CALIFORNIA REAL ESTATE – Chapter 12 (Real Estate Mathematics) – Questions

#1. A property sells for $500,000 and the agent’s commission rate is 6%. What is the total commission?

$25,000

$35,000

$30,000

$50,000

#2. Convert 0.075 to a percentage.

0.75%

7.5%

75%

0.075%

#3. A borrower takes out a $200,000 loan at 5% annual interest. What is the monthly interest payment for the first month?

$1,000.00

$416.67

$833.33

$10,000.00

#4. A property has an assessed value of $400,000 and the tax rate is 1.25%. What is the annual property tax?

$5,000

$4,000

$5,500

$3,200

#5. A rectangular lot measures 150 feet by 200 feet. What is the area in square feet?

35,000 sq ft

30,000 sq ft

25,000 sq ft

20,000 sq ft

#6. Convert the fraction 5/8 to a decimal.

0.580

0.750

0.525

0.625

#7. A property sells for $750,000 with a 5% commission split equally between buyer’s and seller’s agents. How much does each agent receive?

$37,500

$18,750

$15,000

$22,500

#8. A home has a market value of $600,000 and the outstanding loan balance is $400,000. What is the seller’s equity?

$400,000

$600,000

$100,000

$200,000

#9. An investment property was purchased for $500,000 with an estimated salvage value of $50,000 and a useful life of 25 years. Using straight-line depreciation, what is the annual depreciation expense?

$20,000

$22,500

$15,000

$18,000

#10. A property has a sale price of $500,000 and generates $50,000 in annual gross rental income. What is the Gross Rent Multiplier (GRM)?

8

10

12

15

#11. Annual property taxes are $3,650. Closing is July 1 and the seller owned the property from January 1 to June 30 (181 days). Using 365 days, the seller’s share is approximately:

$1,825

$1,810

$1,850

$1,750

#12. A property’s monthly PITI payment consists of which four components?

Price, Income, Taxes, and Interest

Principal, Investment, Transfer, and Insurance

Principal, Interest, Taxes, and Insurance

Price, Interest, Title, and Insurance

#13. Under Proposition 13 in California, the maximum annual increase in assessed property value is:

5%

10%

2%

3%

#14. A borrower obtains a $300,000 mortgage at 4% for 30 years. The total number of monthly payments is:

360

300

180

120

#15. A property sells for $800,000. The transfer tax rate is $1.10 per $1,000 of value. What is the transfer tax?

$880

$800

$8,800

$88

#16. A warehouse measures 50 feet long, 30 feet wide, and 20 feet tall. What is the volume in cubic feet?

25,000 cu ft

30,000 cu ft

35,000 cu ft

40,000 cu ft

#17. An agent earns a 3% commission on a property that sells for $400,000. What is the commission?

$12,400

$12,000

$11,000

$15,000

#18. A property has an assessed value of $350,000. Under California Proposition 13, the base tax rate is 1%. What is the annual property tax before additional assessments?

$3,150

$4,000

$2,800

$3,500

#19. A property owner’s equity is $175,000. If closing costs are $12,000 and there is a $3,000 lien, what are the net proceeds?

$160,000

$175,000

$163,000

$172,000

#20. A property generates $60,000 in annual gross rent and has a GRM of 12. What is the estimated property value?

$600,000

$500,000

$72,000

$720,000

#21. Under California law, property taxes are paid in two installments. The first installment is due on:

November 1

January 1

July 1

March 1

#22. A lot has two sections: a rectangle (60 ft × 40 ft) and a triangle (base 40 ft, height 20 ft). What is the total area?

2,400 sq ft

2,800 sq ft

3,200 sq ft

2,000 sq ft

#23. A $300,000 loan at 4% interest over 30 years has a monthly P&I payment of approximately $1,432.25. If annual property taxes are $3,600 and annual insurance is $1,200, what is the total monthly PITI?

$1,432.25

$2,232.25

$1,632.25

$1,832.25

#24. An investor is evaluating two properties. Property A has a GRM of 8 and Property B has a GRM of 12. Which property generates more income relative to its price?

Property B, because a higher GRM means more income

Both are equally efficient

GRM cannot be used for comparison

Property A, because a lower GRM indicates the property generates more income per dollar of price

#25. The first installment of California property taxes becomes delinquent if not paid by:

January 10

November 30

February 1

December 10

#26. A seller’s equity is $250,000. Closing costs total $18,000. A second mortgage lien of $15,000 must be paid off. Net proceeds to the seller are:

$250,000

$232,000

$235,000

$217,000

#27. A property is purchased for $600,000. The buyer makes a 20% down payment. What is the loan amount?

$480,000

$120,000

$500,000

$540,000

#28. Residential rental properties are depreciated over how many years under MACRS?

39 years

27.5 years

25 years

30 years

#29. Commercial properties are depreciated over how many years under MACRS?

27.5 years

25 years

31.5 years

39 years

#30. A property’s annual operating expenses are $24,000 and the property generates $80,000 in effective gross income. What is the operating expense ratio (OER)?

20%

40%

24%

30%

#31. A property sold for $1,200,000. The county transfer tax rate is $1.10 per $1,000 and the city adds $3.30 per $1,000. What is the total transfer tax?

$1,320

$5,280

$3,960

$12,000

#32. A 30-year mortgage has a higher total interest cost than a 15-year mortgage for the same loan amount and rate because:

The interest rate is higher on 30-year mortgages

The monthly payment is higher on 30-year mortgages

The lender charges a prepayment penalty on 30-year mortgages

The principal remains outstanding longer, resulting in more total interest accrued over the extended term

#33. A property is assessed at $500,000 under Proposition 13. If the CPI increase is 1.8% for the year, the new assessed value is:

$510,000

$509,000

$500,000

$518,000

#34. An investor pays $800,000 for a property generating $80,000 annual gross rent. The property has $30,000 in annual operating expenses. What is the capitalization rate?

6.25%

10%

3.75%

8%

#35. Monthly rent is $1,800 and the closing date is the 15th of a 30-day month. The seller owes the buyer a rent credit of:

$1,800

$450

$900

$1,350

#36. A buyer obtains an 80% LTV loan on a property priced at $450,000. What is the loan amount?

$90,000

$405,000

$360,000

$315,000

#37. A property’s Net Operating Income (NOI) is $50,000 and the investor paid $625,000 for the property. What is the cap rate?

8%

6.25%

10%

5%

#38. The second installment of California property taxes is due on:

April 10

January 1

March 15

February 1

#39. An investor purchases a property for $1,000,000 with a salvage value of $100,000 and a useful life of 30 years. Annual straight-line depreciation is:

$30,000

$33,333

$36,000

$25,000

#40. A property sells for $550,000 with total closing costs of $22,000. The commission is 5% of the sale price. What is the total commission?

$22,000

$28,600

$25,000

$27,500

#41. A rectangular building has dimensions of 80 ft × 60 ft × 15 ft. What is the volume?

64,000 cu ft

80,000 cu ft

48,000 cu ft

72,000 cu ft

#42. A borrower has a monthly PITI payment of $2,200. Of this, $1,500 is P&I, $400 is taxes, and $300 is insurance. What percentage of the monthly payment goes to taxes?

Approximately 25%

Approximately 13.6%

Approximately 18.2%

Approximately 30%

#43. Annual property taxes are $4,380. Closing is October 1. The seller owned the property for 273 days (Jan 1 to Sept 30). The seller’s prorated share is approximately:

$3,276

$1,104

$4,380

$2,190

#44. A property has a market value of $500,000 and a loan-to-value ratio of 75%. What is the maximum loan amount?

$400,000

$375,000

$350,000

$125,000

#45. Convert 37.5% to a fraction in simplest form.

3/4

3/8

5/8

1/4

#46. A property’s annual gross rental income is $120,000 and the vacancy rate is 5%. What is the effective gross income?

$114,000

$120,000

$108,000

$126,000

#47. A property has an NOI of $75,000 and annual debt service of $60,000. What is the debt service coverage ratio (DSCR)?

0.80

1.25

1.50

1.00

#48. A property sells for $425,000. The buyer’s agent receives 2.5% commission. What is the buyer’s agent’s commission?

$10,000

$12,500

$10,625

$8,500

#49. A building lot is shaped as a trapezoid with parallel sides of 100 ft and 80 ft, and a height of 50 ft. What is the area?

4,000 sq ft

5,000 sq ft

4,500 sq ft

3,600 sq ft

#50. A $250,000 loan at 6% annual interest has a monthly interest payment in the first month of:

$1,500

$1,250

$625

$15,000

#51. If a property’s NOI increases from $50,000 to $55,000 while the cap rate remains at 8%, the property value increases from $625,000 to:

$650,000

$687,500

$700,000

$675,000

#52. A property has annual property taxes of $6,000. The first installment (due Nov 1) is $3,000. If the tax is delinquent after Dec 10, the penalty is:

$600

$30

$3,000

$300 (10% of the delinquent installment)

#53. A seller’s market value is $700,000 and the outstanding first mortgage is $450,000. There is a second mortgage of $50,000. The seller’s equity is:

$250,000

$150,000

$200,000

$700,000

#54. An investor wants to purchase a property with a cap rate of at least 7%. If the property’s NOI is $63,000, the maximum price the investor should pay is:

$441,000

$900,000

$630,000

$1,000,000

#55. A property depreciates by $20,000 per year using straight-line depreciation. After 10 years, the total accumulated depreciation is:

$100,000

$300,000

$200,000

$20,000

#56. A rental property generates $3,600 per month in gross rent. Annual operating expenses are $15,600. What is the monthly NOI?

$3,600

$1,300

$2,300

$4,900

#57. A property is purchased for $400,000 with 25% down. The loan amount is $300,000 at 5% for 30 years. What is the monthly interest payment for the first month?

$1,250

$1,666.67

$833.33

$2,500

#58. Using the GRM approach, if a property generates $48,000 annual gross rent and the prevailing GRM in the area is 11, the estimated value is:

$480,000

$528,000

$440,000

$576,000

#59. A homeowner pays $1,200 per year in homeowner’s insurance. What is the monthly insurance cost?

$120

$150

$100

$50

#60. A property’s effective gross income is $90,000 and operating expenses are $36,000. The NOI is:

$90,000

$36,000

$54,000

$126,000

#61. A $500,000 property generates $40,000 in annual net operating income. What is the overall rate of return (cap rate)?

10%

6%

5%

8%

#62. Convert 12.5% to a decimal.

1.25

0.125

0.0125

12.5

#63. A property sells for $350,000. The seller’s agent commission is 3% and the buyer’s agent commission is 2.5%. What is the total commission paid?

$17,500

$21,000

$15,750

$19,250

#64. Annual property taxes are $5,200. Closing is May 16 (seller owned 136 days out of 365). The seller’s prorated share is approximately:

$2,600

$3,263

$1,424

$1,937

#65. A property’s gross rent multiplier is 9.5 and the annual gross rent is $72,000. The estimated value is:

$720,000

$612,000

$684,000

$756,000

#66. A buyer puts 15% down on a $500,000 property. The loan amount is:

$450,000

$375,000

$425,000

$75,000

#67. A property has a vacancy rate of 8% and potential gross income of $100,000. What is the effective gross income?

$100,000

$108,000

$92,000

$80,000

#68. An investor’s property generates $36,000 NOI with a property value of $450,000. The cap rate is:

6%

10%

8%

12%

#69. A property is sold for $620,000. The county transfer tax ($1.10/$1,000) is:

$620

$6,820

$68.20

$682

#70. Under California law, if property taxes remain unpaid after June 30, the property may face:

An automatic 5% discount

No consequences until the following year

A grace period of 1 additional year

Additional charges and eventually a tax lien or foreclosure proceedings

#71. A 15-year mortgage at 4% on $300,000 results in approximately $99,431 in total interest. A 30-year mortgage at 4% on $300,000 results in approximately $215,609 in total interest. The 30-year mortgage costs more in interest by approximately:

$116,178

$99,431

$215,609

$50,000

#72. A property has the following monthly expenses: mortgage P&I $1,200, taxes $350, insurance $150, and HOA $200. The total monthly housing cost is:

$1,700

$1,900

$1,550

$2,100

#73. An agent lists a property at $650,000. After negotiations, the property sells for $625,000 with a 5.5% total commission. The total commission is:

$35,750

$32,500

$36,000

$34,375

#74. A property is assessed at $275,000. Local tax rate is 1% plus a 0.3% Mello-Roos assessment. Total annual tax is:

$2,750

$3,575

$3,025

$4,125

#75. An investor pays $900,000 for a 12-unit apartment building. Monthly rent per unit is $1,500. Annual gross rental income is:

$180,000

$18,000

$1,080,000

$216,000

#76. A property’s NOI is $85,000 and the cap rate is 7%. What is the property’s estimated value?

Approximately $1,214,286

$850,000

$595,000

$1,000,000

#77. A lot measures 200 ft × 150 ft = 30,000 sq ft. How many acres is this approximately? (1 acre = 43,560 sq ft)

Approximately 0.69 acres

Approximately 1 acre

Approximately 0.50 acres

Approximately 0.85 acres

#78. A borrower’s loan has an original balance of $350,000. After 5 years of payments, the remaining balance is $320,000. What amount of principal has been paid?

$30,000

$320,000

$350,000

$35,000

#79. A property generates $4,500 per month in gross rent. Annual operating expenses total $18,000. What is the annual NOI?

$36,000

$54,000

$18,000

$4,500

#80. A property valued at $1,500,000 has a GRM of 12.5. What is the annual gross rent?

$120,000

$150,000

$100,000

$187,500

#81. A buyer purchases a property for $475,000. The buyer pays 3 discount points on their $380,000 loan. How much are the discount points?

$11,400

$14,250

$9,500

$3,800

#82. A property’s assessed value is $320,000. The tax rate is 1.1% (base tax plus assessments). Annual property tax is:

$3,200

$3,840

$2,880

$3,520

#83. Mortgage interest is calculated on the outstanding balance. As payments are made, the interest portion:

Remains constant throughout the loan term

Increases over time

Decreases over time while the principal portion increases, because the outstanding balance shrinks

Is recalculated annually by the lender

#84. A seller has a $450,000 mortgage balance. The property sells for $620,000 with 5% commission ($31,000) and $12,000 in closing costs. Net proceeds are:

$177,000

$170,000

$127,000

$620,000

#85. Using a 360-day year (banker’s year), a $200,000 loan at 6% has a daily interest rate of:

$32.88

$33.33

$36.00

$30.00

#86. A property with annual gross income of $96,000 and operating expenses of $38,400 has an operating expense ratio of:

30%

50%

40%

60%

#87. A property sold for $580,000. The buyer’s loan is 80% LTV. The buyer’s down payment is:

$116,000

$464,000

$58,000

$145,000

#88. An investment property generates NOI of $42,000. If the investor wants an 8% return, the maximum purchase price should be:

$420,000

$336,000

$600,000

$525,000

#89. A property has potential gross income of $150,000 and a 6% vacancy rate. Effective gross income is:

$150,000

$141,000

$144,000

$135,000

#90. A homeowner refinances from a 30-year mortgage to a 15-year mortgage. The monthly payment will:

Increase because the same principal is paid over a shorter term

Decrease because the loan term is shorter

Remain the same

Depend entirely on the interest rate change

#91. A rectangular property is 300 feet deep and 125 feet wide. The total area in acres is approximately:

0.86 acres

1.0 acre

0.75 acres

0.50 acres

#92. A property tax bill shows: base tax $4,500, Mello-Roos $800, special assessment $350. Total annual tax is:

$4,500

$5,300

$5,650

$6,000

#93. An investor buys a duplex for $600,000. Each unit rents for $2,000/month. The GRM is:

25

6.25

12.5

15

#94. A property’s NOI is $100,000 and annual debt service is $70,000. Cash flow after debt service is:

$100,000

$70,000

$30,000

$170,000

#95. A $400,000 property depreciates at 2.564% per year (straight-line for residential, building value only, assuming 80% is building). Annual depreciation deduction is:

Approximately $8,205 ($320,000 × 1/27.5 × 0.7065 ≈ simplified: $400,000 × 0.80 ÷ 27.5 ≈ $11,636)

$10,256

$14,545

$8,000

#96. Convert 3/16 to a decimal and then to a percentage.

0.316 and 31.6%

0.1667 and 16.67%

0.1875 and 18.75%

0.1563 and 15.63%

#97. A property has annual income of $200,000, operating expenses of $80,000, and debt service of $90,000. The DSCR is:

2.22

1.33

0.75

2.50

#98. A seller’s net sheet shows: sale price $575,000, commission $28,750 (5%), closing costs $8,500, mortgage payoff $380,000. Approximate net proceeds are:

$157,750

$186,500

$575,000

$165,750

#99. A property is bought for $350,000 with the building representing 80% of value ($280,000). Using 27.5-year depreciation, the annual deduction is approximately:

$12,727

$14,000

$8,400

$10,182

#100. A buyer obtains a $320,000 mortgage at 5.5% for 30 years. The first month’s interest payment is approximately:

$1,760

$880

$1,333.33

$1,466.67

#101. A property sells for $950,000. The listing agent’s brokerage receives 3% and the buyer’s agent’s brokerage receives 2.5%. If the listing agent receives 60% of their brokerage’s share, the listing agent’s commission is:

$28,500

$23,750

$17,100

$14,250

#102. An investor purchases a 10-unit building. Each unit rents for $1,200/month. Annual vacancy is 5%. Effective gross income is:

$144,000

$120,000

$136,800

$129,600

#103. A property’s annual insurance premium increases from $1,400 to $1,680. The percentage increase is:

16.8%

28%

20%

12%

#104. A property sold for $485,000. The seller paid a 5.5% commission. What was the commission amount?

$24,250

$27,170

$26,675

$25,850

#105. An investor purchased a 12-unit apartment building for $1,800,000. Each unit rents for $1,250/month. What is the Gross Rent Multiplier (GRM)?

125

115

120

130

#106. A rectangular lot is 125 feet wide and 200 feet deep. How many acres does it contain?

0.625 acres

0.574 acres

0.500 acres

0.650 acres

#107. A borrower takes out a $320,000 loan at 6.5% annual interest. What is the monthly interest payment for the first month?

$1,600.00

$1,733.33

$1,866.67

$1,700.00

#108. Property taxes are $4,800/year. The seller closes escrow on September 15. Using a 360-day year, how much does the seller owe in prorated taxes?

$3,200

$3,600

$3,400

$3,000

#109. A home appraised at $550,000 has a 1.1% tax rate under Proposition 13. What are the annual property taxes?

$5,500

$6,050

$6,600

$5,050

#110. An agent earns a 3% commission on a $720,000 sale. The agent’s broker split is 70/30 in favor of the agent. How much does the agent receive?

$6,480

$21,600

$14,400

$15,120

#111. A property generates $96,000 in annual gross income and has operating expenses of $38,400. Using a 9% capitalization rate, what is the property’s value?

$640,000

$1,066,667

$426,667

$580,000

#112. A building cost $450,000 to construct and has a useful life of 27.5 years using straight-line depreciation. What is the annual depreciation?

$18,000.00

$15,000.00

$16,363.64

$16,000.00

#113. A buyer makes a 20% down payment on a $625,000 home. What is the loan amount?

$525,000

$500,000

$475,000

$510,000

#114. Property was purchased for $200,000 five years ago and sold for $260,000. What is the percentage of appreciation?

23%

25%

13%

30%

#115. A lot measures 150 ft × 180 ft. If the front footage is 150 ft and the cost is $45 per front foot, what is the lot value?

$8,100

$6,750

$5,400

$7,200

#116. An investor’s property has a net operating income of $72,000 and a value of $900,000. What is the capitalization rate?

8%

7.5%

9%

8.5%

#117. A seller nets $412,000 after paying a 6% commission. What was the selling price?

$436,720.00

$440,000.00

$437,021.28

$438,297.87

#118. Monthly rent is $2,100. The tenant pays rent on the 1st. If the property closes on March 18, how much rent credit does the buyer receive (30-day month)?

$910

$840

$1,260

$980

#119. A home was purchased for $380,000 with a loan-to-value ratio of 80%. The interest rate is 5.75%. What is the first month’s interest?

$1,456.67

$1,520.83

$1,388.33

$1,600.00

#120. A property’s assessed value is $425,000. Under Proposition 13, the maximum annual increase in assessed value is?

3%

1%

2.5%

2%

#121. A broker sold a property for $950,000 and earned a 5% commission. The listing agent receives 60% of the listing side (2.5%). How much does the listing agent earn?

$14,250

$23,750

$28,500

$11,875

#122. An apartment building has 8 units, each renting for $1,500/month. If the vacancy rate is 5%, what is the effective gross income?

$144,000

$136,800

$132,000

$140,400

#123. A triangular lot has a base of 200 feet and a height of 150 feet. What is its area in square feet?

30,000 sq ft

22,500 sq ft

10,000 sq ft

15,000 sq ft

#124. A $400,000 mortgage at 6% interest is amortized over 30 years. The monthly P&I payment is $2,398.20. How much of the first payment goes to principal?

$2,000.00

$400.00

$398.20

$398.00

#125. Property sold for $375,000. The buyer paid 2 discount points on an 80% LTV loan. How much did the buyer pay in points?

$6,000

$7,500

$5,000

$6,500

#126. A commercial property has annual gross income of $180,000 and a GRM of 8.5. What is the estimated property value?

$1,440,000

$1,620,000

$1,530,000

$1,350,000

#127. The annual property tax is $7,200. Escrow closes on July 31. The fiscal year starts July 1. How much tax has the seller accrued?

$620

$660

$580

$600

#128. A home’s replacement cost is $350,000. It has accrued depreciation of 15%. The land is valued at $120,000. What is the property value using the cost approach?

$297,500

$415,000

$470,000

$417,500

#129. A buyer can qualify for a monthly PITI of $2,800. If taxes are $500/month and insurance is $150/month, how much is available for P&I?

$2,300

$2,150

$2,100

$2,250

#130. An investor paid $1,200,000 for a 20-unit building. Monthly rent per unit is $950. What is the GRM?

100.00

105.26

110.53

95.00

#131. A property’s NOI is $54,000. If the cap rate increases from 6% to 8%, how much does the property value decrease?

$200,000

$250,000

$175,000

$225,000

#132. Convert 3/8 to a decimal and then to a percentage.

38.5%

37.5%

35%

40%

#133. A seller owes $285,000 on their mortgage. They sell for $425,000 and pay 6% commission and $3,500 in closing costs. What are the net proceeds?

$115,500

$111,000

$108,000

$114,000

#134. A rectangular building is 60 ft × 40 ft with 2 stories. What is the total square footage?

2,400 sq ft

3,600 sq ft

5,200 sq ft

4,800 sq ft

#135. An adjustable-rate mortgage starts at 4.5% with a 2% annual cap and 6% lifetime cap. What is the maximum possible rate?

10.5%

8.5%

12.5%

6.5%

#136. A property valued at $800,000 has a first mortgage of $500,000 and a second mortgage of $100,000. What is the owner’s equity?

$300,000

$400,000

$250,000

$200,000

#137. A 40-acre parcel is subdivided into half-acre lots. If 20% is used for roads, how many lots can be created?

80

72

60

64

#138. Quarterly interest on a $250,000 loan is $4,687.50. What is the annual interest rate?

7.0%

8.0%

7.5%

6.5%

#139. A property assessment is $350,000. The tax rate is $1.25 per $100 of assessed value. What are the annual taxes?

$4,250

$4,375

$4,500

$4,125

#140. A home sold for $510,000. The buyer’s down payment was $102,000. What percentage was the down payment?

18%

22%

15%

20%

#141. An investor wants a 10% return on a property with NOI of $85,000. What is the maximum purchase price?

$850,000

$800,000

$900,000

$750,000

#142. A property generates $5,200/month in rent. Annual expenses are $22,400. What is the NOI?

$62,400

$40,000

$44,800

$39,200

#143. A lot is described as the NW 1/4 of the SE 1/4 of Section 10. How many acres is this parcel?

40 acres

160 acres

80 acres

20 acres

#144. A borrower pays 1.5 discount points on a $380,000 loan. How much do the points cost?

$5,000

$6,000

$5,700

$5,500

#145. The listing price is $599,000. The property sells for 97% of list. The commission is 5%. What is the commission amount?

$29,950.00

$28,155.00

$29,051.50

$30,000.00

#146. A property was purchased for $300,000. Land value is $75,000. Using 27.5-year straight-line depreciation, what is the annual depreciation for the improvements?

$10,909.09

$8,000.00

$8,181.82

$9,000.00

#147. Monthly PITI: P&I = $1,850, Taxes = $420, Insurance = $135. What is the total PITI?

$2,405

$2,270

$2,385

$2,450

#148. A buyer assumes a $275,000 loan. The interest rate is 5.25%. What is the daily interest (360-day year)?

$39.58

$40.10

$42.19

$38.54

#149. An office building has 12,000 sq ft of rentable space at $2.50/sq ft/month. With 8% vacancy, what is the effective gross income?

$360,000

$331,200

$324,000

$345,600

#150. Assessed value was $400,000 in 2020. Under Proposition 13’s 2% annual cap, what is the maximum assessed value in 2025?

$440,000.00

$441,632.26

$448,000.00

$436,000.00

#151. A property is purchased for $520,000 with an 80% LTV loan at 6.25% for 30 years. What is the loan amount?

$400,000

$425,000

$416,000

$410,000

#152. An agent sells two properties: one for $350,000 at 6% and another for $275,000 at 5%. What is the total commission earned?

$33,000

$35,500

$34,750

$31,250

#153. A property’s value decreased from $480,000 to $432,000. What was the percentage decrease?

10%

12%

8%

15%

#154. A seller carries back a $100,000 second mortgage at 7% interest-only. What is the monthly interest payment?

$700.00

$500.00

$583.33

$625.00

#155. A 6,000 sq ft lot sold for $54,000. What was the price per square foot?

$8.50

$9.50

$9.00

$10.00

#156. Proration: Annual insurance premium is $1,800 paid in advance. Seller closes escrow on April 15. How much credit does the buyer get (360-day year)?

$1,350

$1,200

$1,275

$1,125

#157. A borrower’s gross monthly income is $8,500. Using a 28% front-end ratio, what is the maximum monthly housing expense?

$2,380

$2,400

$2,125

$2,550

#158. Using the income approach, a property has potential gross income of $120,000, vacancy at 5%, and operating expenses of $42,600. If the cap rate is 7%, what is the value?

$1,106,000

$980,000

$1,020,000

$1,050,000

#159. A property sold at a tax sale for $180,000. The delinquent taxes were $12,600. What percentage of the sale price were the delinquent taxes?

6%

8%

5%

7%

#160. A home’s market value is $650,000. The first mortgage is $400,000 and HELOC balance is $75,000. What is the LTV ratio for all liens?

73.08%

61.54%

76.92%

80.00%

#161. An FHA buyer puts 3.5% down on a $400,000 purchase. What is the down payment and loan amount?

$12,000 down / $388,000 loan

$16,000 down / $384,000 loan

$15,000 down / $385,000 loan

$14,000 down / $386,000 loan

#162. A warehouse measures 100 ft × 80 ft × 20 ft high. What is the volume in cubic feet?

80,000 cu ft

200,000 cu ft

120,000 cu ft

160,000 cu ft

#163. A condominium’s monthly HOA fee is $450. Over 5 years, what is the total HOA cost?

$25,000

$27,000

$30,000

$22,500

#164. The mill rate is 45 mills. On an assessed value of $320,000, what are the property taxes?

$12,800

$16,000

$14,400

$13,500

#165. A property produces $7,500/month gross rent. The operating expense ratio is 40%. What is the monthly NOI?

$4,500

$3,000

$5,000

$3,750

#166. A 10-acre parcel is split into quarter-acre lots. If each lot sells for $85,000, what is the total sales revenue?

$3,400,000

$3,200,000

$3,600,000

$2,800,000

#167. Under Proposition 13, a property’s base year value was $300,000 in 2015. With 2% annual increases, what is the assessed value in 2020?

$330,000.00

$336,000.00

$331,224.48

$325,000.00

#168. A duplex generates $2,800/month total rent. If the GRM is 140, what is the property value?

$392,000

$4,704,000

$470,400

$336,000

#169. A loan balance is $195,000. The payoff includes 3 months of interest at 5.5%. What is the total payoff amount?

$198,225.00

$197,000.00

$196,500.00

$197,681.25

#170. A property is assessed at $500,000 with a homeowner’s exemption of $7,000. At a 1.1% tax rate, what are the taxes?

$5,423

$5,500

$5,390

$5,470

#171. An investor purchases property for $750,000 with 25% down. Annual NOI is $48,000. What is the cash-on-cash return?

6.4%

25.6%

8.53%

32%

#172. A seller pays the buyer a 2% credit for repairs on a $395,000 sale. What is the credit amount?

$7,900

$7,500

$8,000

$7,700

#173. A lot measures 0.75 acres. How many square feet is this?

34,848 sq ft

30,000 sq ft

36,000 sq ft

32,670 sq ft

#174. If a property’s NOI is $60,000 and the cap rate is 7.5%, what is the indicated value?

$750,000

$850,000

$800,000

$700,000

#175. A buyer obtains a $350,000 loan. The origination fee is 1% and the appraisal costs $500. What are the total loan costs?

$4,000

$3,500

$4,500

$3,850

#176. Escrow closes October 20. Annual taxes of $6,000 are due December 10 for Jul 1 – Dec 31. How much does the seller owe in prorated taxes?

$3,666.67

$3,333.33

$4,000.00

$3,000.00

#177. A building’s reproduction cost is $600,000. Physical deterioration is 10%, functional obsolescence is 5%. Land value is $150,000. What is the total property value using the cost approach?

$510,000

$750,000

$600,000

$660,000

#178. A commercial lease is $3.25/sq ft/month for 2,500 sq ft. What is the annual rent?

$8,125

$97,500

$93,750

$100,000

#179. A property sold for $465,000. Transfer taxes in the county are $1.10 per $1,000. What is the transfer tax?

$511.50

$465.00

$558.00

$500.00

#180. A borrower has a $220,000 loan at 6% for 30 years. Monthly payment is $1,319.01. After the first payment, what is the remaining balance?

$219,700.00

$219,780.99

$219,581.99

$219,900.00

#181. An appraiser determines a comparable sold for $520,000 but needed a $15,000 adjustment for an extra bathroom and -$8,000 for inferior location. What is the adjusted value?

$493,000

$527,000

$535,000

$512,000

#182. A property owner has an assessed value of $450,000. Special assessments add $800/year. At a 1.0% tax rate, what are total annual tax obligations?

$4,500

$5,250

$5,300

$5,000

#183. A construction loan for $500,000 has an interest reserve of 12 months at 8%. What is the interest reserve amount?

$40,000

$48,000

$36,000

$50,000

#184. A buyer’s debt-to-income ratio cannot exceed 36%. Monthly gross income is $7,200. Total monthly debt is $1,100. What maximum PITI can the buyer qualify for?

$1,492

$2,592

$1,396

$1,500

#185. A 16-unit building sells for $2,400,000. Average monthly rent is $1,100/unit. What is the GRM?

136.36

109.09

125.00

113.64

#186. A property’s effective age is 15 years and total economic life is 50 years. Reproduction cost is $400,000. What is the depreciation?

$100,000

$120,000

$150,000

$80,000

#187. A seller accepts an offer of $389,000. Closing costs are 3% of the sale price. Mortgage payoff is $245,000. What are the seller’s approximate net proceeds?

$144,000

$130,000

$132,330

$136,330

#188. Convert 0.0625 to a fraction.

1/16

1/8

1/12

1/20

#189. A buyer purchases a $550,000 home with PMI required because the down payment is 10%. PMI is 0.5% of the loan annually. What is the monthly PMI?

$229.17

$206.25

$187.50

$275.00

#190. An investor’s before-tax cash flow is $36,000. The initial equity investment was $150,000. What is the equity dividend rate?

20%

18%

28%

24%

#191. The documentary transfer tax in an unincorporated area is $1.10 per $1,000 of sale price. A property sold for $825,000. What is the transfer tax?

$907.50

$825.00

$990.00

$750.00

#192. A rental property has 4 units renting at $1,600/month each. Vacancy is 10%. Annual operating expenses are $28,800. What is the NOI?

$40,320

$48,000

$38,400

$42,000

#193. A section of land contains how many acres?

320 acres

160 acres

640 acres

1,280 acres

#194. A property tax bill is $5,400/year. The first installment (Jul 1 – Dec 31) is due November 1. If the buyer closes on August 15, how much does the seller owe?

$2,025

$675

$1,350

$900

#195. A contractor estimates building costs at $185/sq ft. For a 2,200 sq ft home, what is the estimated construction cost?

$407,000

$370,000

$444,000

$396,000

#196. A lease has a base rent of $4,000/month plus 3% of gross sales over $500,000/year. If gross sales are $800,000, what is the total annual rent?

$48,000

$72,000

$54,000

$57,000

#197. A home was reassessed at sale for $475,000 under Proposition 13. In year 3, inflation is 1.5%. What is the assessed value in year 3?

$485,000.00

$494,250.00

$490,000.00

$489,356.88

#198. An appraiser values land at $200,000 and improvements at $350,000. Physical depreciation is $52,500 and functional obsolescence is $17,500. What is the property’s value?

$480,000

$550,000

$500,000

$462,500

#199. A trust deed sale yields $310,000. The first mortgage balance is $225,000 and foreclosure costs are $15,000. What surplus goes to the former owner (assuming no other liens)?

$85,000

$60,000

$75,000

$70,000

#200. A buyer’s loan has a 4.875% rate for 15 years on $300,000. The total interest paid over the life of the loan is $124,000. What is the total amount paid?

$400,000

$424,000

$450,000

$412,000

Chapter 12 (Real Estate Mathematics)

Results

#1. A property sells for $500,000 and the agent’s commission rate is 6%. What is the total commission?

#2. Convert 0.075 to a percentage.

#3. A borrower takes out a $200,000 loan at 5% annual interest. What is the monthly interest payment for the first month?

#4. A property has an assessed value of $400,000 and the tax rate is 1.25%. What is the annual property tax?

#5. A rectangular lot measures 150 feet by 200 feet. What is the area in square feet?

#6. Convert the fraction 5/8 to a decimal.

#7. A property sells for $750,000 with a 5% commission split equally between buyer’s and seller’s agents. How much does each agent receive?

#8. A home has a market value of $600,000 and the outstanding loan balance is $400,000. What is the seller’s equity?

#9. An investment property was purchased for $500,000 with an estimated salvage value of $50,000 and a useful life of 25 years. Using straight-line depreciation, what is the annual depreciation expense?

#10. A property has a sale price of $500,000 and generates $50,000 in annual gross rental income. What is the Gross Rent Multiplier (GRM)?

#11. Annual property taxes are $3,650. Closing is July 1 and the seller owned the property from January 1 to June 30 (181 days). Using 365 days, the seller’s share is approximately:

#12. A property’s monthly PITI payment consists of which four components?

#13. Under Proposition 13 in California, the maximum annual increase in assessed property value is:

#14. A borrower obtains a $300,000 mortgage at 4% for 30 years. The total number of monthly payments is:

#15. A property sells for $800,000. The transfer tax rate is $1.10 per $1,000 of value. What is the transfer tax?

#16. A warehouse measures 50 feet long, 30 feet wide, and 20 feet tall. What is the volume in cubic feet?

#17. An agent earns a 3% commission on a property that sells for $400,000. What is the commission?

#18. A property has an assessed value of $350,000. Under California Proposition 13, the base tax rate is 1%. What is the annual property tax before additional assessments?

#19. A property owner’s equity is $175,000. If closing costs are $12,000 and there is a $3,000 lien, what are the net proceeds?

#20. A property generates $60,000 in annual gross rent and has a GRM of 12. What is the estimated property value?

#21. Under California law, property taxes are paid in two installments. The first installment is due on:

#22. A lot has two sections: a rectangle (60 ft × 40 ft) and a triangle (base 40 ft, height 20 ft). What is the total area?

#23. A $300,000 loan at 4% interest over 30 years has a monthly P&I payment of approximately $1,432.25. If annual property taxes are $3,600 and annual insurance is $1,200, what is the total monthly PITI?

#24. An investor is evaluating two properties. Property A has a GRM of 8 and Property B has a GRM of 12. Which property generates more income relative to its price?

#25. The first installment of California property taxes becomes delinquent if not paid by:

#26. A seller’s equity is $250,000. Closing costs total $18,000. A second mortgage lien of $15,000 must be paid off. Net proceeds to the seller are:

#27. A property is purchased for $600,000. The buyer makes a 20% down payment. What is the loan amount?

#28. Residential rental properties are depreciated over how many years under MACRS?

#29. Commercial properties are depreciated over how many years under MACRS?

#30. A property’s annual operating expenses are $24,000 and the property generates $80,000 in effective gross income. What is the operating expense ratio (OER)?

#31. A property sold for $1,200,000. The county transfer tax rate is $1.10 per $1,000 and the city adds $3.30 per $1,000. What is the total transfer tax?

#32. A 30-year mortgage has a higher total interest cost than a 15-year mortgage for the same loan amount and rate because:

#33. A property is assessed at $500,000 under Proposition 13. If the CPI increase is 1.8% for the year, the new assessed value is:

#34. An investor pays $800,000 for a property generating $80,000 annual gross rent. The property has $30,000 in annual operating expenses. What is the capitalization rate?

#35. Monthly rent is $1,800 and the closing date is the 15th of a 30-day month. The seller owes the buyer a rent credit of:

#36. A buyer obtains an 80% LTV loan on a property priced at $450,000. What is the loan amount?

#37. A property’s Net Operating Income (NOI) is $50,000 and the investor paid $625,000 for the property. What is the cap rate?

#38. The second installment of California property taxes is due on:

#39. An investor purchases a property for $1,000,000 with a salvage value of $100,000 and a useful life of 30 years. Annual straight-line depreciation is:

#40. A property sells for $550,000 with total closing costs of $22,000. The commission is 5% of the sale price. What is the total commission?

#41. A rectangular building has dimensions of 80 ft × 60 ft × 15 ft. What is the volume?

#42. A borrower has a monthly PITI payment of $2,200. Of this, $1,500 is P&I, $400 is taxes, and $300 is insurance. What percentage of the monthly payment goes to taxes?

#43. Annual property taxes are $4,380. Closing is October 1. The seller owned the property for 273 days (Jan 1 to Sept 30). The seller’s prorated share is approximately:

#44. A property has a market value of $500,000 and a loan-to-value ratio of 75%. What is the maximum loan amount?

#45. Convert 37.5% to a fraction in simplest form.

#46. A property’s annual gross rental income is $120,000 and the vacancy rate is 5%. What is the effective gross income?

#47. A property has an NOI of $75,000 and annual debt service of $60,000. What is the debt service coverage ratio (DSCR)?

#48. A property sells for $425,000. The buyer’s agent receives 2.5% commission. What is the buyer’s agent’s commission?

#49. A building lot is shaped as a trapezoid with parallel sides of 100 ft and 80 ft, and a height of 50 ft. What is the area?

#50. A $250,000 loan at 6% annual interest has a monthly interest payment in the first month of:

#51. If a property’s NOI increases from $50,000 to $55,000 while the cap rate remains at 8%, the property value increases from $625,000 to:

#52. A property has annual property taxes of $6,000. The first installment (due Nov 1) is $3,000. If the tax is delinquent after Dec 10, the penalty is:

#53. A seller’s market value is $700,000 and the outstanding first mortgage is $450,000. There is a second mortgage of $50,000. The seller’s equity is:

#54. An investor wants to purchase a property with a cap rate of at least 7%. If the property’s NOI is $63,000, the maximum price the investor should pay is:

#55. A property depreciates by $20,000 per year using straight-line depreciation. After 10 years, the total accumulated depreciation is:

#56. A rental property generates $3,600 per month in gross rent. Annual operating expenses are $15,600. What is the monthly NOI?

#57. A property is purchased for $400,000 with 25% down. The loan amount is $300,000 at 5% for 30 years. What is the monthly interest payment for the first month?

#58. Using the GRM approach, if a property generates $48,000 annual gross rent and the prevailing GRM in the area is 11, the estimated value is:

#59. A homeowner pays $1,200 per year in homeowner’s insurance. What is the monthly insurance cost?

#60. A property’s effective gross income is $90,000 and operating expenses are $36,000. The NOI is:

#61. A $500,000 property generates $40,000 in annual net operating income. What is the overall rate of return (cap rate)?

#62. Convert 12.5% to a decimal.

#63. A property sells for $350,000. The seller’s agent commission is 3% and the buyer’s agent commission is 2.5%. What is the total commission paid?

#64. Annual property taxes are $5,200. Closing is May 16 (seller owned 136 days out of 365). The seller’s prorated share is approximately:

#65. A property’s gross rent multiplier is 9.5 and the annual gross rent is $72,000. The estimated value is:

#66. A buyer puts 15% down on a $500,000 property. The loan amount is:

#67. A property has a vacancy rate of 8% and potential gross income of $100,000. What is the effective gross income?

#68. An investor’s property generates $36,000 NOI with a property value of $450,000. The cap rate is:

#69. A property is sold for $620,000. The county transfer tax ($1.10/$1,000) is:

#70. Under California law, if property taxes remain unpaid after June 30, the property may face:

#71. A 15-year mortgage at 4% on $300,000 results in approximately $99,431 in total interest. A 30-year mortgage at 4% on $300,000 results in approximately $215,609 in total interest. The 30-year mortgage costs more in interest by approximately:

#72. A property has the following monthly expenses: mortgage P&I $1,200, taxes $350, insurance $150, and HOA $200. The total monthly housing cost is:

#73. An agent lists a property at $650,000. After negotiations, the property sells for $625,000 with a 5.5% total commission. The total commission is:

#74. A property is assessed at $275,000. Local tax rate is 1% plus a 0.3% Mello-Roos assessment. Total annual tax is:

#75. An investor pays $900,000 for a 12-unit apartment building. Monthly rent per unit is $1,500. Annual gross rental income is:

#76. A property’s NOI is $85,000 and the cap rate is 7%. What is the property’s estimated value?

#77. A lot measures 200 ft × 150 ft = 30,000 sq ft. How many acres is this approximately? (1 acre = 43,560 sq ft)

#78. A borrower’s loan has an original balance of $350,000. After 5 years of payments, the remaining balance is $320,000. What amount of principal has been paid?