    Why the other options are wrong

    • AThis is the annual tax amount, not the monthly amount requested.
    • BThis is the annual tax divided by 10 instead of 12, possibly from misreading the question.
    • CThis is simply the assessed value divided by 1,000, ignoring the tax rate.

15. Question 15 of 25Medium

    A property closes on July 10 of a nonleap year. The annual property tax is $4,200, covers the calendar year, and is payable in arrears. The tax is unpaid at closing. The seller is responsible for taxes through and including July 10. Using actual days and a 365-day year, what is the seller's prorated share of the tax at closing?

    1. AA. $2,100.00
    2. BB. $2,197.81
    3. CC. $2,046.58
    4. DD. $2,301.37
    Show answer to question 15

    Answer: B. $2,197.81

    Count the seller's days from January 1 through July 10: 31 + 28 + 31 + 30 + 31 + 30 + 10 = 191 days. The seller's share is $4,200 × (191 ÷ 365) = $2,197.81, rounded to the nearest cent. Retain full precision until the final rounding. Because these taxes are unpaid and payable in arrears, this amount is a debit to the seller and a credit to the buyer, who will pay the tax bill when due.

    Why the other options are wrong

    • AThis equals half the annual tax: $4,200 ÷ 2 = $2,100.00. The seller owes taxes for 191 days, which is more than half of a 365-day year.
    • CThis amount equals neither party's share. The seller owes $2,197.81 for 191 days; the buyer's share for the remaining 174 days is $2,002.19.
    • DThis equals 200 days of taxes: $4,200 × (200 ÷ 365) = $2,301.37. The seller owes only 191 days, so this overstates the seller's share.

16. Question 16 of 25Hard

    A property sells for $450,000. The total commission is 6%, split 55% to the listing broker and 45% to the selling broker (from a different firm). The listing broker has a 60/40 split with the listing agent (agent gets 60%). How much commission does the listing agent receive?

    1. AA. $27,000
    2. BB. $8,910
    3. CC. $7,290
    4. DD. $14,850
    Show answer to question 16

    Answer: B. $8,910

    Total commission: $450,000 × 0.06 = $27,000. Listing broker share: $27,000 × 0.55 = $14,850. Listing agent share: $14,850 × 0.60 = $8,910.

    Why the other options are wrong

    • AThis is the total commission, not the agent's portion.
    • CThis incorrectly uses the selling broker's 45% share instead of the listing broker's 55% share: $27,000 × 0.45 × 0.60 = $7,290.
    • DThis is the listing broker's gross commission before the agent split.

17. Question 17 of 25Medium

    A rectangular lot measures 200 feet by 300 feet. How many acres does the lot contain? (Round to the nearest tenth)

    1. AA. 2.0 acres
    2. BB. 0.7 acres
    3. CC. 1.5 acres
    4. DD. 1.4 acres
    Show answer to question 17

    Answer: D. 1.4 acres

    The area is 200 × 300 = 60,000 square feet. Since one acre equals 43,560 square feet, 60,000 ÷ 43,560 = 1.377 acres, which rounds to 1.4 acres.

    Why the other options are wrong

    • AThis might result from dividing 60,000 by 30,000, a common approximation error.
    • B0.7-acre could result from incorrectly using the triangle area formula: (200 × 300) ÷ 2 = 30,000 square feet; 30,000 ÷ 43,560 rounds to 0.7 acre.
    • CThis would come from mistakenly dividing 60,000 by 40,000 instead of the correct 43,560.

18. Question 18 of 25Medium

    A borrower decides to refinance a mortgage that has an outstanding principal balance of $180,000 at a fixed interest rate of 6%. The promissory note states that early payoff incurs a prepayment penalty equal to six months of interest on the remaining balance. How much must the borrower pay for the prepayment penalty?

    1. AA. $10,800
    2. BB. $5,400
    3. CC. $3,600
    4. DD. $2,700
    Show answer to question 18

    Answer: B. $5,400

    The annual interest on the remaining balance is $10,800 ($180,000 × 0.06). Because the penalty equals six months of interest, divide the annual amount by 2, which gives $5,400. Calculating a full year of interest yields $10,800, which ignores the six-month term in the agreement.

    Why the other options are wrong

    • ACharging a full year of interest gives $180,000 × 0.06 = $10,800, but the note requires only six months of interest.
    • CUsing four months instead of six gives $180,000 × 0.06 × 4/12 = $3,600, understating the penalty period specified in the note.
    • DHalving the six-month interest twice gives $180,000 × 0.06 ÷ 2 ÷ 2 = $2,700, incorrectly charging only three months of interest.

19. Question 19 of 25Hard

    An investor is comparing valuation methods for a six-unit building with $180,000 in annual scheduled rent, 6% vacancy and collection loss, $62,400 in annual operating expenses, a 6% market cap rate, and a 9.6 gross rent multiplier. How do the two indicated values compare?

    1. AA. Capitalization value, higher by $52,000
    2. BB. Capitalization value, higher by $104,000
    3. CC. GRM value, higher by $52,000
    4. DD. GRM value, higher by $104,000
    Show answer to question 19

    Answer: A. Capitalization value, higher by $52,000

    The GRM indication uses gross rent before vacancy and expenses: $180,000 × 9.6 = $1,728,000. The capitalization indication uses net operating income of $106,800 divided by 0.06, producing $1,780,000, which is $52,000 higher.

    Why the other options are wrong

    • BThe $104,000 figure doubles the actual $52,000 difference between the two value indications.
    • CThe GRM indication is $1,728,000, which is lower than the $1,780,000 capitalization indication.
    • DThis choice both reverses the higher method and doubles the difference.

20. Question 20 of 25Medium

    A rectangular ranch measures 1.25 miles in length by 0.5 miles in width. If a 40-acre conservation easement is excluded from the usable area, how many usable acres remain on the ranch?

    1. AA. 400 acres
    2. BB. 440 acres
    3. CC. 360 acres
    4. DD. 320 acres
    Show answer to question 20

    Answer: C. 360 acres

    Multiplying the dimensions shows the ranch covers 0.625 square miles (1.25 miles multiplied by 0.5 miles). Because one square mile equals 640 acres, the gross area is 400 acres (0.625 multiplied by 640). Subtracting the 40-acre easement leaves 360 usable acres. The figure of 400 acres represents the gross acreage before deducting the easement, while 440 acres incorrectly adds the easement to the gross total.

    Why the other options are wrong

    • ACalculating 1.25 × 0.5 × 640 = 400 acres gives the gross area but fails to subtract the 40-acre easement.
    • BCalculating 400 + 40 = 440 acres incorrectly adds the easement acreage instead of subtracting it from the gross area.
    • DCalculating 400 − (2 × 40) = 320 acres incorrectly deducts the 40-acre easement twice instead of once.

21. Question 21 of 25Medium

    A buyer assumes an existing mortgage with a principal balance of $180,000 at a 5% annual interest rate. The monthly mortgage payment is paid in arrears on the first of each month. Closing occurs on April 10, with the day of closing charged to the seller. Using a 360-day statutory year, what is the interest proration on the closing disclosure?

    1. AA. $225 debit to the seller and $225 credit to the buyer
    2. BB. $500 debit to the seller and $500 credit to the buyer
    3. CC. $250 debit to the buyer and $250 credit to the seller
    4. DD. $250 debit to the seller and $250 credit to the buyer
    Show answer to question 21

    Answer: D. $250 debit to the seller and $250 credit to the buyer

    Because mortgage interest is paid in arrears, the buyer will pay the full month of April's interest when making the May 1 payment. The seller is responsible for the 10 days of interest accrued during seller ownership from April 1 through April 10, which equals $250 ($180,000 × 0.05 ÷ 360 × 10). The seller must credit the buyer $250 and be debited $250 so that the buyer is properly reimbursed; reversing this entry mistakenly treats interest as if it were collected in advance.

    Why the other options are wrong

    • AExcluding April 10 incorrectly assigns only nine days to the seller: $180,000 × 0.05 ÷ 360 × 9 = $225. The question explicitly charges the closing day to the seller.
    • BCharging the seller for the buyer’s remaining 20 days of April produces $180,000 × 0.05 ÷ 360 × 20 = $500. The seller owes only the first 10 days.
    • CThe $250 amount is correct, but the entries are reversed. Because the buyer will pay April’s interest in arrears, the seller must reimburse the buyer through a seller debit and buyer credit.

22. Question 22 of 25Medium

    A residential triplex generates an annual gross rental income of $57,600. The property carries annual operating expenses of $18,000 and has an estimated vacancy rate of 5%. If the prevailing monthly gross rent multiplier (GRM) in the area is 120, what is the estimated market value of the property?

    1. AA. $576,000
    2. BB. $396,000
    3. CC. $367,200
    4. DD. $547,200
    Show answer to question 22

    Answer: A. $576,000

    Apply the monthly gross rent multiplier (GRM) to monthly gross rent without deducting vacancy or operating expenses. Monthly gross rent = $57,600 ÷ 12 = $4,800. Estimated market value = $4,800 × 120 = $576,000. Vacancy allowances and operating expenses are considered when calculating net operating income, but neither is deducted in this GRM calculation.

    Why the other options are wrong

    • B$396,000 results from incorrectly deducting operating expenses: ($57,600 − $18,000) ÷ 12 × 120. This GRM calculation uses gross rent, not income after operating expenses.
    • C$367,200 results from incorrectly deducting both vacancy and operating expenses: ($57,600 × 0.95 − $18,000) ÷ 12 × 120. Neither deduction belongs in this GRM calculation.
    • D$547,200 results from incorrectly deducting the vacancy allowance: ($57,600 × 0.95) ÷ 12 × 120. This GRM calculation uses gross rent before the vacancy deduction.

23. Question 23 of 25Medium

    An investor purchased a commercial parcel for $400,000. The property appreciated by 10% during the first year, depreciated by 5% during the second year, and then appreciated by 8% during the third year. What was the value of the parcel at the end of the third year?

    1. AA. $418,000
    2. BB. $452,000
    3. CC. $451,440
    4. DD. $475,200
    Show answer to question 23

    Answer: C. $451,440

    Each annual percentage change must be applied consecutively to the running balance: after year one the property is worth $440,000 ($400,000 × 1.10); after year two it falls to $418,000 ($440,000 × 0.95); and after year three it rises to $451,440 ($418,000 × 1.08). The figure $452,000 is incorrect because it assumes simple addition and subtraction of the percentages (10% − 5% + 8% = 13%) against the initial purchase price instead of compounding each period.

    Why the other options are wrong

    • AStopping after year two gives $400,000 × 1.10 × 0.95 = $418,000, omitting the third year's 8% appreciation.
    • BAdding the percentage changes gives $400,000 × (1 + 0.10 − 0.05 + 0.08) = $452,000, incorrectly applying all changes to the original price instead of each year's updated value.
    • DIgnoring the second year's 5% depreciation gives $400,000 × 1.10 × 1.08 = $475,200, overstating the final value.

24. Question 24 of 25Medium

    A home sells for $195,000. The county charges a transfer tax of $0.45 per $100 of the sale price. What is the transfer tax?

    1. AA. $780.00
    2. BB. $975.00
    3. CC. $1,170.00
    4. DD. $877.50
    Show answer to question 24

    Answer: D. $877.50

    Divide the sale price by 100 to find the number of $100 units: $195,000 ÷ $100 = 1,950 units. Multiply by the tax rate per unit: 1,950 × $0.45 = $877.50.

    Why the other options are wrong

    • A$780.00 results from using a rate of $0.40 per $100.
    • B$975.00 results from using a rate of $0.50 per $100.
    • C$1,170.00 results from using a rate of $0.60 per $100.

25. Question 25 of 25Medium

    Two similar properties have the same gross rent. Property J has a gross rent multiplier of 9.4 and a capitalization rate of 7.9%. Property K has a gross rent multiplier of 11.2 and a capitalization rate of 6.5%. What conclusion is best supported by both ratios?

    1. AA. Property K has a higher price relative to rent and a higher NOI relative to price.
    2. BB. Property J has a higher price relative to rent and a lower NOI relative to price.
    3. CC. Property K has a lower price relative to rent and a higher NOI relative to price.
    4. DD. Property J has a lower price relative to rent and a higher NOI relative to price.
    Show answer to question 25

    Answer: D. Property J has a lower price relative to rent and a higher NOI relative to price.

    A lower gross rent multiplier means a lower price for each dollar of gross rent when rent is held constant. A higher capitalization rate means higher net operating income relative to price, so both ratios support Property J.

    Why the other options are wrong

    • AProperty K does have the higher gross rent multiplier, but its lower capitalization rate indicates lower net operating income relative to price.
    • BThis states the opposite of both given ratio relationships for Property J.
    • CThis reverses both comparisons even though Property K has the higher gross rent multiplier and lower capitalization rate.

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The full Real Estate bank has 409 Math questions. See plans