Math Flashcards
A rectangular parcel of unimproved property was valued at $4.40 per square foot, was 200 feet deep and was sold for its value of $100,000. Based upon these numbers, how much is the property valued by the front foot (closest figure):
A) - $88
B) - $227
C) - $880
D) - $113
C) - $880
Answer: C—$100,000 (selling price) / $4.40 per sq. ft. = 22,727 sq. ft. in parcel
22,727 sq. ft. / 200 feet deep = 113.6 front feet
$100,000 / 113.6’ = $880 per front foot
What is the dollar difference between an $8,600 loan at 6% interest and a savings account at 4 1/2% simple interest?
A) - $26.75
B) - $516.00
C) - $387.00
D) - $129.00
D) - $129.00
Answer: D—6% - 4 1/2% = 1 1/2%
$8,600 loan x 1 1/2% =
$8,600 x .015 = $129.00 difference
Mr. Jones listed his home with broker Brown for $250,000. The broker presented an offer that was 10% below the listed price. Mr. Jones and broker Brown discussed the situation and Mr. Jones finally agreed to counter-offer at 6% below the listed price providing broker Brown would agree to reduce his commission by 1%. The commission agreed to originally was 6%. Using only the numbers presented in this problem, what would the seller receive for his house if the buyer accepted the seller’s counter-offer and assuming the only deduction from the selling price would be the broker’s commission?
A) - $235,000
B) - $223,250
C) - $222,600
D) - None of the above are correct
B) - $223,250
Answer: B—$250,000 (list price) x 94% (100% - 6%, counter-offer) =
$235,000 selling price
6% - 1% reduction = 5% commission to broker
$235,000 (selling price) x 95% (100% - 5% commission to broker)
$223,250 to seller
A seller received a check from escrow in the amount of $43,190.50. Escrow deducted the following amounts from the selling price: A commission of 8% of the selling price and other expenses of $509.50. Based upon these numbers, what was the selling price?
A) - $47,196
B) - $47,500
C) - $47,000
D) - None of the above are correct
B) - $47,500
Answer: B—$43,190.50 + $509.50 = $43,700
$43,700 / 92% (100% - 8%) = $47,500 selling price
Martin sold a house and took back a note for $3,740 secured by a second trust deed. He immediately sold this note for $2,431. The rate of discount was:
A) - 28%
B) - 35%
C) - 55%
D) - 65%
B) - 35%
Answer: B—$3,740 - $2,431 = $1,309
$1,309 / $3,740 = .35 or 35%
A man owns a rental unit that nets him $37.50 per month. He realizes a 9% return on his investment each year. What is his investment in the property?
A) - $5,000
B) - $4,167
C) - $4,050
D) - None of the preceding
A) - $5,000
Answer: A—$37.50 per month x 12 months =
$450 net per year. $450 is 9% of value.
$450 / 9% = $450 + .09 = $5,000 investment
The seller received a check from escrow in the amount of $37,187.10. From the total selling price, the escrow had deducted a commission of 6% and other expenses of $403.50. The gross selling price was:
A) - $37,590
B) - $39,990
C) - $39,418
D) - $39,846
B) - $39,990
Answer: B—This is a commonly encountered problem. We can categorize this as a “net listing” type problem. A general rule can be developed as follows:
(Net to seller + cost of sale) / (100% - % commission) = Gross selling price
($37,187.10 + $403.50) / 94% (100% - 6%) = 37,590.60
37,590.60 / .94 = $39,990 gross selling price
Assuming the total value of a property is $190,000 and the total net income is $13,860; the capitalizaton rate would be:
A) - 6.5%
B) - 7%
C) - 7.2%
D) - 7.5%
C) - 7.2%
Answer: C—Net is ___% of Value
$13,860 / $190,000 = .072 or 7.2% Capitalization Rate
Leland uses an 8% capitalization rate for a 40-unit apartment building that generates $174,000 in net income. Which of the following is the most appropriate value of this property?
A) - $1,392,000
B) - $1,566,000
C) - $2,175,000
D) - Cannot be determined from the information given
C) - $2,175,000
Answer: C—$174,000 / .08 = $2,175,000
A $10,000 note is to be paid off at the end of 12 months. It bears interest at the rate of 9% per annum and is purchased by the investor for $9,500. What is the % return on the invested principal?
A) - 9%
B) - 11.2%
C) - 13.5%
D) - 14.7%
D) - 14.7%
Answer: D—$10,000 x .09 (interest rate) = $900 interest return per year
$10,000 (loan) - $9,500 (invested) = $500 profit when loan is paid off
$500 (profit on loan) + $900 (interest) = $1,400 total profit over his investment of $9,500
$1,400 / $9,500 = 14.7+% return on investment
In order to earn $75 per month, the amount one would have to invest at 5% would be:
A) - $6,000
B) - $12,000
C) - $18,000
D) - $24,000
C) - $18,000
Answer: C—$75 per month x 12 months = $900
$900 / .05 = $18,000
A merchant paid $9,300 for the stock in trade of a retail business. He sold it for 33 1/3% more than he paid for it. If he lost 15% of the gross sales price because of bad credit risks, the net percent profit on his original investment would be:
A) - $1,240
B) - 13 1/3%
C) - 10%
D) - 18 1/3%
B) - 13 1/3%
Answer: B—$9,300 (cost) x 33 1/3% = $9,300 x .333 = $3,100 profit
$9,300 (cost) + $3,100 (profit) = $12,400 (selling price)
$12,400 (selling price) x 15% (loss) = $1,860 (loss to bad credit risks)
Net profit is ___% of cost ($3,100 - $1,860 = $1,240 Net Profit)
$1,240 / $9,300 = 13 1/3% net profit
A variation of this question on the state exam asks for the amount of net profit in dollars ($1,240).
What would be the value of a four-plex rental property if each unit rented for $206.25 per month. Vacancies were 5% of gross rents, operating expenses were $4,140 per year, and the net earnings represented an 8% return on the investment?
A) - $65,812.50
B) - $68,400
C) - $71,484
D) - $72,000
A) - $65,812.50
Answer: A—$206.25 (rent per unit) x 4 units = $825 (total rent per month)
$825 x 12 months = $9,900 (annual rent)
$9,900 x .95 (100% - 5% vacancies) = $9,405 (effective gross income)
$9,405 - $4,140 (expenses) = $5,265 (net income)
$5,265 / .08 (rate of return) = $65,812.50
Mr Williams borrowed $750 and signed a straight note bearing interest at the rate of 12% per annum. During the term of the note he paid $135.00 interest. What was the term of the note?
A) - 12 months
B) - 15 months
C) - 18 months
D) - 24 months
C) - 18 months
Answer: C—Divide the total interest paid during the term of the note by the interest due each month. This will give the number of payments (months).
$750 (loan) x 12% (annual interest rate) =
$750 x .12 = $90.00 interest per year.
$90.00 (interest per year) / 12 months =
$7.50 (interest per month)
$135 (total interest paid) / $7.50 (interest per month) = 18 months
Jones bought a house for $125,000. He obtained a loan for 88% of the purchase price payable, $1,549 per month at 12% interest. Before he made his first payment, he sold the house for $139,750. His equity at the time of the sale was:
A) - $15,000
B) - $29,750
C) - $139,750
D) - None of the above
B) - $29,750
Answer: B—$125,000 x .88 = $110,000 loan
$139,750 - $110,000 = $29,750 equity
The value of a parcel of real property is $45,500. One-half of the annual real property tax is $227.50. Which of the following most nearly represents the tax rate?
A) - $1.00
B) - $.50
C) - $2.00
D) - Not determinable from the information given
A) - $1.00
Answer: A—Taxes per year = 2 x $227.50 = $455.00. Divide this by $45,500 = .01 = 1%. This means that the taxes are 1% of the property value. This can be converted into a dollar tax rate which is always expressed in dollars per $100 of assessed value. In this case, the tax rate is $1.00 per $100.
A property sold for $31,000. The broker agreed to a 6% sales commission. What would the salesman receive if his share was 45% of the agreed commission?
A) - $1,860
B) - $837
C) - $1,023
D) - None of the preceding
B) - $837
Answer: B—$31,000 selling price x 6% =
$1,860 total commission x 45% =
$837 salesperson
A home sold for $220,000 which represented an increase of 10% over the seller’s cost. The seller’s cost was:
A) - $198,000
B) - $200,000
C) - $210,000
D) - $244,444
B) - $200,000
Answer: B—$220,000 is 110% of cost
$220,000 / 110% = $200,000 cost
McHugh purchased a home for $80,000 paying 21.25% down and financing the balance on a 30-year amortized loan with interest at 10.25% per annum. The lender will require monthly impounds or taxes ($800 per year) and casualty insurance ($978 for a three-year policy). Assuming that the first monthly payment on the principal is $119, the total amount McHugh will have to pay the first month would be approximately:
A) - $932
B) - $751
C) - $597
D) - $213
B) - $751
Answer: B—$80,000
$17,000 (Down payment)
$63,000 (Loan)
$800 / 12 mo. = $66.67 impounds per month
$978 / 36 mo. = $27.17 insurance per month
$63,000 x .1025 = $6,457.50 interest per year
$6,457.50 / 12 mo. = $538.13 interest per month
$119 + 538.13 = $657.13 P&I
$ 657.13 (P&I) $+ 66.67 $+ 27.17 \_\_\_\_\_\_\_\_\_ $ 750.97 or $751
A lot contains a 14-year old single-family home with a replacement cost of $89,000. The value of the land is $22,000. Considering a depreciation figure of 1 1/2 percent per year, what is the value of the entire property?
A) - $111,000
B) - $92,310
C) - $70,310
D) - $67,000
B) - $92,310
Answer: B—14 yrs. x 1.5% (1 1/2%) = 21%
$89,000 - $18,690 ($89,000 x 21%) = $70,310 present value of the improvements
$70,310 + $22,000 (land) = $92,310
A tract of land in a recreational area is measured at 395,340 square feet. A corner of the tract, 30 feet wide and 110 feet deep is owned by the county. The privately owned land sold for $5,250 per acre. What was the total amount realized from the sale?
A) - $11,250
B) - $32,500
C) - $44,300
D) - $47,250
D) - $47,250
Answer: D—30’ x 110’ = 3,300 (owned by county)
395,340 sq. ft. - 3,300 sq. ft. = 392,040 sq. ft.
392,040 sq. ft. / 43,560 sq. ft. (one acre) =
9 acres (privately owned land)
9 acres x $5,250 per acre = $47,250
Simple interest was calculated at 8 1/2% per annum on a loan of $1,968 for three years, ten months and twenty days. The interest was most nearly:
A) - $589
B) - $607
C) - $650
D) - $668
C) - $650
Answer: C—$1,968 x .085 = $167.28 interest per year
$167.28 / 12 = $13.94 interest per month
$13.94 / 30 days = .46 cents interest per day
$167.28 x 3 years = $501.84
$13.94 x 10 mo. = $139.40
$0.46 x 20 days = $9.20 $501.84 + 139.40 + 9.20 = $650.44
$650.44 or $650 closest answer
A seller received $15,000 from the sale of property. The only expenses involved in the sale were the escrow costs of $213 and the broker’s commission of 6%. Assuming no other expenses other than those mentioned, how much did the property sell for?
A) - $16,115
B) - $16,183
C) - $16,125
D) - $15,213
B) - $16,183
Answer: B—The important thing to remember in this type of question (this is a net listing type) is that the broker’s commission is 6% of the selling price.
$15,213 is 94% of the selling price.
$15,213 / .94 = $16,183 Selling Price
This problem could be changed next week to ask for the amount of the broker’s commission: $970.
The commission on the sale of a $170,000 property was 6% of the selling price. Two salesmen had worked on the property, one listed and the other sold. It was agreed that they would split the commission, 35% to one salesman, 25% to the listing salesman, and 40% going to the employing broker. How much did the selling salesman receive?
A) - $3,570
B) - $2,550
C) - $4,080
D) - $10,200
A) - $3,570
Answer: A—$170,000 x .06 = $10,200
$10,200 x .35 = $3,570
A man purchased a property for 20% less than the listed price, then sold it for the original listed price. What was his % profit based on cost?
A) - 25%
B) - 20%
C) - 80%
D) - Cannot be worked out, insufficient information.
A) - 25%
Answer: A—You can make up numbers to help you solve this problem.Example: Listed price $100. Purchased for $80 (20% less than listed price). Sold for $100
Profit is $20 on a cost of $80.
$20 is % of $80
$20 / $80 = 25% profit
A man owned a building that contained 20,000 square feet. He planned to carpet 60% of the building. If the carpeting cost $8.00 per square yard, the cost of the carpeting would be:
A) - $10,000
B) - $12,500
C) - $15,000
D) - $18,000
A) - $10,000
Answer: A—20,000 sq. ft. x 60% = 12,000 sq. ft.
12,000 / 9 sq. ft. per sq. yd. = 1,333.3333
1,333.333 x $8.00 per sq. yd. = $10,666.66
Closest answer: $10,000
An investor was going to have a building constructed at a cost of $300,000. He had a tenant who was willing to lease the property for $5,000 a month on a long-term lease. He calculated that the expenses would amount to $12,000 per year. The desired rate of return was 12%. How much could he afford to pay for the land?
A) - $80,000
B) - $100,000
C) - $104,850
D) - $110,000
B) - $100,000
Answer: B—$5,000 x 12 mo. = $ 60,000
$60,000 + $ 12,000 (expenses) = $ 48,000 (net income)
$48,000 / .12 = $400,000
$400,000 - $300,000 (building value) = $100,000 (Land)
Two brokers agreed to split a 4 1/2% commission on a 50-50 basis on the sale of a property for $162,500. The listing salesperson agreed to a 50-50 split with his employing broker. The salesperson would be paid a commission of:
A) - $8,125.00
B) - $4,875.00
C) - $3,656.25
D) - $1,828.13
D) - $1,828.13
Answer: D—$162,500 x .045 = $7,312.50
$7,312.50 / two brokers = $3,656.25 (to each broker)
$3,656.25 split 50/50 = $1,828.13 (to the salesperson)
Leland uses an 8% capitalization rate for a 40-unit apartment building that generates $174,000 net income. Which of the following is the most appropriate value of this property?
A) - $1,392,000
B) - $1,566,000
C) - $2,175,000
D) - Cannot be determined from the information given
C) - $2,175,000
Answer: C—$174,000 / .08 = $2,175,000
Mr. Jones sold his home for $169,500 which was 9% more than he paid for the property. How much did he pay for the property?
A) - $145,000
B) - $155,000
C) - $155,500
D) - $160,000
C) - $155,500
Answer: C—$169,500 is 109% of his cost.
(Remember: Profit is always a % of cost)
$169,500 / 109% = $169,500 / 1.09 = $155,500
Several years ago, Mr. Tite suffered some personal reverses and borrowed $5,000 to take care of his needs. Just recently, he noted that he had paid $100 interest over a 90-day span. Since this was a straight note, what was the interest rate?
A) - 7%
B) - 10%
C) - 6%
D) - 8%
D) - 8%
Answer: D—$100 for 3 months = $400 for 12 months (1 year)
$400 per year is ___% of $5,000 loan balance
$400 / $5,000 = .08 = 8% interest rate on straight note
Which of the following is the largest parcel of land?
A) - 10% of a township
B) - 2 sections
C) - 4 square miles
D) - 5,280 feet x 10,560 feet
C) - 4 square miles
Answer: C—Choice (A): 10% of a township = 3.6 sections or 3.6 square miles
Choice (B): 2 sections = 2 square miles or 55,756,800 square feet
Choice (D): 5,280 feet x 10,560 feet also equals 55,756,800 sq. ft.
Choice (C): 4 square miles is the largest parcel of land.
A broker earns 8% from the sale of property. The salesperson received 35% of the 8%. If the salesperson received $6,000, what was the selling price?
A) - $75,000
B) - $18,514
C) - $214,286
D) - $300,000
C) - $214,286
Answer: C—$6,000 is 35% of the total commission
$6,000 / 35% = $17,142.86 total commission
$17,142.86 is 8% of the selling price
$17,142.86 / 8% = $214,285.71 selling price
A man bought 2 lots for $6,000 and divided them into 3 lots which he sold for $4,800 each. What was his percentage profit?
A) - 125%
B) - 20%
C) - 240%
D) - 140%
D) - 140%
Answer: D—$4,800 x 3 lots = $14,400 selling price of 3 lots - 6,000 original cost of 2 lots \_\_\_\_\_\_\_ $ 8,400 profit
Profit is a % of Cost
$8,400 is____% of $6,000
$8,400 / $6,000 = 1.4 = 140% profit
A bank purchased an existing straight note for $17,370 which was discounted 3 1/2% off of its face value. The face value of the note was:
A) - $16,782.61
B) - $17,977.95
C) - $18,000.00
D) - $18,070.35
C) - $18,000.00
Answer: C—$17,370 is 96 1/2% of the face amount
$17,370 / 96 1/2% = $18,000 face amount
Carter bought 10 acres of vacant land for $20,000 per acre, making a down payment of $20,000 and executing a straight note and a blanket deed of trust for the balance. As a part of the note, the lender agreed that when Carter made an additional payment of $20,000 on the principal, the trustee would issue a partial reconveyance for one acre. Carter has paid a total of $40,000 on the note and now owns two acres free and clear. The percentage of his equity in the encumbered property:
A) - has been eliminated.
B) - remains the same.
C) - has increased.
D) - has decreased.
C) - has increased.
Answer: C—10 acres x $20,000 per acre = $200,000
$200,000 - $20,000 down = $180,000 loan with $20,000 equity
Carter’s percentage of equity is now 10%
Every $20,000 payment increases the equity by 10%
$20,000 + $40,000 = $60,000
$60,000 / $200,000 = 30% equity
The equity has increased.
An income property shows the following information: $94,500 in expenses have been deducted from the gross income to arrive at the net income. This amount represents 60% of the gross income. If an investor anticipates a 12 1/2% return on his investment, approximately how much would he offer:
A) - $81,000
B) - $196,000
C) - $504,000
D) - $787,500
C) - $504,000
Answer: C—$ 94,500 (expenses) represent 60% of the gross
$ 94,500 / 60% = $157,500 gross
$157,500 - $94,500 = $63,000 net
$63,000 / 12 1/2% = $504,000 value
$63,000 / 12 1/2% = $504,000 value
If a lot is 220 feet wide and 330 feet deep, it contains approximately:
A) - 3/4ths of an acre
B) - 1 acre
C) - 1-3/5ths of an acre
D) - 1-2/3rds of an acre
D) - 1-2/3rds of an acre
Answer: D—220’ x 330’ = 72,600
72,600 / 43,560 (one acre) =
1.6666 acres or 1 2/3rds of an acre
The expenses on a property increased by $900. If the area capitalization rate is 10%, how has the value changed?
A) - Up $9,000
B) - Down $9,000
C) - No change at all
D) - Not determinable due to insufficient information
B) - Down $9,000
Answer: B—A decrease in income will cause a decrease in value.$900 / 10% = $9,000 value decrease.
A man owns a lot that measures 150 foot deep by 50 feet wide. The local zoning laws require a 20 foot front setback and a 4 foot setback on both sides and at the back. The buildable area of this lot is:
A) - 5,292 square feet
B) - 5,460 square feet
C) - 6,500 square feet
D) - None of the above
A) - 5,292 square feet
Answer: A—50’ x 150’ = 7,500 total sq. ft.
7,500 total sq. ft. -1,000 (20'x 50') - 200 (4' x 50') - 504 (4' x 126') - 504 (4' x 126') \_\_\_\_\_\_\_ 5,292 sq. ft.
Mr. Smith purchased a property for $20,000 with $5,000 down and assumed a $15,000 loan with interest payments of $150 per month plus interest. Before any payments were made, the property sold for twice the amount of the original price. For every dollar invested, how much did Mr. Smith receive in return?
A) - $4
B) - $25
C) - $5
D) - $20
C) - $5
Answer: C—The first thing to keep in mind is that Mr. Smith invested $5,000 not $20,000.
$20,000 (purchase price) - $15,000 (assumed loan) = $5,000 invested
$40,000 (sold for twice purchase price) - $15,000 (existing loan) = $25,000 (cash out at time of sale)
For every dollar invested he took out $5.00.
$25,000 / $5,000 = $5
If a person borrowed $26,500 for 20 years at 15% interest per annum, using a straight note, he would pay interest of:
A) - $33,300
B) - $62,200
C) - $79,500
D) - $95,400
C) - $79,500
Answer: C—$26,500 x .15 = $3,975 interest per year
$3,975 x 20 yrs. = $79,500
A loan of $26,000 was made on a property which represented 80% of the appraised value. What was the appraised value?
A) - $80,000
B) - Less than $32,000
C) - More than $32,000 but less than $34,000
D) - $34,000
C) - More than $32,000 but less than $34,000
Answer: C—$26,000 is 80% of appraised value
$26,000 / .80 = $32,500 appraised value
Prices have risen 20%. What has happened to the purchasing power of the dollar if the base index was 100?
A) - Down by 16 2/3%
B) - Down by 20%
C) - Down by 25%
D) - Up by 20%
A) - Down by 16 2/3%
Answer: A—To calculate the change in the purchasing power of the dollar, divide the present cost of living index by 100. In this problem, the index changed from 100 to 120. 120 is the current index.
100 / 120 = 83 1/3%. This means that the purchasing power of the dollar is currently 83 1/3% of what it was when the index was 100. If the purchasing power of the dollar is 83 1/3%, it has dropped (decreased) by 16 2/3%.
Mr. Smith owned an income property. He deducted from his gross income $75,000 for operating expenses. If the operating expenses represented 80% of his gross income, what would the value of the property be if he used an 8% capitalization rate?
A) - $937,500
B) - $1,171,875
C) - $234,375
D) - $187,500
C) - $234,375
Answer: C—$75,000 is 80% of his gross;
$75,000 / 80% = $93,750 gross income
$93,750 (gross) x 20% (net) = $18,750 net
(or $93,750 - $75,000 expenses = $18,750 net)
$18,750 / 8% capitalization rate = $234,375 property value
You sold a property and made a 10% profit above all costs and received $35,200. Your profit was:
A) - $3,520
B) - $3,200
C) - $3,911.11
D) - $35.20
B) - $3,200
Answer: B—In real estate, profit is a % of cost, and selling price minus cost equals profit.
$35,200 is 110% of cost: $35,200 / 110% = $32,000 cost
$35,200 (selling price) - $32,000 (cost) = 3,200 profit
$125 is 4% of:
A) - $500.00
B) - $312.50
C) - $3,125.00
D) - $5,000.00
C) - $3,125.00
Answer: C—$125 / 4% ($125 / .04) = $3,125
A man held a 5-year trust deed and note which was payable at 7.2% interest only. If the total interest received from the borrower during the term of the loan was $4,140, what was the approximate original amount of the loan?
A) - $57,500
B) - $11,500
C) - $5,900
D) - $29,700
B) - $11,500
Answer: B—$4140 ÷ 5 years = $828 interest paid per year
$828 interest per year is 7.2% of the loan
$828 ÷ .072 (7.2%) = $11,500 loan balance
Mr. Kent is interested in purchasing an existing loan. The interest rate is 10 1/2% per annum with the unpaid balance due in 12 months. The borrower is paying $87.50 per month. Mr. Kent plans to offer the beneficiary 60% of the face value of the note. If this is a straight loan, how much should Mr. Kent offer the beneficiary?
A) - $3,600
B) - $8,750
C) - $10,000
D) - $6,000
D) - $6,000
Answer: D—$87.50 per month (interest only) x 12 months =
$1,050 interest per year
$1,050 / 10 1/2% interest = $10,000 loan balance
$10,000 x 60% = $6,000
A broker lists a property for $240,000. His commission on the sale was to be 10% of the listed price. One month later, he brings in an offer that is 8% below the listed price. The owners agreed to accept the offer if the broker would reduce his commission to 6%. What would the broker’s commission be if the sale was consummated on the above offer?
A) - $19,200
B) - $14,400
C) - $13,248
D) - $24,000
C) - $13,248
Answer: C—$240,000 x 92% (100% - 8% below listed price) =
$220,800 selling price
$220,800 (selling price) x 6% (commission) =
$13,248 commission to broker
If a ranch is 36 miles square, how many townships could it contain?
A) - 1
B) - 6
C) - 36
D) - 108
C) - 36
Answer: C—Remember, “36 miles square” is different than “36 square miles.” A parcel of land 36 miles square is 36 miles on each side. Since a township is “6 miles square,” a parcel of land 36 miles square would contain 36 townships.
A rectangular lot contains 540 square yards. It has a 45 foot frontage. The depth of the lot would be:
A) - 72 feet
B) - 108 feet
C) - 216 feet
D) - None of the preceding
B) - 108 feet
Answer: B—540 square yards = 4,860 square feet (there are 9 square feet per square yard) 4,860 square feet / 45 front feet = 108 feet deep
Mr. Ramsey purchased a parcel of land for $17,424. It contained 21,780 square feet with a depth of 140 feet. He wants to sell the property and make a 40% profit after paying the broker a commission of 10% of the selling price. He also wants to list the property at a price per front foot. The listed price per front foot should be nearest to which of the following?
A) - $158
B) - $174
C) - $189
D) - $198
B) - $174
Answer: B—21,780 sq. ft. / 140 feet deep = 155.57
$17,424 x 140% (100% of cost + 40% cost) = $24,393.60 net seller
$24,393.60 / 90% (100% of selling price - broker’s commission of 10%) = $27,104 (Selling Price)
$27,104 / 155.57 front feet = $174 per front foot (rounded)
Upon examination of a business statement, a broker discovers that the operating expenses are $124,500 which represents 80% of the gross income. If an investor wanted a 15% return on his investment, how much would he have to invest to realize this return?
A) - $207,500
B) - $124,500
C) - $155,625
D) - $220,000
A) - $207,500
Answer: A—$124,500 (operating exp.) / 80% = $155,625 gross income
$155,625 (gross) - $124,500 (expenses) = $31,125 net
$ 31,125 / 15% (cap rate) = $207,500 investment
A certain bank customarily charges four points on their loans and then later sells these loans at a 3.5% discount. If the bank received $14,475 when it sold a loan at the stated discount rate, what was the original amount of the loan?
A) - $14,900
B) - $15,500
C) - $14,500
D) - $15,000
D) - $15,000
Answer: D—$14,475 is 96 1/2% of the original amount of the loan.
$14,475 / 96 1/2% = $15,000 original amount of loan.
Each unit in a fourplex rents for $1,200 per month. With a price of $576,000, the monthly gross multiplier would be:
A) - 15
B) - 120
C) - 30
D) - 240
B) - 120
Answer: B—The total monthly gross income for the fourplex is:
$4,800 ($1200 x 4)
$576,000 / $4,800 = 120
A parcel of land which measures 1/2 mile by 1/2 mile contains:
A) - 40 acres
B) - 80 acres
C) - 160 acres
D) - 320 acres
C) - 160 acres
Answer: C—2,640 x 2,640 = 6,969,600 square feet
6,969,600 / 43,560 (area of 1 acre) = 160 acres
Mr. Able invested in a 24-unit apartment building. In 1964, he rented each apartment for $85.00 per month with no vacancies. In 1965, he increased his rent to $95.00 per apartment and realized a 10% overall vacancy. Based on the above information which of the following statements is correct?
A) - More in 1964
B) - Less in 1965
C) - More in 1965
D) - Both years were equal
C) - More in 1965
Answer: C—You could work this problem using a 10% vacancy on 1 unit and be just as accurate as if you had used 24 units.
$95.00 rent per month - 10% vacancy due to the increased rent = $95.00 - $9.50 = $85.50 (more in 1965)
DO NOT presume that an increase in the gross rent will always result in an increase in effective rent.
An income property rents for $1,000 per month. During the past five years, it has been vacant for three months. The operating expenses are $3,000 per year. The capitalization rate is 12%. What is the value of the property?
A) - $60,000
B) - $70,000
C) - $84,320
D) - $110,000
B) - $70,000
Answer: B—$1,000 rent/mo. x 12 mo. = $12,000 gross income
$12,000 - $600 vacancy ($3,000 / 5) - $3,000 operating expenses = $ 8,400 Net Income
$8,400 / .12 = $70,000
How many square miles in a section?
A) - 6
B) - 1
C) - 36
D) - 64
B) - 1
Answer: B—The state has many variations of this question in their pool of questions. A section is 1 mile on each side and contains 1 square mile. You should be able to reproduce the diagram shown below by memory.
One section is one square mile.
One section contains 640 acres.
A section is 5,280 feet or one mile on each side.
Cameron owns a 30-unit apartment building next to a loud night club. Cameron loses $400 net income per month because of the loud noise. Many appraisers suggest using a 12% capitalization rate for this type of property in that neighborhood. Cameron’s property suffers a loss in value of approximately:
A) - $4,800
B) - $48,000
C) - $40,000
D) - $2,400
C) - $40,000
Answer: C—$400 x 12 = $4,800
$4,800 / .12 = $40,000
Morgan sold her residence which was unencumbered. Morgan received a closing check from escrow amounting to $91,740 after paying closing costs in the amount of $1,291.80 plus 6% for the broker’s commission. The selling price was most nearly:
A) - $87,765
B) - $98,887
C) - $97,596
D) - $98,970
D) - $98,970
Answer: D—$91,740.00 + $1,291.80 (closing costs) = $93,031.80
$93,031.80 / .94 = $98,970
A short time ago a man bought a lot on speculation. He paid $10,000 with $1,000 down in cash and the balance on a deed of trust and note. Before any payments became due on the loan, he sold the lot for $20,000. Under these circumstances, his invested dollar is now worth:
A) - $10.00
B) - $100.00
C) - $11.00
D) - $1.10
C) - $11.00
Answer: C—When he sold the property for $20,000, $9,000 went to pay the loan and this left him with $11,000. In this problem, it would be improper to assume any additional expenses. If you assume anything, the problem could not be worked.
He invested $1,000 and walked away with $11,000. Each invested dollar is now worth $11.00.
Similar problem: There is a similar problem that asks, “By how much has each invested dollar increased.” In this question, the answer is $10.00. Look this problem over carefully before answering. Make sure you are answering the question they are asking. It is easy to get careless and select the wrong answer.
If a man purchased two 75-foot lots at a price of $9,000 each and proceeded to merge and redivide the parcel into three 50-foot lots which he sold for $7,500 each, his percentage profit was:
A) - 24%
B) - 25%
C) - 26%
D) - 30%
B) - 25%
Answer: B—$ 7,500 per lot x 3 lots = $22,500 selling price
$22,500 - $18,000 (cost of two lots) = $4,500 profit
$ 4,500 is ___% of $18,000 (Profit is a % of cost)
$ 4,500 / $18,000 = 25% profit
A parcel of land sold for $800 less than the listed price of $20,000. If the broker agreed to reduce his commission to 4%, his commission would amount to:
A) - $1,152.00
B) - $768.00
C) - $76.80
D) - $115.20
B) - $768.00
Answer: B—$20,000 - $800 =
$19,200 Selling Price
x .04 Broker’s commission
____________________________
$768.00 commission
A subdivider purchased 45 acres, paying $67,500 for the entire parcel. He estimates that he can obtain 3 lots per acre and that he will have to pay $100 per lot for engineering expenses. If he sells each lot at a price that will give him a profit of 114% on his investment, his profit would be:
A) - $684 per lot
B) - $1,284 per lot
C) - $1,366 per lot
D) - $766 per lot
A) - $684 per lot
Answer: A—45 acres x 3 lots per acre = 135 lots
$67,500 (cost) / 135 lots = $500 cost per lot
$500 per lot + $100 engineering costs per lot = $600 invested per lot
$600 per lot x 114% = $684 profit per lot
A property which was originally purchased for $10,000, returned an annual gross income of 8%. The owner’s only expense was 6% annual interest on a trust deed of $9,000. What percent of return did the owner receive on his equity?
A) - 8%
B) - 10%
C) - 20%
D) - 26%
D) - 26%
Answer: D—$10,000 Value x 8% = $800 Gross Income
- 9,000 Loan x 6% = -540 Interest
_____________ _________________
$ 1,000 Equity $260 Net
Net Income is % return of Equity
$260 is _____% of $1,000
$260 / $1,000 = 26%
Mr. Smith bought a property for $72,000 with a $20,000 cash down payment and a $52,000 loan. The loan did not require interest and did not require any payments for one year. One year later, he sold the property for double its purchase price. Each dollar of his original cash investment is now equal to:
A) - $2.00
B) - $4.60
C) - $7.30
D) - $9.20
B) - $4.60
Answer: B—$144,000 (selling price) - $ 52,000 (existing loan) = $92,000
$ 92,000 / $20,000 = $4.60
Mr. King owned a 120-room apartment house. Twelve four-room apartments were rented for $625.00 per month; twelve three-room apartments were rented for $500.00 per month; eleven two-room apartments were rented for $375.00 per month, and the remaining one-room apartments were rented for $200.00 per month. Assuming no vacancies, the gross annual rent would be:
A) - $245,100
B) - $300,000
C) - $315,000
D) - $400,000
A) - $245,100
Answer: A—12x4=48 rooms;12 4-rm apts@$625/mo=$7500/mo=$90,000/yr
12x3=36 rooms;12 3-rm apts@$500/mo=$6000/mo=$72,000/yr
11x2=22 rooms;11 2-rm apts@$375/mo=$4125/mo=$49,500/yr
14x1=14 rooms;14 1-rm apts@$200/mo=$2800/mo=$33,600/yr
_________ : __________
120 rooms : $245,100/yr
A certain property is valued at $390,000 and earns a net profit before income taxes of $18,600. This net income is attributable to the improvements only. Using a 6% capitalization rate on the improvements, what would be the value of the land?
A) - $310,000
B) - $111,600
C) - $80,000
D) - None of the above are correct
C) - $80,000
Answer: C—$18,600 / 6% = $310,000 value of the improvements only.$390,000 (land and improvements) - $310,000 (improvements only) = $80,000 value of land.
A man bought two 60 foot lots for $18,000 net each and divided them into three lots of equal frontage which he sold for a price of $15,000 each. His percentage of gross profit was most nearly:
A) - 15%
B) - 20%
C) - 25%
D) - 40%
C) - 25%
Answer: C—$18,000 x 2 lots = $36,000 (purchase price of original lots)
$15,000 x 3 lots = $45,000 (selling price of newly subdivided lots)
$45,000 - $36,000 = $9,000 profit
$9,000 / $36,000 = .25 or 25%
Broker Balduf is negotiating a twenty-five year commercial lease at a straight annual rental of $30,000. Balduf is to receive compensation for negotiating this lease as follows: 7% of the annual rental for the first year; 5% of the annual rental for each of the next four years; 3% of the yearly rental for each of the next fifteen years; and 1% of the yearly rental for every year, thereafter during the term of the lease. By the end of the nineteenth year, Balduf will have received a total brokerage commission of most nearly:
A) - $10,800
B) - $19,000
C) - $20,700
D) - $20,160
C) - $20,700
Answer: C—7% first year…$2,100 x 1yr = $2,1005% next 4 yrs…$1,500 x 4yrs= $6,0003% next 15 yrs..$13,500 (only use 14 yrs. = $12,600)1% of remaining.$300 x 5yrs = $1,5001yr + 4yr + 14yr + 5yr = 19yrs$2,100 + $6,000 + $12,600 + $1,500 = $20,700
As a condition for making a home loan, a bank charged the seller 4 points on the loan amount. The bank immediately sold the loan to an insurance company at a discount of 3 1/2 points and received $34,790. The original amount of the loan was most nearly:
A) - $35,850
B) - $35,975
C) - $36,050
D) - $36,200
C) - $36,050
Answer: C—100% - 3 1/2% = 96 1/2% or 96.5%
$34,790 / .965 = $36,051.81 Closest answer is $36,050
An individual owns an income property which is worth $100,000, based on a capitalization rate of 6%. If an appraiser uses a capitalization rate of 8% on the same property, the estimate of value would be:
A) - $70,000
B) - $75,000
C) - $80,000
D) - $90,000
B) - $75,000
Answer: B—Using a 6% capitalization rate, the net income is determined by multiplying the value by the capitalization rate: $100,000 x .06 = $6,000. Then capitalize the $6,000 at 8%: $6,000 / .08 = $75,000.
Lots A, B, and C are contiguous. Lot A measures 80’ x 120’ and sold for $4,000. Lot C measures 90’ x 120’ and sold for $5,000. If lot B measures 85’ x 120’, how much should it have sold for by the comparative method?
A) - $4,500.00
B) - $4,499.90
C) - $4,486.30
D) - $4,400.00
C) - $4,486.30
Answer: C—Lot A: $4,000 / 80’ = $ 50.00 cost per front foot
Lot C: $5,000 / 90’ = $ 55.56 cost per front foot
$50.00 + 55.56 = $105.56 / 2 = $52.78 average cost per front foot
$52.78 x 85’(Lot B) = $4,486.30 cost of Lot B
A man bought the contents of a store for $9,300. He sold the goods for 1/3 more than they cost him. He lost 15% of the selling price in bad debts. His entire profit on this investment was:
A) - $1,000
B) - $1,240
C) - $1,860
D) - $3,100
B) - $1,240
Answer: B—$ 9,300 / 3 = $3,100 $ 9,300 + $3,100 = $12,400 (selling price) $12,400 x .15 = $1,860 (bad debts) $12,400 - $1,860 = $10,540 $10,540 - $9,300 = $1,240 Profit
An investor bought two lots for $8,500. He wanted to resell them for a 20% profit over the purchase price but could not, and finally reduced his price by 10%. The lots sold at the reduced price and an 8% commission was paid. What was his gain or loss?
A) - $37.40 gain
B) - $54.40 loss
C) - $85.00 loss
D) - $16.40 gain
B) - $54.40 loss
Answer: B—$8,500 (cost) x 120% = $10,200 original asking price
$10,200 x 90% (considering 10% reduction) = $9,180 new selling price
$9,180 - broker’s commission = $9,180 - $734.40 ($9,180 x 8%) = $8,445.60 to seller
$8,500 (cost) - $8,445.60 (to seller) = $54.40 loss to seller
Assuming the total value of the property to be $190,000 and the total net income to be $13,680; the capitalization rate would be:
A) - 6.5%
B) - 7%
C) - 7.2%
D) - 7.5%
C) - 7.2%
Answer: C—The basic capitalization formula is:
Value = Net Income / Capitalization Rate
From this we get: Capitalization Rate = Net Income / Value
$13,680 / $190,000 = .072 or 7.2%
What is the reciprocal of an 8% capitalization rate?
A) - 1.125
B) - .125
C) - 12.5
D) - 125
C) - 12.5
Answer: C—The reciprocal (reverse) of an 8% capitalization rate is the same as: 1/08 or 1 / .08 = 12.5
Perez owned and sold a house. Perez took back a $11,220 note secured by a 2nd mortgage and immediately sold the paper for $7,293. The amount of the discount expressed as a percentage is:
A) - 28%
B) - 35%
C) - 55%
D) - 65%
B) - 35%
Answer: B—$11,220 - $7,293 = $3,927$3,927 ÷ $11,220 = 35%
Farrington is the holder of a trust deed and note secured by real property. The annual interest rate is 8.4% for a 5-year term. The interest for the 5 years total amounts to $5460. Therefore, the principal amount of the loan is most nearly:
A) - $10,250
B) - $11,500
C) - $13,000
D) - $15,000
C) - $13,000
Answer: C—$5,460 / 5 years) = $1,092 (interest per year)
$1,092 / .084 = $13,000
Johnson bought a parcel of land for $63,360. Disregarding interest charges on any financing involved, property taxes, and all other variables, if it costs 12% of the future selling price to market this lot, how much must the property increase in value before it can be resold without loss:
A) - 24%
B) - 112%
C) - $4,320
D) - $8,640
D) - $8,640
Answer: D—$63,360 / .88 (100% - .12%) = $72,000
$72,000 - $63,360 = $8,640
Mr. Hanson sold his home for $25,000. The borrower secured a loan of $19,500 and paid the maximum origination fee allowed by law. The seller was required to pay a 2 1/2 point loan fee in addition to closing costs of $231. If the seller paid the broker a 6% commission, how much money did the seller receive when escrow closed assuming no other costs?
A) - $5,500
B) - $25,000
C) - $22,781.50
D) - $3,281.50
C) - $22,781.50
Answer: C—$19,500 loan x 2 1/2 points =
$19,500 x .025 (2 1/2%) = $487.50 loan fee
$25,000 selling price x 6% commission = $1,500 commission
$ 487.50 loan fee \+$ 231.00 closing costs \+$1,500.00 commission \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ $2,218.50 costs to seller
$25,000 selling price - $2,218.50 costs to seller =
$22,781.50 to seller
One home rents for $1,300/month. The home across the street rents for $1,200 per month and was recently valued at $178,000. What is the value of the first home?
A) - $192,829
B) - don’t know
C) - don’t know
D) - don’t know
A) - $192,829
Answer: A—$178,000 ÷ $1,200 = 148.33 (GRM) $1,300 x 148.33 = $192,829
Capitalization is most closely related to:
A) - investment to equity ratio.
B) - income to equity ratio.
C) - income to value ratio.
D) - cost to equity ratio.
C) - income to value ratio.
Answer: C—The formula for capitalization is:
VALUE = NET INCOME / CAPITALIZATION RATE or V = I / R
A high rise office building has a quarterly income of $265,000. The expenses amount to 32% of the income. What is the annual net income?
A) - $180,200
B) - $720,800
C) - $106,00
D) - $349,800
B) - $720,800
Answer: B—$265,000 x 4 quarters = $1,060,000 yearly income
$1,060,000 x .32 = $339,200 expenses
$1,060,000 - $339,200 = $720,800 annual net income
