Real Estate Math questions

Question 1

A broker was paid 6% commission on the first $60,000 of a sale price and 4% for everything above that. What would the sale price be if the total commission was $4,375?

Answer 1

$79, 375

6% * $60,000 = $3,600

$4,375 - $3,600 = $775

$775 / 4% = $19,375

$19,375 + $60,000 = $79,375

Question 2

Calder’s Construction Company built a home in a new subdivision. It sold 6 months later for $48,500. This amount reflected a depreciation of 3%. Knowing this, what was the original asking price on the home?

Answer 2

$50,000

To figure this out, take the sale price and divide it by 97% (or .97), which is the amount remaining after 3% depreciation:
$48,500 ÷ .97 = $50,000

Question 3

Joe’s duplex has depreciated 3% per year for the 5 years he has owned it. Since the building originally cost $20,000, what is the current value of the duplex?

Answer 3

$17,000

3% * 5 years = 15%

$20,000 * 15% = $3,000

$20,000 -$3,000 = $17,00

Question 4

If Skylar’s property has a net income of $5,480, and returns 8 percent annually on the investment, then what is her property’s value?

Answer 4

$ 68, 500

The formula for finding a property’s value when you have the net operating income and cap rate is:

Current Market Value (CMV) = Net Operating Income (NOI) ÷ Cap Rate

CMV = $5,480 ÷ .08 (8% in decimal form)

CMV = $68,500

Question 5

An individual borrowed $7,000 on a straight note at 9% interest. If the total interest paid on the note was $945, what was the term of the loan?

Answer 5

18 Months

$7,000 * 9% = $630

$945 Interest per year / $630 = 1.5 years or 18 months

Question 6

John and Sandi Samson, who file a joint income tax return, pay 28 percent income tax on their earnings. If they have an $85,000 mortgage at 8 percent interest, their allowable tax savings would be:

Answer 6

$1,904

$85,000 * 8% = $6,800

$6,800 *28% = $1,904

Question 7

What is the selling price of a property if the seller paid $3500 for taxes due, has a $125,000 mortgage, paid a 6% broker commission, and netted $70,000 on the sale?

Answer 7

$211,170.21

$3,500 + $125,000 + $70,000 = $198,500

$198,500 is equal to 94% of the selling price, with the brokers 6% commission

$198,500 / 94% = $211,170.21

Question 8

A building that cost $300,000 to construct 10 years ago has depreciated 25%. The land costs $51,000, so the appraised value is:

Answer 8

$276,000

$300,000 * 25% depreciation = $75,000

$300,000 - $75,000 = $225,000

$225,000 + $51,000 = $276,000

Question 9

An office building earns $850,000 per year, and expenses are 35% of that amount. If the property is capitalized at 12%, what is its approximate value?

Answer 9

$4,604,167

$850,000 * 35% = $297,500

$850,000 - $297,500 = $552,500

$552,500 / 12% = $4,604,167

Question 10

What is the cubic footage of a driveway that measures 60 feet long, 8 feet wide, and is 3 inches deep?

Answer 10

120 Cubic Feet

60 ft * 8 ft / 1/4 = 120 Cubic feet

on a calculator

60 ft * 8ft / 4 = 120 Cubic Feet

Question 11

If the assessed valuation of a property is $20,000, with a tax rate of $4.00 per $100, what is the annual tax?

Answer 11

$800

$20,000 / 100 = $200

$200 * $4 = $800

Question 12

Madison Davidson negotiated for a $30,000 loan with $400 monthly payments and a 9 percent interest charge. What is her first month’s interest payment?

Answer 12

$225

$30,000 * 9% = $2,700

$2,700 / 12 = $225

Question 13

Wayne Goodspeed falls in love with a house and buys it for 5% more than the appraised value. He secures a loan for $220,000, which represents the appraised value minus a 10% down payment. What was the purchase price, and how much did Wayne have to come up with in cash?

Answer 13

$256,666 / $36,666

Step 1, find the appraised value - $220,000 divided by 90% = 244,444.44

Step 2, find the purchase price - $244,444.44 X 105% = $256,666.67

Step 3, find the down payment - $256,666.67 minus $220,000 = $36,666

Question 14

How much less are the monthly payments on a $36,000 home than on a $40,000 home if a 75% loan is obtained at $8.70 per month per $1000 of value?

Answer 14

$26.10

$4,000 x .75 = $3,000

$3,000 ÷ $1000 = 3

3 x $8.70 = $26.10

Question 15

If Chris’s house depreciates at the rate of 2.5% per year for 10 years and has a present value of $12,500, what was the original value of the house?

Answer 15

$16,666

2.55 * 10 years = 25%

100% 25% = 75%

$12,500/.75 = $16,666

Question 16

What are the actual measurements of a property shown as 5-3⁄4 inches long and 4-1⁄2 inches wide, if the scale is 1⁄8 inch = 1 foot?

Answer 16

46 X 36

First, convert your scale to feet. If 1⁄8 in. = 1 foot, then 1 in. = 8 feet (multiply both sides of the equation by 8). Use this to solve the problem.

8 x 5 3⁄4 is the same as 8 x 5.75 = 46
8 x 4 1⁄2 is the same as 8 x 4.5 = 36
The area is 46’ x 36’.

Question 17

Freddy Froghammer owns a lot measuring 80 ft. x 120 ft. The city puts in a new street on the front and the side of his house and assesses him 6 cents per square foot based on the area of this lot. His costs are:

Answer 17

$576.00

120 x 80 = 9,600 sq. ft.

9,600 x $.06 = $576.00

Question 18

Find the capitalization rate on a building that is worth $430,000, and rents for $1,500 a month.

Answer 18

4%

$1,500 x 12 = $18,000 in yearly rent.

$18,000 ÷ $430,000 = 4%

Question 19

Jones purchased a home for $80,000 using a down payment of 21.25% of the purchase price, and financing the balance on a 30-year amortized loan with interest at 10.25% per annum. The lender requires monthly impounds for property taxes of $800 per year and casualty insurance costing $978 for a three year policy. Assuming that the first monthly payment on the principal is $119, the total amount Jones will have to pay the first month will be approximately:

Answer 19

$751

$80,000 x .2125 (the same as 21.25%) = $17,000 down payment

$80,000 - $17,000 = $63,000 loan

$63,000 x 10.25% = $6,457.50 interest per year

$6,457 ÷ 12 (months) = $538.125 interest per month

Taxes: $800 ÷ 12 (months) = $66.67 month

Insurance: $978 ÷ 36 months = $27.17 per month

Now, add the principal (given in the problem), interest, taxes and insurance to find the first month’s payment:
$119.00 + $538.125 + $66.67 + $27.17 = $750.95, which is approximately $751

Question 20

The reciprocal of 8% is:

Answer 20

12.5

In math, the reciprocal is the inverse of a number. This means that the product of a number and its reciprocal yields 1. So the reciprocal of 8⁄100 is 100⁄8.

8% is equivalent to .08
.08 is equal to the fraction 8⁄100
The opposite of 8⁄100 is 100⁄8
100 divided by 8 = 12.5

Question 21

Sage owned an income property with an adjusted cost basis of $150,000 and a fair market value of $200,000. He exchanged the property for another income property, which has a fair market value of $210,000. Both parties had no loans against them and no adjustment was made for the difference in value. For federal income tax purposes, the new property will have a basis for Sage of:

Answer 21

$150,000

n a tax deferred exchange transaction, the cost basis of the property transferred becomes the cost basis of the property which is acquired or received. Even though Sage’s new property had a higher fair market value, no adjustment was made for the difference in value so the basis for the new property remained the same as the basis for the old property.

Question 22

A prospect is considering the purchase of an income property. The property’s operating statement shows the deductions subtracted from a gross income of $94,500. The deductions amount to 60% of the gross income. If the prospect wants a 12% return on the purchase price of any investment he makes, what should he pay for the property?

Answer 22

$315,000

60% - 100% = 40%

$94,500 * 40% = $37,800

$37,800 ÷ 12% = $315,000

Question 23

After subtracting $140.00 escrow fees and 6% commission on gross sales price, a seller receives $13,584.00. What is the selling price?

Answer 23

$14,600

$13,584 + $140 = $13,724

$13,724 ÷ .94 = $14,600

Question 24

An acre is to be divided into four equal lots. If the lots are parallel to each other, rectangular, and 200 feet long, the width of each lot would most nearly be:

Answer 24

55 feet.

One Acre = 43,560 sq ft

43,560sq ft / 200 ft = 217.8 ft

217.8 ft / 4 = 54.45 ft rounded to 55 ft

Question 25

Which of the following is the largest parcel of land?

A. 5,280 x 10,560 feet

B. 2 sections

C. 10% of a township

D. A 2 mile square

Answer 25

A 2 mile square

A two mile square would be a square measuring two miles on each side. It would contain four sections and have an area of 4 square miles.

Question 26

Andrew purchased a property at 20% less than the listed price and later sold the property for the original listed price. What was the percentage of profit?

Answer 26

25%

This problem can be figured using any list price, but let’s assume that the property was listed at $10,000.

20% * $10,000 = $2,000

$10,000 -$2,000 = $8,000

Andrew sold the property for the original list price, so his profit is $10,000 - $8,000 = $2,000.

To find the percentage of profit, divide the profit by purchase price: $2,000 ÷ $8,000 = .25, or 25% profit.

Question 27

An owner depreciated the improvements based on a cost basis of $160,000 using the straight line method. Improvements are depreciated 37.5% to date and the remaining economic life is estimated to be 15 years. Which of the following is correct?

Answer 27

Rate of depreciation exceeds 4% per annum

100% - 37 1⁄2% = 62 1⁄2% remaining to depreciate 62 1⁄2% divided by 15 years = 4.17% per year

Question 28

Selwyn was the owner of a straight note with an annual interest rate of 8.4%. In 5 years, he had received $5,460 in interest. What was the principal amount of the note?

Answer 28

$13,000

$5,460 divided by 5 years = $1,092 annual interest

$1,092 divided by .084 = $13,000 principal amount

Question 29

Solly bought a home for $31,680 and now wishes to sell. He is informed that the cost of selling will amount to 12% of the selling price. He wants to sell at a high enough price that he doesn’t take a loss. How much does the home need to appreciate in value to offset the selling costs?

Answer 29

$4,320

Start by finding his desired sales price, which is the original purchase price divided by 88%:
$31,680 ÷ .88 = $36,000

$36,000 - $31,680 = $4,320

Question 30

A building has interior dimensions of 26 feet by 30 feet. The walls are 6 inches thick on every side. How much square footage of land does it cover?

Answer 30

837

To find the total square footage of land covered by a building, you’ll need to add the wall thickness from each end (6 inches) of the building to the internal dimension. When you measure the width, there are two walls, when you measure the length there are two walls. Once you have the total length by the total width, multiple them together to find the square footage:

26 ft. (internal dimension) + 6 in. (one wall) + 6 in. (the other wall) = 27 ft. on one side;
30 ft. (internal dimension)+ 6 in. (one wall) + 6 in. (the other wall) = 31 ft. on the other.
31 ft. x 27 ft. = 837 sq ft.

Question 31

A house is appraised for $25,000, and shows an assessed value of $20,000. The taxes on the house are $300 annually. What would the tax be on a house that is appraised at $45,000, with an assessed value of $40,000?

Answer 31

$600

$300/$20,000=.015 mill levy

$40,000 x .015 = $600

Question 32

A small studio sold for $16,350, which was a 9% appreciation over the original cost of the studio. What was the original cost of the studio?

Answer 32

$15,000.00

$16,350 ÷ 1.09 = $15,000

Question 33

A house sold for $345,000, which was 9% more than the cost of the house. The original cost of the house was most nearly:

Answer 33

$316,514

The Original Cost (OC) is Current Cost (CC) divided by Adjusted Cost Ratio (ACR).

The Current Cost is $345,000, the Adjusted Cost Ratio is 100% plus or minus the appreciation/depreciation of the house.

Because the house is now worth 9% more than OC, the ACR is 109% (or 1.09).

OC = CC ÷ ACR, so OC = $345,000 ÷ 1.09

$345,000 ÷ 1.09 = $316,513.76, so the answer is “most nearly” $316,514.

Question 34

If $150 interest is paid in 8 months on a straight note loan of $2,500, what is the annual rate of interest?

Answer 34

9%

In 8 months, or 2⁄3 of a year, $150 interest was paid. Divide $150 by 2⁄3 to find the total paid in a year, so $150 ÷ (2⁄3) = $225 interest per year.
Divide interest per year by total loan amount to find the interest rate, so $225 ÷ $2500 = .09, or 9% APR.

150 / 66.66% = $225

$225 / $2500 = 9%

Question 35

An investor is going to have a building constructed which would cost $150,000. When completed, it will be leased for $2,500 per month. The annual operating expenses for the property will be $6,000. How much should he invest to realize a 12% return?

Answer 35

$50,000

First, calculate how much the building would earn per year by renting it out:
$2,500 x 12 = $30,000

Next, subtract the projected annual operating expenses:
$30,000 - $6,000 = $24,000

Now, divide that number by a 12% capitalization rate to determine the projected asset value:
$24,000 ÷ .12 = $200,000

Finally, subtract the construction cost from the asset value to determine the dollar amount of the required investment:
$200,000 - $150,000 = $50,000

Question 36

Sage obtained a loan in the amount of $20,000 and paid the mortgage lender 4 discount points and an origination fee of 2%. If the payments on the loan were $163.00 per month including 8% interest, and the average balance over a 5-year period was $18,500, the gross amount earned by the lender over those 5 years was most nearly:

Answer 36

$8600

The lender earned the discount points, origination fee and interest.
$20,000 X 4% = $800 in points
$20,000 X 2% = $400 in origination fee
$18,500 X 8% = $1480 annual interest X 5 years = $7400.
Total of these three amounts is $8600.

Question 37

Jones sold his home for $17,200. If this represents 9% more than what he paid for it, the cost of the home was most nearly:

Answer 37

$15,800

Selling price = cost + 9% or 109%
$17,200 divided by 1.09 = $15,779
Closest answer is $15,800

Question 38

A borrower signed a straight note for a term of eight months in the amount of $2500. If she paid $150 in interest on the loan, the interest rate was:

Answer 38

9%

$150 divided by 8 months = $18.75 per month
$18.75 X 12 = $225 per year (APR is Annual Percentage Rate, so you must figure the rate for 1 year)
$225 divided by $2500 = 9%

Question 39

An income property was appraised for $100,000 based on a 6% capitalization rate. If an investor used an 8% cap rate, the value of the property would be:

Answer 39

$75,000

First, multiply the appraisal value by the capitalization rate:
$100,000 X 6% = $6000 net income

Then, divide the net income by the alternate cap rate to find the alternate value:
$6000 divided by 8% = $75,000 value.

Question 40

A married couple purchased a property for a total price of $18,000. The down payment was $5,000 and the seller took back a First Trust Deed in the amount of $13,000. The terms of the $13,000 Trust Deed called for no payments in the first year. If they were to sell the property for twice its original cost at the end of the first year, their original dollar is now worth:

Answer 40

$4.60

The owners had an initial equity (or investment) of $5000. If the property doubled in value to $36,000, you would deduct the $13,000 loan to find their new equity of $23,000. Divide the current equity by the intial equity to find the increase of dollar value:

$23,000 ÷ $5000 = $4.60

Question 41

An investor purchased two lots and paid $18,000 for each one. Since each lot had a 60’ frontage he was able to subdivide the combined parcels in three lots with equal front footage. If the three lots sold for $15,000 each, his rate of profit on his investment was:

Answer 41

25%

First, find the selling price of the three lots:
3 lots X $15,000 each = $45,000 selling price.

Next, find the purchase price:
2 lots X $18,000 each = $36,000 purchase price.

Now we find the difference between selling price and purchase price:
$45,000 selling price - $36,000 purchase price = $9000 profit.

Finally, we divide the profit by the purchase price to determine the rate of profit on the investment:
$9000 ÷ $36,000 = .25, or 25%