Math Real Estate
What did it cost to construct a building that is worth $155,200 today if it has depreciated at the rate of 2% per year (50 years useful life) for the past 4 years? A) $143,703.70 B) $168,695.65 C) $167.616 D) $167,993.47
The answer is $168,695.65. Depreciation is 2% per year for 4 years = 8% depreciation. Original cost at 100% ‒ depreciation at 8% = 92%. $155,200 (the current value) ÷ 92% (0.92) = $168,695.65 (the original cost).
A buyer purchased two parcels of land. One parcel was 2 miles square and the other contained 30 acres. If the price of the land was $2,000 an acre, what was the purchase cost? A) $1,340,000 B) $1,800,000 C) $1,626,000 D) $2,620,000
The answer is $2,620,000. One square mile is 640 acres, so 2 square miles is 1,280 acres. The two parcels together contain 1,310 acres (1,280 + 30 = 1,310). To find the cost, multiply the cost per acre by the total acres: 1,310 × $2,000 = $2,620,000.
An agent who works for XYZ Realty referred a buyer to a broker, who works for ABC Realty. The referring agent is to receive 25% of the buyer's agent's share of the commission when the transaction closes. The buyer purchased a $350,000 home, and the 7% commission was split as follows: listing brokerage, 2%; listing agent, 2%; buyer's brokerage, 1.5%; buyer's agent, 1.5%. How much was the referring agent paid? A) $24,500 B) $5,250.50 C) $7,000 D) $1,312.50
The answer is $1,312.50. $350,000 × 1.5% (0.015) = $5,250 $5,250 × 25% (0.25) = $1,312.50
A property has an appraised value of $400,000, secured by a $360,000 loan. What is the loan-to-value ratio (LTV)? A) 90% B) 70% C) 80% D) 75%
The answer is 90%. To find the LTV, divide the amount of the loan by the appraised value of the property: 360,000 ÷ 400,000 = 90% (0.9).
The listing price of a property was $135,000. The buyer made an offer of 90% of the listing price, which was accepted by the sellers. The property appraised for the offer price, and the buyers secured an 85% loan at 9% interest for 30 years. How much interest will be paid in the first payment? A) $774.56 B) $747.56 C) $860.62 D) $839.24
The answer is $774.56. $135,000 × 90% (0.90) = $121,500 sales price $121,500 × 85% (0.85) = $103,275 loan amount $103,275 × 9% (0.09) = $9,294.75 annual interest $9,294.75 ÷ 12 = $774.56
The buyers applied for a U.S. Department of Veterans Affairs (VA) loan to purchase a property for $79,500. The property appraised at $79,000. They agreed to pay a 1% loan origination fee. How much did they pay in origination fees? A) $970 B) $790 C) $795 D) $975
The answer is $790. $79,000 (100% loan) × 1% (0.01) = $790
Four units are renting for $450 each per month. There is a 5% vacancy factor and annual expenses are $3,547. The owner wants an 8% return on his investment, and the property has additional monthly income of $464. What is the effective gross income (EGI) of the property? A) $25,810 B) $21,796 C) $21,976 D) $20,984
The answer is $25,810. 4 × $450 × 12 = $21,600 $464 × 12 = $5,568 annual interest $21,600 + 5,568 = $27,168 potential gross income (PGI) $27,168 ‒ $1,358.40 (5% vacancy rate) = $25,809.60, round to $25,810
Three years ago, the owner paid $165,000 for her investment property. During her period of ownership, she added a family room valued at $16,500 and $10,000 worth of other improvements. If she sells the property for $240,000 and pays a 7% commission, what capital gains may she exclude? A) $38,700 B) $48,500 C) $31,700 D) $25,300
The answer is $31,700. $240,000 - $16,800 (7%) = $223,200 $165,000 + $16,500 + $10,000 = $191,500 $223,200 - $191,500 = $31,700
Buyers negotiated a $75,000 loan at 8% interest for 30 years, with the first payment due in arrears on April 1. If the closing takes place on February 24, with the seller having the day of closing, and using a 360-day year, how much interest must the buyers pay on the day of closing? A) $566.78 B) $66.67 C) $656.78 D) $56.68
The answer is $66.67. The buyers will owe interest for the portion of the month they own the home. Total amount due ÷ total days × days owed. The buyers will own the house for 4 days in February (February 28 - 24 = 4 days) $75,000 × 8% (0.08) = $6,000 interest for the year. $6,000 ÷ 360 × 4 = $66.67.
A seller wants to net $65,000 on the sale of his house after paying the broker a fee of 6%. How much must the gross selling price be? A) $67,035 B) $69,149 C) $66,091 D) $68,093
The answer is $69,149. $65,000 (net price) ÷ 94% (0.94) (100% - 6% (0.06) commission) = $69,148.936 round to $69,149 (sales price rounded up).
If the effective gross annual income generated by an apartment house is $112,000 and operating expenses are $53,700, what capitalization rate is used to obtain an indicated value of $542,325? A) 9.75% B) 10.50% C) 10.25% D) 10.75%
The answer is 10.75%. $112,000 (effective gross income (EGI)) ‒ $53,700 (expenses) = $58,300 (net operating income (NOI)) $58,300 ÷ $542,325 (property value) = 10.75% (0.1075) (the capitalization rate).
An apartment building with a $90,000 net operating income (NOI) and an 8% cap rate has a value of A) $1,720,000. B) $1,500,000. C) $1,125,000. D) $1,000,000.
The answer is $1,125,000. $90,000 ÷ 8% (0.08) = $1,125,000.
A homeowner purchased his home for $80,000 and later sold it for $10,000 more than she paid for it. What percentage of profit did she realize when she sold it? A) 12.5% B) 110% C) 10% D) 11.1%
The answer is 12.5%. $80,000 (purchase price) + $10,000 (the increase) = $90,000 (total sales price) ÷ $80,000 (the original purchase price) = 112.5% ‒ 100% = 12.5%. To check your answer: $10,000 (increase from original price) ÷ $80,000 (original price) = 12.5% (0.125) (percentage of profit).
A property was listed for $450,000. A buyer's offer of 95% of the list price was accepted. He had a 20% down payment and secured a 30-year fixed-rate loan at 6.75% interest. How much interest will he pay the first month of the loan? A) $23,085 B) $1,923.75 C) $3,847.50 D) $7,695
The answer is $1,923.75. Step 1, determine the sales price: $450,000 × 95% (0.95) = $427,500. Step 2, determine the loan amount: $427,500 × 0.80 = $342,000. Step 3, determine the annual interest: $342,000 × 6.75% (0.0675) = $23,085 ÷ 12 = $1,923.75 monthly interest.
A borrower secured an $80,000 loan at 8.25% interest, and the lender's cash outflow was $77,600. What was the effective yield to the lender? A) 8.85% B) 8.38% C) 8.63% D) 8.50%
The answer is 8.63% $80,000 - 77,600 = $2,400 2,400 ÷ $80,000 = 3 points (0.03) 0.125 × 3 = 0.375 8.25% + 0.375 = 8.63%
The replacement cost of a building is $250,000. It has an annual depreciation of 8%, a site value of $50,000, and annual taxes of $3,950. What is the value of the property? A) $283,950 B) $230,000 C) $276,050 D) $280,000
The answer is $280,000. $250,000 - $20,000 (8%) = $230,000 $230,000 + 50,000 = $280,000
A seller is interviewing agents to list her property. She has the following quotes from two different companies: XYZ Realty, 7% commission; and LMN Realty, 5.5% commission. If her house sells for $225,000, how much will she save if she lists her property with LMN Realty? A) $3,375 B) $3,357 C) $4,500 D) $5,400
The answer is $3,375. $225,000 × 7% (0.07) = $15,750 $225,000 × 5.5% (0.055) = $12,375 $15,750 - $12,375 = $3,375 savings
A building has a semiannual effective gross income (EGI) of $250,000. If the annual expenses are 20% of the EGI, what is the net operating income (NOI)? A) $100,000 B) $400,000 C) $500,000 D) $200,000
The answer is $400,000. $250,000 × 2 = $500,000 $500,000 ‒ $100,000 (20%) = $400,000
When the owners sold their property, they paid a 6% commission. Their check after the commission was paid was $470,000. What was the selling price of the property? A) $800,000 B) $500,000 C) $900,000 D) $783,333
The answer is $500,000. 100% - 6% = 94% seller's percentage $470,000 ÷ 94% (0.94)= $500,000
When the seller listed a property, he agreed to pay a 7% commission. The property sold for $190,000. If the listing agent was paid 2%, and the selling agent was paid 1.5%, how much was the broker paid after paying his agents? A) $6,650 B) $3,800 C) $2,850 D) $13,300
The answer is $6,650. 7% - 2% - 1.5% = 3.5% to the broker. $190,000 × 3.5% (0.035) = $6,650
A savings and loan agreed to make a $65,000 mortgage at 8% interest for 30 years and charged three points to negotiate the loan. What was the effective yield to the lender? A) 8.35% B) 8.25% C) 8.735% D) 8.38%
The answer is 8.38%. The lender yield per point is 1.25% (0.125). 0.125 × 3 = 0.375 8% + 0.38 = 8.38%
A buyer has an annual income of $82,000 with recurring monthly debt of $500 that does not include housing expenses. If the lender's qualifying ratios are 28% and 36%, what is the maximum monthly house payment for which he can qualify? A) $1,960 B) $1,913 C) $2,460 D) $1,413
The answer is $1,913. $82,000 ÷ 12 = $6,833.33 × 28% (0.28) = $1,913.33, round to $1,913 $6,833.33 × 36% (0.36) = $2,460 − $500 = $1,960
The buyers secured a loan with a 75% loan-to-value (LTV) ratio. The interest rate was 7.125%, and the term was for 30 years. The first month's interest payment was $477.82. What was the appraised value of the property? A) $79,239 B) $107,300 C) $80,475 D) $103,700
The answer is $107,300. $477.82 × 12 = $5,733.84 annual interest $5,733.84 ÷ 7.125% (0.07125) = $80,475 $80,475 ÷ 75% (0.75) = $107,300
The market value of a property is $65,000 and is assessed for 45% of its value. If the owner's semiannual tax bill was $511.88, what was the tax rate per $100? A) $1.75 B) 350 mills C) $3.50 D) 175 mills
The answer is $3.50. $65,000 × 45% (0.45) = $29,250 assessed value $511.88 × 2 = $1,023.75 annual taxes $1,023.75 ÷ $29,250 = 0.035 0.035 × 100 = $3.50
The effective gross annual income from a property is $112,000. Total expenses for this year are $53,700. What capitalization rate was used to obtain a valuation of $542,325? A) 9.75% B) 10.25% C) 10.5% D) 10.75%
The answer is 10.75%. The capitalization rate may be found by dividing the net operating income (NOI) by the value of the property (rate = NOI ÷ value). In this case, the annual NOI is found by subtracting the yearly expenses from the gross annual income: $112,000 (annual income) ‒ $53,700 (total expenses) = $58,310 (the NOI). $58,301 (ROI) ÷ $542,325 (the value) = 10.75% (0.1075)
A rectangular lot is 275 ft. deep, and it contains 2/3 of an acre. What is the length of the lot? A) 106.5 ft. B) 158.4 ft. C) 105.6 ft. D) 290.04 ft.
The answer is 105.6 ft. 43,560 ÷ 3 = 14,520 × 2 = 29,040 sq. ft. 29,040 ÷ 275 ft. = 105.60 ft. 43,560 × 0.6667 (2 ÷ 3 = 0.6667) = 29,041.45 sq. ft. 29,041.45 ÷ 275 ft. = 105.6052 ft.
If an interest payment of $1,500 is made every 3 months on a $50,000 loan, what is the interest rate? A) 9% B) 12% C) 6% D) 3%
The answer is 12%. $1,500 × 4 (every 3 months is ¼ of a year) = $6,000 (the annual interest). $6,000 ÷ $50,000 (the loan amount) = 12% (0.12)
How many cubic yards of concrete must a builder buy to pour a sidewalk that measures 45 ft. × 3.25 ft. and is 5 inches thick? A) 6.7708 B) 2.2571 C) 60.9375 D) 0.4167
The answer is 2.2571. 5 in. ÷ 12 in. = 0.4167 in. 45 ft. × 3.25 ft. × 0.4167 ft. = 60.9423 cu. ft. 60.9423 ÷ 27 = 2.2571 cu. yds.
A lot contains 9/10 of an acre. What is the depth of the lot if the front measures 150 feet? A) 216.36 ft. B) 323.67 ft. C) 322.67 ft. D) 261.36 ft.
The answer is 261.36 ft 9 ÷ 10 = 90% 43,560 × 90% (0.90) = 39,204 39,204 ÷ 150 = 261.36 ft.
To secure a $100,000 loan, the buyer paid $3,000 in discount points, and the seller paid $2,000 in discount points. How many points were charged? A) 5 B) 3 C) 4 D) 2
The answer is 5. Knowing each point is 1% of the loan amount and with the total amount of $5,000 being paid, it is easy to see 5 points. $5,000 ÷ $100,000 = 5 points (0.05)
A property sold for $235,000, and the selling broker's half of the commission was $8,225. What was the commission rate? A) 7% B) 5% C) 4% D) 6%
The answer is 7%. $8,225 × 2 = $16,450 total commission paid $16,450 ÷ $235,000 = 7% (0.07)
The area of a rectangle that is 50 ft. × 170 ft. is A) 2,200 linear ft. B) 8,500 sq. ft. C) 440 linear ft. D) 4,400 sq. ft.
The answer is 8,500 square feet. 50 ft. × 170 ft. = 8,500 sq. ft. The area of a rectangle is length × width.
Ann listed her property with XYZ Realty, which charges a flat fee of $2,995 to list the property. If a sales associate within XYZ sells the property, the total commission paid is $2,995. However, if a sales associate from another company brings the buyer that purchases the property, the owner agreed to pay that company an additional 3% commission. A sales associate from ABC Realty presented an offer of $425,000. If the offer is accepted, the total commission that the owner will pay is A) $15,745. B) $12,750. C) $10,500. D) $11,250.
The answer is $15,745. $425,000 × 3% (0.03) = $12,750 $12,750 + 2,995 = $15,745
Two years ago, a buyer paid $175,000 for a house. Since that time, the property has depreciated 3% each year. What is the value of the property today? A) $164,500 B) $185,657 C) $185,500 D) $164,658
The answer is $164,658. $175,000 - 3% (0.03) - 3% (0.03) = $164,657.50, round up to $164,658
A loan officer is paid 45% of the origination fee that her company charges. The loan officer negotiated a reverse mortgage, and her company was paid 2% of the appraised value of $190,000. How much was the loan officer paid? A) $5,200 B) $6,400 C) $3,800 D) $1,710
The answer is $1,710. $190,000 × 2% (0.02) = $3,800 total origination fee $3,800 × 45% (0.45) = $1,710
How much monthly PITI payment can a purchaser qualify for if he earns $6,600 gross income monthly and the lender applies 28/36 qualifying ratios? A) $1,848 B) $2,300 C) $2,376 D) $1,650
The answer is $1,848. $6,600 income × 28% (0.28) = $1,848 (monthly PITI payment). The lender's 28/36 qualifying ratios mean that the purchaser's total monthly housing expenses should be no more than 28% of his total monthly gross income, and that the purchaser's total monthly obligations must not exceed 36% of his total monthly gross income.
An agent is managing a 15-unit apartment building and is paid 9% of the gross income. She leases five apartments for $500, five for $550, and five for $600. There is a 3% vacancy rate and additional income of $450 per month. The monthly operating expenses are $1,749, and the owner is generating an 8% return on the investment. What is the effective gross income (EGI) on the building? A) $96,030 B) $99,000 C) $101,430 D) $80,442
The answer is $101,430. 5 × $500 × 12 = $30,000 5 × $550 × 12 = $33,000 5 × $600 × 12 = $36,000 Total potential gross income (PGI) = $99,000 $99,000 ‒ $2,970 (3%) = $96,030. $450 × 12 = $5,400. $ 96,030 + 5,400 = $101,430.
A property is now worth $117,978. If it has appreciated 6% each year for the past 2 years, what was the original investment? A) $110,899 B) $105,000 C) $104,245 D) $111,300
The answer is $105,000. Year 1 $117,978 ÷ 106% (100% + 6%) (1.06) = $111,300 Year 2 $111,300 ÷ 106% (1.06) = $105,000
A house is now worth $105,000. The lot is now worth $50,000. If the house depreciated 4% each year for the past 2 years, and the lot appreciated 6% each year for the past 2 years, what was the approximate combined original value of the house and lot? A) $156,544 B) $109,375 C) $158,432 D) $113,932
The answer is $158,432. House Year 1: $105,000 ÷ 96% (100% ‒ 4%) (0.96) = $109,375 ÷ 96% (0.96) = $113,932 Lot year 1: $50,000 ÷ 106% (100% = 6%) (1.06) = $47,170 Lot year 2: $47,170 ÷ 106% (1.06) = $44,500 Total of house and lot together: $113,932 + $44,500 = $158,432
The owners received a semiannual tax bill of $984.38. Property in the jurisdiction is assessed at one-fourth the market value. If the tax rate is $4.50 per $100, what is the estimated market value of the property? A) $195,000 B) $43,750 C) $53,750 D) $175,000
The answer is $175,000. Tax rate= $4.50 ÷ 100 = 0.045 $984.38 × 2 = $1,968.76 Annual taxes $1,968.76 ÷ 0.045 = $43,750 Assessed value $43,750 ÷ 25% (0.25) = $175,000
A broker sold a property and received a 6.5% commission. The broker gave the listing salesperson $3,575, which was 30% of the firm's commission. What was the selling price of the property? A) $183,333 B) $55,000 C) $152,580 D) $95,775
The answer is $183,333. The answer requires two steps: (1) find the firm's full commission, and (2) find the selling price using the full commission and the rate. $3,575 (the listing salesperson's commission) = 30% × full commission (1) To find the full commission, divide the listing salesperson's commission by the salesperson's share of 30%: full commission = $3,575 ÷ 30% (0.30) = $11,916.67. (2) To find the sales price, divide the full commission by the brokerage commission rate: full commission ($11,916.67) ÷ brokerage rate (6.5%) = sales price ($183,333).
Five years ago, a homeowner bought a home for $250,000. Home values in her area have improved, and the current market value of the house has increased by 15%. If she has $95,875 left to pay on her mortgage loan, what is the current equity in her home? A) $250,000 B) $154,125 C) $138,712 D) $191,625
The answer is $191,625. The homeowner's equity is the difference between the market value of her property and the debt that encumbers it. Original cost ($250,000) + increase in value ($250,000 × 15% (0.15) = $37,500) = Current market value ($287,500). Current market value ($287,500) - mortgage debt ($95,875) = the homeowner's equity ($191,625).
If the interest rate on an FHA-insured mortgage loan is 5.5% and the monthly payment is $1,012, the principal sum would be A) $184,000. B) $192,000. C) $667,920. D) $220,800.
The answer is $220,800. To find the principal sum, multiply the monthly payment by 12 (12 months in a year) and divide that amount by the interest rate. $1,012 × 12 = $12,144 (annual payments) $12,144 ÷ 5.5% (0.055) (interest rate) = $220,800 (the principal amount)
A homeowner has a property valued at $125,000 that is assessed at 35% of its value. If the local tax rate is 6,400 mills per $100 of the assessed value, what are the monthly taxes? A) $233.33 B) $480 C) $280.00 D) $140.33
The answer is $233.33. Tax rate = 6,400 mills ÷ 1,000 = 6.40 ÷ 100 = 0.064 Assessed value = $125,000 × 35% (0.35) = $43,750 $43,750 × 0.064 = $2,800 annual tax $2,800 ÷ 12 = $233.33 monthly tax
A sales associate for XYZ Realty listed and sold a $175,000 home. The seller paid a 6% commission of which the sales associate received 2% for listing the property, and 1.5% for selling the property. How much was the brokerage's share of the commission? A) $5,250 B) $10,500 C) $4,375 D) $6,125
The answer is $4,375. Total commission = $175,000 × 6% (0.06) = $10,500. Sales associate's share = 3.5% (2% + 1.5%) $175,000 × 3.5% (0.035) = $6,125. $10,500 ‒ $6,125 = $4,375 for the brokerage. Or 6% ‒ 3.5% = 2.5% for the brokerage times the sales price.
An investment property was purchased for $250,000. The owner added a tennis court at a cost of $10,000. Two years later, the property sold for $325,000 and the seller paid a 7% commission plus $250 in attorney fees. If he purchases another property for $350,000, how much capital gains will he exclude? A) $42,520 B) $22,750 C) $42,000 D) $42,250
The answer is $42,000. $250,000 + 10,000 = $260,000 $325,000 - 22,750 (7%) = $302,250 - 250 = $302,000 $302,000 - 260,000 = $42,000
The N½ of the SW¼ of the NE¼ sold for $2,500 per acre. What was the selling price? A) $40,000 B) $50,000 C) $20,000 D) $10,000
The answer is $50,000. Use the denominator for each section to determine how many acres. Chain them in the calculator without totaling. 640 ÷ 4 ÷ 4 ÷ 2 = 20 acres 20 × $2,500 = $50,000
If a lender agrees to make a loan based on an 80% loan-to-value (LTV) ratio, what is the amount of the loan if the property appraises for $114,500 and the sales price is $116,900? A) $83,200 B) $92,900 C) $91,600 D) $91,300
The answer is $91,600. The LTV ratio will be based on the relationship of the loan to either the appraisal or the purchase price, whichever is less. In this case, the appraisal is less. Therefore, the loan will be 80% of $114,500, which equals $91,600. $114,500 × 80% (0.80) = $91,600
A building sold for $157,000. The broker charged a 6% commission and gave 10% to the salesperson who took the listing. What was the listing salesperson's commission? A) $942 B) $1,570 C) $4,239 D) $239
The answer is $942. $157,000 (sales price) × 6% (0.06) = $9,420;(listing commission) $9,420 × 10% (0.10) commission percentage) = $942 (listingsalesperson's commission)
The owners live in a county were taxes are paid in arrears and 360 days are used to compute the property tax bill. The house closed on April 13, with the seller owning the day of closing. If the annual tax bill is $3,355, how much will be credited to the buyer on the settlement statement for taxes for this year? A) $2,441.84 B) $959.90 C) $2,407.78 D) $946.57
The answer is $959.90. The taxes were paid in arrears, and the buyer will pay the bill next year. The seller will owe the buyer for the time the seller owns the house—January 1 to April 13. Total owed ÷ total days × days owed = amount due $3,355 ÷ 360 × 103= 959.90.
