Chapter 18: Real Estate Arithmetic

Question 1

Broker Bob receives 55% of all commissions he generates. He just sold a property listing for $250,000 at 6% brokerage commission. How much will Broker Bob earn in commission for this sale?

Answer 1

$8,250
First calculate the amount of the total commission. ($250,000 x .06 = $15,000).
Next, determine Bob’s commission ($15,000 x .55 = $8,250)

Question 2

An owner of a duplex earns a 12% return on his investment of $273,000. What is his annual net income?

Answer 2

$32,760
Multiply the amount of the annual return (12%) times the amount of the original investment. This number will represent the annual net income received on the investment. ( $273,000 x .12 = $32,760)

Question 3

An investment property is offered for sale at $400,000. An investor purchasing the property at that price would receive a 12.5% return on his investment from the net income earned by the property. If the investor wanted to realize a 14% return, what would he have to purchase the property for? (Round your answer to the nearest whole dollar.)

Answer 3

$357,143
First, the net income of the property must be calculated. It is known that the building at $400,000 will realize a 12.5% return. Therefore, to find the net income at the $400,000 figure, multiply the purchase price times the 12.5% return. ($400,000 × .125 = $50,000)

Once the net income amount is known, then the purchase price at a 14% return can be calculated. To determine the purchase price, divide the rate of return into the net income. ( $50,000 ÷ .14 = $357,142.85). This figure may be rounded up to $357,143

Question 4

A note is dated June 6, 2012, in the amount of $3,900. The annual interest rate is 6% simple interest. The maturity date of the note is May 6, 2013, at which time all of the interest will be due in addition to the principal. What is the total amount due? (Use a 365 day year to calculate and round your answer to the nearest penny from three decimal points)

Answer 4

$4,114.13
First calculate the amount of interest that will be paid on the note in one year. ($3,900 x .06 = $234).

Next, divide the annual amount of interest by the number of days in the calendar year. This will give the daily interest charge expressed as a daily percentage.
( $234 / 365 = .641).

Now multiply the daily interest rate times the number of days between June 6 and May 6, or 334 days. (334 x .641 = $214.13) Then add the interest to the principal ($3,900 + $214.13 = $4,114.13)

Question 5

Nate borrowed $62,000 at 9.4% interest per year. If he owed a total of $910.90 interest when he repaid the loan, how many days did he keep the money for? (use a 365 day calendar year to calculate)

Answer 5

57 days
Calculate the annual interest by multiplying the amount of the loan by the annual interest. ($62,000 x .094 = $5,828).

Next, divide the total annual interest by the number of days in a year to determine the daily dollar interest charge. ($5,828 / 365 = 15.967%)

Then determine the number of days he paid interest by dividing the actual amount of interest paid by the daily interest figure. ($910.90 / 15.967% = 57 days)

Question 6

.25 as a fraction is:

Answer 6

1/4

Expressed as a decimal, .25 is one of 4 equal parts. Expressed as a fraction the answer would be 1 of 4, or 1/4.

Question 7

The owner of a duplex has a scheduled gross income of $3,000 per month. The vacancy rate is 5% and expenses average $19,300 per year. If a buyer purchases the property for $241,500, and the income and expenses stay the same, what will the buyer’s rate of return be?

Answer 7

6%
First determine the net income of the duplex on an annual basis. To do this first calculate the amount of the gross annual rents. ($3,000 x 12 = $36,000)

Since the vacancy rate is 5%, subtract 5% vacancy from the gross rents. This can be accomplished in one of two ways.

First method: Multiply the gross rents times the vacancy rate and subtract this number from the annual gross rents to arrive at the gross rents less vacancy number. ( $36,000 x .05 = $1,800) ( $36,000 - $1,800 = $34,200)
Second method: The remaining balance of gross rents after subtracting the vacancy rate would be 95% of gross rents. Therefore multiply the gross rent figure times 95% to arrive at the gross rents less vacancy rate figure. ( $36,000 x .95 = $34,200)
Next determine the net operating income. To do this take the gross rent figure less the vacancy factor and subtract from this number the annual expenses of $19,300. ($34,200 - $19,300 = $14,900)

Divide the net income by the purchase price of the duplex to determine the rate of return. ($14,900 / $241,500 = .06)

Then convert the decimal to a percentage by moving the decimal two places to the right. (6.0%)

Question 8

A 5,000 square foot lot sold for $128,000. What was the cost per square foot?

Answer 8

$25.60
Divide the total sale price by the square footage of the lot. The result is the amount per square foot. ($128,000 / 5,000 sq. ft. = $25.60)

Question 9

A broker received a commission check in the amount of $31,600. The property sold for $395,000. What was the commission rate?

Answer 9

8%

$31,600 / $395,000 = .08, or 8%

Question 10

Mary received $3,843, which represented a 6% commission on a lot she had listed. How much did the lot sell for?

Answer 10

$64,050

Divide the amount of the commission received by the commission percentage. ($3,843 / .06 = $64,050)

Question 11

A seller wants to sell her existing house and owes $290,000 on mortgage. At closing of the sale she will pay $1,400 in closing costs, plus a 6% brokerage fee. She wants to realize at least $55,000 for a down payment for the purchase price of a new house. What is the minimum amount she must sell her house for to net $55,000?

Answer 11

$368,510
To solve this problem, first determine the total amount which must be paid at closing. These items include the existing mortgage of $290,000, closing costs of $1,400, plus the amount of $55,000 that the seller wants to net on the sale. ($290,000 + $1,400 + $55,000 = $346,400). This is the total of the known items which must be realized or paid at closing.

Once this number is known, the house will have to sell for a price which includes a 6% brokerage fee. This means that the $346,400 must equal 94% of the sale price of the property. The other 6% of the sale price is represented by the brokerage fee. Therefore, convert 94% to a decimal (.94) and divide into the $346,400. ($346,400 / .94 = $368,510.64). The house would have to sell for $368,510 in order for the owner to realize her objectives.

Question 12

Office space is renting for $19.00 a square foot annually. If the total square footage is 12,000 square feet, what is the amount of the monthly rent?

Answer 12

19,000
To calculate annual rent, multiply $19.00 per square foot times the amount of square footage rented. ($19 x 12,000’ = $228,000). To find the monthly rental amount, divide the annual rental amount by 12. ($228,000 / 12 months = $19,000).

Question 13

What is the number of cubic feet in a brick wall that measures 2 feet deep, 6 feet high, and 55 feet long?

Answer 13

660 cu. ft.
The formula to find an area of a cube is multiply the length times the width times the depth. (2’ x 6’ x 55’ = 660 cubic feet)

Question 14

If the interest rate is 12% per year simple interest and the monthly interest payment is $115, what is the amount of the loan?

Answer 14

11,500

$115 × 12 months = $1,380 ÷ .12 = $11,500

Question 15

A lot measures 97’ X 125’. The zoning code specifies maximum lot coverage of 55%. The maximum size of a house, in whole numbers, would be:

Answer 15

6,668 sq. ft.
Remember, the house size cannot exceed the 55% set in the zoning code. First, calculate the square footage of the city lot (97’ x 125’ = 12,125 sq. ft.). Then multiply the lot square footage by the amount of permissible lot coverage. (12,125 sq. ft. x .55 = 6,668.75 or 6,668 sq. ft. in whole numbers)

Question 16

3/10 as a percent would be:

Answer 16

30%
Divide 3 by 10. The result of dividing 3 by 10 is .30, and to convert to a percent move the decimal point 2 places to the right or 30%

Question 17

A 20-year-old building has been depreciated to $420,000 in value. It has been depreciated at 2.5% per year. What was its original value?

Answer 17

$840,000
Multiply the number of years the building has been depreciated times the annual depreciation rate. (20 years x .025 = .5). The result of this calculation represents the depreciated value of the building.

To find the original value, divide the remaining depreciated value by the percent the building has been depreciated to date. ($420,000 / .5 = $840,000)

Question 18

An investor paid $650,000 for a four-plex. Each unit rents for $950 per month. If the investor’s annual expenses total $8,000, what is the rate of return he will earn on his $650,000?

Answer 18

5.78%
First, calculate the net operating income. This is done by first calculating the amount of annual rents received and then subtracting from the annual rent figure the annual expenses. ( $950 x 4 units x 12 months = $45,600)

Subtract the annual expenses from the gross rental income to arrive at the net operating income ($45,600 - $8,000 = $37,600)

Then divide the net income by the amount paid for the building to arrive at the annual rate of return. ($37,600 / $650,000 = .0578).
After that, convert the decimal to a whole to a percent by moving the decimal two places to the right. (5.78%)

Question 19

If a house sold for $290,000, which was 19% more than it originally cost, what was the original cost? (in whole dollars)

Answer 19

$243,697
If the house sold for 19% more than the original cost, it sold for the full amount of the original cost plus 19% of that price. Expressed as a percentage this would be 119% of the original price. Convert the percentage to a decimal by moving the decimal two places to the left. Then divide the converted percentage into the sale price of the property. ($290,000 / 1.19 = $243,697.47).

Question 20

6 1/4 % expressed as a decimal rounded to four decimal places is:

Answer 20

.0625
First express 1/4 as a decimal. 1/4 expressed as a decimal is .25. Next, attach the whole number, 6, to .25. The result is 6.25%. To express 6.25% as a decimal, the decimal point must be moved 2 places to the left, which becomes .0625.

Question 21

A building with a 40-year useful life depreciates at what percentage per year?

Answer 21

2.5%
100% of value divided by the useful life equals the percentage loss in value each year. This is the depreciation rate. ( 100% / 40 years = 2.5%)

Question 22

A broker received a commission check in the amount of $31,600. The property sold for $395,000. What was the commission rate?

Answer 22

8%

$31,600 / $395,000 = .08, or 8%

Question 23

How many square feet are in a triangle that is 50 feet wide and 30 feet in height?

Answer 23

750 sq. ft.
The formula for calculating the area of a triangle is ½ base times the height. Therefore, the base is 50’ and the height is 30’. (50’ x 30’ = 1,500 square feet). Divide 1,500 by 2, which equals 750 square feet.

Question 24

Nate borrowed $62,000 at 9.4% interest per year. If he owed a total of $910.90 interest when he repaid the loan, how many days did he keep the money for? (use a 365 day calendar year to calculate)

Answer 24

57 days
Calculate the annual interest by multiplying the amount of the loan by the annual interest. ($62,000 x .094 = $5,828).

Next, divide the total annual interest by the number of days in a year to determine the daily dollar interest charge. ($5,828 / 365 = 15.967%)

Then determine the number of days he paid interest by dividing the actual amount of interest paid by the daily interest figure. ($910.90 / 15.967% = 57 days)

Question 25

If the interest rate is 12% per year simple interest and the monthly interest payment is $115, what is the amount of the loan?

Answer 25

$11,500

$115 × 12 months = $1,380 ÷ .12 = $11,500

Question 26

$250,000 is 109% of what number?

Answer 26

$229,357.79
Divide the known number of $250,000 by 1.09. To do this, the 109% must first be converted to a decimal. ($250,000 / 1.09 = $229,357.79).

Question 27

A city lot measures 100 feet x 250 feet. The city zoning ordinance specifies that maximum lot coverage is 40% of the lot. What is the maximum size for a building on this lot?

Answer 27

10,000 square feet
100’ x 250’ = 25,000 sq. ft.

40% of 25,000 sq. ft. is 10,000 sq. ft. (25,000 sq. ft x .40 = 10,000 sq. ft.)

Question 28

How many square yards of carpeting would be needed for a room measuring 24 feet by 30 feet?

Answer 28

80 sq. yd.
First calculate the square footage of the room. (24 ft. x 30 ft. = 720 sq. ft)

Then divide the amount of total square feet by the amount of square feet in a square yard. (a square yard contains 9 square feet because 3 feet times 3 feet equals 9 square feet). (720 sq. ft. / 9 = 80 sq. yd.)

Question 29

Mary received $3,843, which represented a 6% commission on a lot she had listed. How much did the lot sell for?

Answer 29

$64,050

Divide the amount of the commission received by the commission percentage. ($3,843 / .06 = $64,050)

Question 30

A house sold for $314,500. After closing costs of $1,400 and a broker’s commission of 6%, the owner earned a profit of 9%. What was the original cost of the house? (Round your answer to the nearest whole dollar)

Answer 30

$269,936
The first step is to solve the unknown dollar amount of the commission. To do this, multiply the commission rate times the sale price of the property. ($314,500 x .06 = $18,870).
Next, the total costs of sale must be calculated. Therefore, add the commission and closing cost figures together. ($18,870 + $1,400 = $20,270). The total costs of sale must next be subtracted from the gross sales price of the property. The result will be how much the homeowner actually realized on the sale. ($314,500 - $20,270 = $294,230).
Once the amount of net sale proceeds is determined, then the final calculation to determine the original purchase price of the property can be made. This calculation is made by dividing the net sale proceeds by the profit percentage earned. First the 9% profit percentage must be converted to a decimal. A 9% profit means that the property sold for the full amount paid for the property plus 9% of that price. In other words, it sold for 109% of its original purchase price. As a decimal 109% is expressed as 1.09. The final calculation would then be $294,230 / 1.09 = $269,935.77. Therefore, the house originally cost $269,936.

Question 31

What is the amount of commission earned if the property sale price is $380,000 and the commission is 6%?

Answer 31

$22,800
Multiply the sale price of the property by the commission percent by converting the commission percentage to a decimal. ($380,000 x .06 = $22,800)

Question 32

A straight note in the amount of $50,000 at 8.5% interest per year is to be paid in one year. How much interest will it earn?

Answer 32

$4,250
On a straight note the amount of interest accrues and is paid at the time of note maturity. Therefore, multiply the amount of the note by the annual rate of interest. ($50,000 x .085 = $4,250)

Question 33

Broker Martin sold a home for $350,000, which was listed with another real estate firm for a 6% brokerage commission. The commission split between the listing firm and the selling firm was 50%-50%. The commission split between Broker Martin and his brokerage is 75% to Martin and 25% to the brokerage.
How much will Martin receive?

Answer 33

$7,875
First calculate the total commission to be paid. ($350,000 x .06 = $21,000)
Next, calculate the amount of commission to be paid to Broker Martin’s brokerage, which is one half of the total. ($21,000 x .5 = $10,500)
Then calculate the amount of commission that Broker Martin will receive. ($10,500 x .75 = $7,875)