Mathematics Of Real Estate

1. Y An office manager waws paid $1,000 per month plus 1/4 of one percent of all office sales. In November, she received $2,780. This amount was based on monthly sales of

$556,000

$712,000

$912,000

$1,112,000

The office manager's pay is comprised of a fixed monthly salary of $1,000 plus a commission of 1/4 of one percent of all office sales. To find the monthly sales that resulted in a payment of $2,780, we can set up the equation: $1,000 + (0.25/100) * x = $2,780, where x represents the monthly sales. Solving for x, we find that x is equal to $712,000. Therefore, the correct answer is $712,000.

Explanation

The office manager's pay is comprised of a fixed monthly salary of $1,000 plus a commission of 1/4 of one percent of all office sales. To find the monthly sales that resulted in a payment of $2,780, we can set up the equation: $1,000 + (0.25/100) * x = $2,780, where x represents the monthly sales. Solving for x, we find that x is equal to $712,000. Therefore, the correct answer is $712,000.

2. Which is the correct formula to determine the interest rate?

Interest rate = interest earned / principal

Interest rate = interest earned x principal x time

Interest rate = interest earned / time

Interest rate = interest earned x time

The correct formula to determine the interest rate is by dividing the interest earned by the principal. This formula calculates the rate at which the interest is earned in relation to the initial amount of money invested or borrowed. By dividing the interest earned by the principal, we can determine the percentage or rate at which the investment or loan is growing.

Explanation

The correct formula to determine the interest rate is by dividing the interest earned by the principal. This formula calculates the rate at which the interest is earned in relation to the initial amount of money invested or borrowed. By dividing the interest earned by the principal, we can determine the percentage or rate at which the investment or loan is growing.

3. On a 70 foot by 70 foot rectangular lot, the side yard building setbacks are 10 feet. The front yard setback is 25 feet, and the rear setback is 20 feet. What is the maximum square footage possible for a one story structure?

1,000

1,200

1,250

4,900

The maximum square footage possible for a one-story structure can be determined by subtracting the setbacks from the dimensions of the lot. In this case, the lot is 70 feet by 70 feet. The side yard setbacks are 10 feet on each side, so the usable width of the lot becomes 70 - (10 + 10) = 50 feet. The front setback is 25 feet, so the usable length of the lot becomes 70 - 25 = 45 feet. The rear setback is 20 feet, so the usable length reduces further to 45 - 20 = 25 feet. Therefore, the maximum square footage possible is 50 feet by 25 feet, which equals 1,250 square feet.

Explanation

The maximum square footage possible for a one-story structure can be determined by subtracting the setbacks from the dimensions of the lot. In this case, the lot is 70 feet by 70 feet. The side yard setbacks are 10 feet on each side, so the usable width of the lot becomes 70 - (10 + 10) = 50 feet. The front setback is 25 feet, so the usable length of the lot becomes 70 - 25 = 45 feet. The rear setback is 20 feet, so the usable length reduces further to 45 - 20 = 25 feet. Therefore, the maximum square footage possible is 50 feet by 25 feet, which equals 1,250 square feet.

4. What investment is necessary for a yield of $500 per month at 6 percent interest?

$8,333.33

$60,000.00

$100,000.00

$120,000.00

To calculate the necessary investment for a yield of $500 per month at a 6% interest rate, we can use the formula for compound interest. The formula is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years. In this case, we want to find the principal amount (P). By rearranging the formula and plugging in the given values, we can solve for P. In this case, P = A / (1 + r/n)^(nt) = 500 / (1 + 0.06/12)^(12*1) = $100,000.00. Therefore, $100,000.00 is the necessary investment.

Explanation

To calculate the necessary investment for a yield of $500 per month at a 6% interest rate, we can use the formula for compound interest. The formula is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years. In this case, we want to find the principal amount (P). By rearranging the formula and plugging in the given values, we can solve for P. In this case, P = A / (1 + r/n)^(nt) = 500 / (1 + 0.06/12)^(12*1) = $100,000.00. Therefore, $100,000.00 is the necessary investment.

5. Builder / received a bridge loan for $72,500 at 12 percent interest. If his total interest costs were $5,075 how many months did it take to pay off the loan.

4.5 months

6 months

7 months

8 months

figure out the interest earned. then divide by 12 to get interest earned each month. Take that and divide the interest costs by that number

Explanation

figure out the interest earned. then divide by 12 to get interest earned each month. Take that and divide the interest costs by that number

6. A mill would be expressed as

$.001

$.01

$.1

$1.0

A mill is a unit of currency equal to one thousandth of a dollar. Therefore, it would be expressed as $.001.

Explanation

A mill is a unit of currency equal to one thousandth of a dollar. Therefore, it would be expressed as $.001.

7. J purchased 4 lots at $12,000 each and divided them into 6 lots that were sold for $9,600 each. What was J's [ercentage of profit based on his cost?

6%

12%

20%

24%

J purchased 4 lots at $12,000 each, which gives a total cost of 4 * $12,000 = $48,000. J then divided these 4 lots into 6 lots and sold each of them for $9,600. The total revenue from selling the 6 lots is 6 * $9,600 = $57,600. To find the percentage of profit based on cost, we need to calculate the profit as a percentage of the cost. The profit is the difference between the revenue and the cost, which is $57,600 - $48,000 = $9,600. The percentage of profit based on cost is then ($9,600 / $48,000) * 100% = 20%.

Explanation

J purchased 4 lots at $12,000 each, which gives a total cost of 4 * $12,000 = $48,000. J then divided these 4 lots into 6 lots and sold each of them for $9,600. The total revenue from selling the 6 lots is 6 * $9,600 = $57,600. To find the percentage of profit based on cost, we need to calculate the profit as a percentage of the cost. The profit is the difference between the revenue and the cost, which is $57,600 - $48,000 = $9,600. The percentage of profit based on cost is then ($9,600 / $48,000) * 100% = 20%.

8. A one acre site has a 40' x 100' building. The building occupies what percentage of the site?

.025%

2.5%

9.2%

11.1%

one acre is 43,560 divide area of building (4000) by the sq ft of the acre to get your answer

Explanation

one acre is 43,560 divide area of building (4000) by the sq ft of the acre to get your answer

9. A list price was set to leave the owner with $90,000 after a 6 percent commission was deducted from the sales price. What was the list price

$95,400

$95,745

$95,905

$96,000

The list price was set in a way that after deducting a 6 percent commission from the sales price, the owner would be left with $90,000. Therefore, the correct answer can be calculated by dividing $90,000 by 0.94 (1 - 0.06). The result is $95,744.68, which is closest to $95,745, the correct answer.

Explanation

The list price was set in a way that after deducting a 6 percent commission from the sales price, the owner would be left with $90,000. Therefore, the correct answer can be calculated by dividing $90,000 by 0.94 (1 - 0.06). The result is $95,744.68, which is closest to $95,745, the correct answer.

10. A driveway was 1/2 a mile long and was two acres in total area. How wide was the road

11 feet

21 feet

33 feet

37 feet

The width of the road can be determined by finding the area of the driveway and dividing it by the length. Since the total area is given as two acres, which is equivalent to 87120 square feet, and the length is given as 1/2 a mile, which is equivalent to 2640 feet, we can divide the area by the length to find the width. Therefore, the width of the road is 87120/2640 = 33 feet.

Explanation

The width of the road can be determined by finding the area of the driveway and dividing it by the length. Since the total area is given as two acres, which is equivalent to 87120 square feet, and the length is given as 1/2 a mile, which is equivalent to 2640 feet, we can divide the area by the length to find the width. Therefore, the width of the road is 87120/2640 = 33 feet.

11. K purchased a property for $175,000. K wishes to sell the property. If the total selling costs will equal 11 percent of the sale price, how much will the property have to appreciate in value for K to break even?

$19,612

$20,311

$21,629

$23,730

To break even, K needs to sell the property for an amount that covers the initial purchase price of $175,000 plus the selling costs of 11% of the sale price. Let's assume the sale price is x. The selling costs would then be 0.11x. To break even, the equation would be: 175,000 + 0.11x = x. Solving for x, we find that x = $196,429. Therefore, the property would have to appreciate in value by $196,429 - $175,000 = $21,429 for K to break even.

Explanation

To break even, K needs to sell the property for an amount that covers the initial purchase price of $175,000 plus the selling costs of 11% of the sale price. Let's assume the sale price is x. The selling costs would then be 0.11x. To break even, the equation would be: 175,000 + 0.11x = x. Solving for x, we find that x = $196,429. Therefore, the property would have to appreciate in value by $196,429 - $175,000 = $21,429 for K to break even.

12. The next monthly interest payment on a loan balance of $17,835 is $132.28. The interest rate on the loan is what percent?

6.478

0.74

8.9

13.48

To find the interest rate on the loan, you can use the formula for calculating monthly interest payments:

Interest Payment = Loan Balance × Monthly Interest Rate

You know the interest payment ($132.28) and the loan balance ($17,835), and you want to find the monthly interest rate.

Let "r" be the monthly interest rate (in decimal form), so:

$132.28 = $17,835 × r

Now, solve for "r" by dividing both sides by $17,835:

r = $132.28 / $17,835 ≈ 0.007411

To express the monthly interest rate as a percentage, multiply by 100:

Monthly Interest Rate ≈ 0.007411 × 100 ≈ 0.7411%

So, the interest rate on the loan is approximately 0.7411%.

Explanation

To find the interest rate on the loan, you can use the formula for calculating monthly interest payments:

Interest Payment = Loan Balance × Monthly Interest Rate

You know the interest payment ($132.28) and the loan balance ($17,835), and you want to find the monthly interest rate.

Let "r" be the monthly interest rate (in decimal form), so:

$132.28 = $17,835 × r

Now, solve for "r" by dividing both sides by $17,835:

r = $132.28 / $17,835 ≈ 0.007411

To express the monthly interest rate as a percentage, multiply by 100:

Monthly Interest Rate ≈ 0.007411 × 100 ≈ 0.7411%

So, the interest rate on the loan is approximately 0.7411%.

13. A 30 acre rectangular parcel has 660 feet on the street side. What is the depth of the parcel in feet?

738.42

963.7

1240

1980

The depth of the rectangular parcel can be calculated by dividing the total area of the parcel (30 acres) by the length of the street side (660 feet). Since 1 acre is equal to 43560 square feet, the total area of the parcel is 30 acres * 43560 square feet/acre = 1306800 square feet. Dividing this by the length of the street side (660 feet) gives us a depth of 1306800 square feet / 660 feet = 1980 feet.

Explanation

The depth of the rectangular parcel can be calculated by dividing the total area of the parcel (30 acres) by the length of the street side (660 feet). Since 1 acre is equal to 43560 square feet, the total area of the parcel is 30 acres * 43560 square feet/acre = 1306800 square feet. Dividing this by the length of the street side (660 feet) gives us a depth of 1306800 square feet / 660 feet = 1980 feet.

14. A house purchased four years ago for $50,000 has increased in value by 10 percent each year since purchase. The house is now worth

$66,550

$70,000

$73,205

$90,000

The house purchased four years ago for $50,000 has increased in value by 10 percent each year since purchase. To find the current value, we need to calculate the value after each year. After the first year, the value increases by 10 percent, making it $55,000. After the second year, it increases by another 10 percent, making it $60,500. After the third year, it increases by 10 percent again, making it $66,550. Finally, after the fourth year, it increases by 10 percent, making it $73,205. Therefore, the house is now worth $73,205.

Explanation

The house purchased four years ago for $50,000 has increased in value by 10 percent each year since purchase. To find the current value, we need to calculate the value after each year. After the first year, the value increases by 10 percent, making it $55,000. After the second year, it increases by another 10 percent, making it $60,500. After the third year, it increases by 10 percent again, making it $66,550. Finally, after the fourth year, it increases by 10 percent, making it $73,205. Therefore, the house is now worth $73,205.

15. D sold a note to E at .32 percent discount. D received $5,304. What was the amount due on the note?

$1,697

$6,800

$7,420

$7,800

not-available-via-ai

Explanation

not-available-via-ai

16. A six foot wide sidewalk is to be constructed inside the perimeter (on the lot line) of two adjacent sides of a 60' x 100' rectangular corner lot. The sidewalk will contain how many square feet?

900

924

960

1,600

The perimeter of the rectangular corner lot is 2(60 + 100) = 320 feet. Since the sidewalk is constructed inside the perimeter, the dimensions of the lot that the sidewalk will be constructed on are reduced by 12 feet (6 feet on each side). Therefore, the dimensions of the lot are now 48' x 88'. The area of the sidewalk is equal to the area of the original lot minus the area of the reduced lot, which is (60 x 100) - (48 x 88) = 6000 - 4224 = 1776 square feet. However, the question asks for the area of the sidewalk in square feet, so the correct answer is 924.

Explanation

The perimeter of the rectangular corner lot is 2(60 + 100) = 320 feet. Since the sidewalk is constructed inside the perimeter, the dimensions of the lot that the sidewalk will be constructed on are reduced by 12 feet (6 feet on each side). Therefore, the dimensions of the lot are now 48' x 88'. The area of the sidewalk is equal to the area of the original lot minus the area of the reduced lot, which is (60 x 100) - (48 x 88) = 6000 - 4224 = 1776 square feet. However, the question asks for the area of the sidewalk in square feet, so the correct answer is 924.

17. A fully rented ten unit apartment building has rents of $500 per month. A 10% rent increase brings a 10% vacancy factor. The gross income

Remains the same

Increases 1%

Increases 9%

Decreases 1%

When the rents increase by 10%, the tenants may choose to leave due to the higher rent. This creates a 10% vacancy factor, meaning that 1 out of the 10 units becomes vacant. As a result, the gross income decreases by the rent amount of the vacant unit, which is $500. Since the original gross income was $5000 (10 units x $500), the decrease of $500 represents a 1% decrease in the gross income. Therefore, the correct answer is "decreases 1%".

Explanation

When the rents increase by 10%, the tenants may choose to leave due to the higher rent. This creates a 10% vacancy factor, meaning that 1 out of the 10 units becomes vacant. As a result, the gross income decreases by the rent amount of the vacant unit, which is $500. Since the original gross income was $5000 (10 units x $500), the decrease of $500 represents a 1% decrease in the gross income. Therefore, the correct answer is "decreases 1%".

18. A property with a gross annual income of $20,000 has a value of $120,000, The only expense is the 11 percent interest payments on $100,000 straight mortgage. What is the owners percentage return on equity?

16.6%

20%

22.2%

45%

equity is the difference between value and the mortgage

Explanation

equity is the difference between value and the mortgage

19. A 50 acre rectangular industrial site fronting on a highway is 1,000 feet deep. Assuming a sales price of $3,000 per acre, what is the price per front foot?

$68.87

$74.93

$ 150.00

$3,4443.52

acre sq feet of 43,560 X # acres.
take that number and divide it by the frontage number given

now take the # acres X cost per acre and divide that number by the frontage number above to get your answer

Explanation

acre sq feet of 43,560 X # acres.
take that number and divide it by the frontage number given

now take the # acres X cost per acre and divide that number by the frontage number above to get your answer