# Real Estate Math Flashcards

A broker has a listing on a vacant lot that is 100 feet wide by 125 feet deep. The lot is for sale at $250 per front foot. The commission at 8% of the sales price is:

a. $2,000

b. $1,500

c. $1,250

d. $2,500

a. $2,000

Correct! The sales price is computed by multiplying the front footage of 100 feet by $250. Front footage is the width of a lot dimension and it is the first dimension given. The sales price in this problem is $25,000 (100 feet by $250).

The commission is $2,000 ($25,000 time 8%).

A broker’s commission was 8% of the first $75,000 of the sales price of a house and 6% on the amount over $75,000. What was the total selling price of the property if the broker received a total commission of $9,000?

a. $93,000

b. $125,000

c. $79,000

d. $105,000

b. $125,000

Correct! To compute the answer to this problem first compute the amount of the commission on the first $75,000 of sales price, which is $6,000 ($75,000 times 8%).

Next, compute the amount of commission that was paid at a 6% rate by subtracting the $6,000 from the total commission of $9,000. The answer of $3,000 is the commission that was paid at a 6% rate. To determine the sales amount that created the $3,000 of commission divided the $3,000 by the rate of 6% giving an answer of $50,000 of the sales price.

Therefore the total sales price was $125,000 ($75,000 plus $50,000.

If a salesperson listed and sold a property for $190,000 and received 60% of the 7% commission paid to her employing broker, how much did the salesperson receive?

a. $6,466

b. $7,980

c. $13,300

d. $5,320

b. $7,980

Correct! First, calculate the total commission on the sale and then compute the portion to be paid to the salesperson.

A seller paid $132,000 for a house and now wants to sell it at a 20% profit after paying a broker a 6% commission. What is the selling price?

a. $148,896

b. $165,000

c. $176,000

d. $168,511

d. $168,511

Correct! The question is asking for the amount of the selling price, so using the “T” formula the question mark goes in the total section or the lower right area. The Part of the total at the top of the “T” is the Net amount the seller wants to receive after paying the 6% commission. The net amount is computed by adding 20% of the $132,000 to the amount paid of $132,000. An easy way to calculate that is $132,000 times 1.20. The resulting net amount the seller wants to receive is $158,400 and that amount should be placed at the top of the “T”.

The rate is the decimal equivalent of the percentage that the $158,400 represents of the total sales price. It is computed by subtracting the sales commission percentage of 6% from 100% since the sales price is the total or 100%. So 100% less 6% equals 94% and the decimal equivalent is determined by moving a decimal point two places to the left. The answer is .94 (point nine four). The answer using the “T” formula is determined by dividing the $158,400 by point nine four and is $168,511.

An owner lists a lot for sale with a broker to net $70,500 after paying the broker a 7% commission.

At what price would the broker have to sell the property to receive a 7% commission?

a. $72,125

b. $75,806

c. $77,585

d. $75,435

b. $75,806

Correct! In this problem the question is “what is the total sales price”; so the question mark goes in the lower right portion of the “T”. The amount the owner wants to net after paying the commission is part of the total sales price so it goes at the top of the”T”. The $70,500 that the owner wants to net represents 93% of the sales price computed by subtracting 7%, the commission rate, from 100%, the total. The decimal equivalent of .93 goes in the lower left part of the “T” and the answer is determined by dividing $70500 by .93. The resulting answer is $75,806.

“T” earns an 8% commission on the first $75,000 of sales for the month and 3% for all sales over that amount. If “T” sold houses totaling $162,100 for the month, how much more would “T” have earned at a straight 6% commission.

a. $1,113

b. $2,613

c. $4,355

d. $8,613

a. $1,113

Correct! The total commission for the salesperson under this program is $8,613, but that is not the correct answer. The question is how much more the salesperson would have earned if the commission was at a straight 6%. The answer is $1,113 which represents the increased earnings if the salesperson was paid at a straight 6%.

A salesperson receives $5,687.50 commission from the sale of a house after the deduction of a 45% brokerage fee and a $425 fee for administrative services was deducted from the total commission. The listing agreement established a 7% commission rate.

What was the sales price of the house?

a. $197,619

b. $158,766

c. $185,835

d. $153,799

d. $153,799

Correct!

The question is asking for the total sales price of the house so using the formula place a question mark in the lower right part of the “T”.

The next step is to determine the total commission that was paid by the seller. The $5,687.50 is only part of the commission since it has been reduced by the 45% brokerage fee and only represents 55% of the commission (100% less 45%). Dividing $5,687.50 by the 55% results in an answer of $10,340.90, but the administrative fee of $425 must be added to get the total commission of $10,765.90.

To determine the sales price the total commission of $10, 765.90 is placed on the top of the T and is divided by the rate of 7% to determine the sales price. The answer you get is $153,799.

Monthly rent on a warehouse was set at $1.75 per cubic yard. Assuming the warehouse was 36 feet by 200 feet and it was 12 feet high, what would be the annual rent?

a. $5,600

b. $151,200

c. $50,400

d. $67,200

d. $67,200

Correct! In this question, the rent rate is the monthly rate, but the question is for the amount of the annual rent. The first step is to calculate the cubic yards. Multiply the three dimensions of 36 times 200 times 12 to get 86,400 cubic feet. The rent rate is per cubic yard so the cubic feet must be converted to cubic yards by dividing it by the number 27 (86,400 divided by 27); the answer is 3,200 cubic yards. the monthly rent is $5,600 (3,200 times 1.75), but the answer is for annual rent which is $67,200 ($5,600 times 12).

A five-acre rectangular parcel is divided into six equal lots, each having a depth of 250’. The width of each lot is approximately:

a. 208.7 feet

b. 174.24 feet

c. 145.2 feet

d. 871.2 feet

c. 145.2 feet

Correct! There are 43,560 square feet in an acre of land; therefore five acres of land would contain 217,800 square feet (43,560 times 5). If five acres is being divided into six equal lots each lot will have 36,300 square feet (217,800 divided by 6). The width of the lot is determined by dividing the 36,300 square footage by the known depth of 250 feet resulting in the answer of 145.2 feet.

If a half-acre lot has a frontage of 75 feet, what is its depth?

a. 189 feet

b. 290 feet

c. 346 feet

d. 272 feet

b. 290 feet

Correct! A half-acre lot contains 21,780 square fee (43,560 divided by 2). To determine the depth divide the total square footage of the lot by the dimension that is provided; the front feet (21,780 divided by 75.)

A 660 foot X 660 foot parcel contains what percentage of land contained in a 1320’ X 1320’parcel?

a. 25%

b. 33.33%

c. 42.50%

d. 50%

a. 25%

Correct! By looking at the description of the two parcels of land it is easy to guess an incorrect answer of 50%. To calculate the correct answer divide the smaller parcel’s square footage of 435,600 by the larger parcel’s square footage of 1,742,400.

A rectangular lot with an apartment on it is worth $193,000. The value is $4.40 per square foot for the lot. If the lot is 200 feet deep, what is its width?

a. 220 feet

b. 100 feet

c. 600 feet

d. 890 feet

a. 220 feet

Correct! To determine the width first the square footage of the lot must be computed. The square footage is determined by dividing the value of $193,000 by the value of $4.40 per square foot for the lot. The width of the lot is calculated by dividing the total square footage of 43,863.64 by the lot depth of 200 feet.

A triangular lot measures 350 feet along the street and 425 feet in depth on the side that is perpendicular to the street. If a broker sold the lot for $1.50 per square foot and his commission rate was 9% what was the amount of commission earned?

a. $10,040.62

b. $13,387.50

c. $20,081.25

d. $18,423.17

a. $10,040.62

Correct! First, the square footage of the lot is calculated. The square footage is 74,375 (350 times 425 divided by two). This is the calculation for a triangular lot. The sales price is $111,562.50 (74,375 times $1.50). The commission is $10,040.62 ($111,562.50 times .09)

How many half-acre lots can be obtained from a parcel of land 660 feet by 1320 feet after removing 15% for streets?

a. 40

b. 17

c. 20

d. 34

d. 34

Correct! The total square footage of the parcel is 871,200 (660 times 1,320) and 85% of it will be developed into half-acre lots. The lot portion of the parcel is 740,520 square feet (871,200 times .85). The number of lots is determined by dividing the 740,520 by the square feet in a half-acre lot of 21,780 (740,520 divided by 21,780).

If a half-acre lot has a frontage of 75 feet, what is its depth?

a. 272 feet

b. 346 feet

c. 290 feet

d. 189 feet

c. 290 feet

Correct! A half-acre lot contains 21,780 square fee (43,560 divided by 2). To determine the depth divide the total square footage of the lot by the dimension that is provided; the front feet (21,780 divided by 75.)