Chapter 18 - Real Estate Arithmetic Flashcards Preview

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Flashcards in Chapter 18 - Real Estate Arithmetic Deck (24)
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1

A note is dated june 6, 2012, in the amount of $3900. 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) 

$4,114.13.

 

First calculate the amount of interest that will be paid on the note in one year. ($3,900 x 0.06 = $234)

Divide the annual amount of interest by the number of days in the calendar year, This will give you the daily interest charge expressed as a daily percentage. ($234/365 = 0.641)

now multiply the daily interest rate times the number of days between June 6 and May 6, or 334 days. (334 x .641 = $214.14) then add the interest to the principal ($3900 + 214.13=$4,114.13)

2

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?

$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)

3

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

8%

 

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

4

Aster corporation decided to develop a downtown office building, and borrowed $6,000,000 repayable in 8 years. The amortized note showed that at the end of the 8 years, Aster corporation would have paid a total of $11,942,400. What was the amount of yearly simple interest charged on the note. 

12.38%

 

First determine the maount of interest paid. to do this subtract the principal amount of the loan from the total amount paid at note maturity. this number will represent the amount of interest paid for the entire 8-year period. (11.942,400 - 6,000,000 = 5,9429400) 

next calculate the amount of interest attributable to one year. (5,942,400 / 8 = 742,800)

divide the amount of interest attributable to one year by the total amount of the loan. The result will be the actual interest rate paid on the loan on an annual basis, (742,800 / 6,000,000 = .1238)

 

then convert the answer to a whole number by moving the decimal point two places to the right. (12.38%)

5

An investor paid $650,000 for a four-plex. each unitrents for 4950 per month. if the investor's annual expenses total $8,000, what is the rate of return he will earn on his $650,000?

5.78%

 

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 - $8000 = $37,600)

 

Then divide the net income by the amount paid for the builiding to arrive at the annual rate of return. ($37,600 / $650,000 = 0.0578)

 

6

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

$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)

7

Jeff buys a house on a rectangular lot that measures 150 feet along the street. The lot has a total of 12000 sq ft. how deep is the lot

 

80 ft 

 

divide the known side of the rectangle (150 ft) into the total areas of the rectangle    (12,000' / 150' = 80')

8

An investment property is offered for sale at $400,000. an investory purchasing the propert 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 you answer to the nearest whole dollar)

$357,143

 

the net income of the property must be calculated. it is known that the building at $400,000 will realize a 12.5% return.t herefore to find the net income at the $400,000 figure, multiply the purchse price times the 12.5% return ($400,000 x .125 = $50,000)

once the net income amount is known, then the purchase price at 14% return can be calculated. to determine the purchase price, divide the rate of return into the net income. ($50,000/0.4 = $357,142.85)

9

a 20-year-old building has been depreciated to a $420,000 in value. it hs been depreciated at 2.5% per year. what was its original value?

$840,000

 

multiply the number of years the buildihng has been depreciated times the annual depreciation rate (20 years x .025 = 0.5) 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 buildng has been depreciated to date. ($420,000 / .5 = $840,000) 

 

10

.02 as a percent would be 

2% 

11

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)

57 days

 

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

 

next, divide the total annual interests by the number of days in a year to determine the daily dollar interest charge ($5828/365 = 15.967%)

 

then determine the number of days he paid interest by dividing the actual amount of interest paid by the dailiy interest figure. ($910.9 / 15.967% = 57 days)

12

if a house sold for $290,000 which was 19% more than it originally cost, what was the original cost?

$243,697

 

if it cost 19% more than original that is 119% of the original cost. convert to a decimal, 1.19, and divide into sale price. $290,000 / 1.19 = $243,697.47 

13

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?

10,000 sq feet

 

100' x 250' = $25,000 sq ft

40% of 25,000 sq ft is 10,000 sq ft (25000 sq ft x .40 = 10,000 sq ft) 

14

How many acres are there in a triangular parcel of land that measures one mile wide by one and a half miles deep?

480 acres

 

1 mile = 5280 feet

1.5 miles = 7290 feet

sq ft in an acre = 43,560

 

1/2(b x h).

 

5280ft x 7290 ft = 41,817,600 / 2 = 20,908,800 sq ft

to determine amount of acres divide the total sq ft by the sq ft in an acre

20,908,800 / 43,560 = 480 acres

 

15

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

$64,050 

divide amount of commission received by the commission percentage ($3,843 / .6 = $64,050) 

16

A property owner wants to build a cyclone fence around their property. The lot is rectangular, 110 feet by 270 feet. The fence is 7 feet high. Cyclone fencing costs $.85 per square foot and the labor to install it is $1.70 per linear foot. How much will the fence cost?

$5814

 

Determine how much fencing is needed; total length is: 110'+110'+270'+270'= 760ft

multiply by the height of the fence 7'...760x 7 = 5320 sq ft 

 

the cost for fence materials is 85 cents per square foot. 5320 sq ft x .85 = $4522

 

the labor is in linear feet, so multiply the length by the cost of installation. 7601 x 1.70 = $1292 

 

add cost of materials and cost of labor to get total cost-- 1292 + 4522 = 5814 

17

a 5,000 sq ft lot sold for $128000. what was the cost per sq ft

$25.60 

 

divide total sale price by sq footage of the lot 

18

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:

6668 sq ft 

 

sq footage of lot is: 97 x 125 = 12125 sq ft

multiply by amount of coverage 12,125 x .55 = 6668.75 

19

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)

$269,936

 

solve unknown dollar amount of the commission: $314,500 x .06 = $18870

add commission and closing ocsts together $18870 + 1400 = 20,270

total costs subtracted from gross sales $314500 - $20270 = $294,230

 

find original purchase price of property, divide net sale proceeds by profit percentage. the 9% profit means property sold for full amount plus 9%, 109% of original price. decimal is 1.09

 

$294,230 / 1.09 = $269,935.77 

20

what is the loan amount if the interest rate is 7.5% per year and the monthly interest payment is $1250

$200,000

 

first convert the amount of monthly interest to an annual interest amount

($1250 x 12 = $15000)

then divide that amount by the interest rate expressed as a decimal

$15000 / .075 = $200,000 

21

what is the number of sq ft in a lot measuring 1000' on the north side, 200' on the east and west sides, and 800' on the south side

180,000

split it into a rectangle and a triangle

 

area of rectangle is 200' x 800' = 160000 sq ft

 

area of triangle 200'x200' = 40000/2 = 20000

add triangel and rectangle together for total 

22

A seller wants to sell her existing house and owes $290,000 on mortgage. At closing of the sale she will pay $1400 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 she must sell her house for to net $55000?

 

$368,510

 

first determine the total amount which must be paid at closing. these items include existing mortgage, closing costs, plus $55,000. 

290,000 + 1400 + 55000 = $346,400. 

 

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. convert to decimal, 0.94, and divide into the $346,400 ($346,400 / .94 = $368,510.64

23

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?

6%

First determine the net income of the duplex on an annual basis:

$3000 x 12 = $36000

 

since the vacancy rate is 5% subtract 5% vacancy from the gross rents (two ways):

1) multiply gross rents times vacancy rate and subtract from annual gross rents to arrive at rents less vacancy:

$36000 x .05 = $1800 --> $36000 - $1800 = $34,200

2) remaining balance of rents after subtracting the vacancy rate would be 95% of gross rents. multiply rent figure times 95% to arrive at rent less vacancy

$36000 x .95 = $34,200

 

next determine the net operating income. take rents less vacancy and subtract the annual expenses:
$34,200 - $19,300 = $14,900

 

divide the net income by purchase price of the duplex to determine the rate of return: 

$14,900 / $241.500 = .06

24

How many square feet are in an acre?

43560 ft