Chapter 18: Real Estate Arithmetic

Question 1

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

Answer 1

$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 2

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

Answer 2

$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 3

An investor paid $65,000 for a duplex that rents for $350 per month per side and has annual expenses total $4,000. Rounded to the nearest single decimal place, what is the rate of return for the $65,000 invested?

Answer 3

6.8%
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. ($350 x 2 units x 12 months = $8,400)

Subtract the annual expenses from the gross rental income to arrive at the net operating income ($8,400 - $4,000 = $4,400)

Then divide the net income by the amount paid for the building to arrive at the annual rate of return. ($4,400 / $65,000 = .0676).

After that, convert the decimal to a whole percent by moving the decimal two places to the right. (6.76%). Rounded to the first decimal place, the ROI is 6.8%.

Question 4

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

Answer 4

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 5

The zoning code specifies maximum lot coverage of 55%. If a lot measures 97’ X 125’, expressed as a whole number, what is the maximum size of a house that could be built?

Answer 5

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 6

Broker Morgan gets 55% of the commissions they generate for the company. Morgan just sold a condo for $2,500,000 at a 6% brokerage commission. How much will Morgan get paid for this sale?

Answer 6

$82,500
First calculate the amount of the total commission. ($2,500,000 x .06 = $150,000).

Next, determine Bob’s commission ($150,000 x .55 = $82,500).

Question 7

7/11 converted to a decimal and rounded up to two places is:

Answer 7

0.64
Divide 7 by 11 ( .63636363 ) Rounded to two places, since 6 is “5 or greater,” the number 3 is rounded up to 4 or .64

Question 8

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

Answer 8

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 9

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

Answer 9

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 10

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

Answer 10

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 11

What is the loan amount if the interest rate is 7.5% per year and the monthly interest payment is $1,250?

Answer 11

$200,000
First convert the amount of monthly interest to an annual interest amount ($1,250 × 12 = $15,000)

Then divide that amount by the interest rate expressed as a decimal ($15,000 ÷ .075 = $200,000)

Question 12

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 12

$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 13

3/8 as a decimal is:

Answer 13

0.375
Divide 3 by 8 and the result is .375

Question 14

If your 6% commission is $3,843 for selling a lot, what was the sales price?

Answer 14

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

Question 15

If a house sold for $490,500, which was 9% more than it originally cost, the original cost was:

Answer 15

$450,000
Divide $490,500 by 1.09 = $450,000 (1.09 = original cost + 9% increase)