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
