# Real Estate Math

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1. How many square feet are there in an acre?

A. 44,890
B. 36,930
C. 43,560
D. 10,000
C. 43,560
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2. How many square feet are in a square yard?

A. 27
B. 81
C. 9
D. 3
C. 9

There are nine square feet in a square yard (3 feet per yard x 3 feet per yard = 9 square feet).
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3. A square parcel measures 1/8th of a mile by 1/8th of a mile. How many acres is this property?

A. 20
B. 10
C. 80
D. 40
B. 10

One-eight of a mile is equivalent to 660 feet (5,280 feet / 8 = 660 feet). Multiply to find its square footage (660 feet x 660 feet = 435,600 square feet), and the divide to find the number of acres (435,600 square feet / 43,560 square feet per acre = 10 acres)
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4. How many acres are there in a section

A. 590
B. 870
C. 456
D. 640
D. 640

A section is 640 acres
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5. A section of land is equivalent to:

A. 460 acres
B. 36 square miles
C. 43,560 acres
D. one square mile
D. one square mile

A section of land, under the government survey system, is one square mile, or 640 acres.
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6. One side of a section (in a government survey) is how many feet long?

A. 43,560
B. 2,640
C. 5,280
D. 100
C. 5,280

A section is one square mile, with each side being one mile long. One mile equals to 5,280 feet.
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7. The asking price is \$145,000. The property sells for \$130,000. The commission is 6%. 60% of the commission goes to the broker and 40% goes to the salesperson. How much did the salesperson receive?

A. \$3,335
B. \$3,120
C. \$2,190
D. \$2,850
B. \$3,120

This is a percentage question that must be solved in two steps. First, calculate what the total commission was, by finding 6% of the \$130,000 sales price.
P = % x W
P = .06 x \$130,000
P = \$7,800
Next, calculate wht the salesperson's share of the commissionwas, by finding 40% of the total commission.
P = % x W
P = .4 x \$7,800
P = \$3,120
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8. A 10-unit apartment building has an annual net income of \$5,000 per unit. If the purchasers wish a 10% return on their investment, how much should they be willing to pay for the property?

A. \$5,000
B. \$500,000
C. \$50,000
D. \$5,000,000
B. \$500,000

\$500,000. The value of the property = net incom/rate of return. Thus value = \$50,000/.10=\$500,000
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9. A rental property has return rate of 8%. The monthly net rental is \$600.00. What is the market value of the property?

A. \$84,000.00
B. \$96,500.00
C. \$90,000.00
D. \$57,600.00
C. \$90,000.00

Rate of return is computed by dividing the annual net income by the rate of return. In this case multiply \$600.00 by 12; the income is given as monthly. The gross annual income, \$7,200.00 divided by 8%, is \$90,000.00
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10. If the loan value is 80%, and the property was appraised at \$86,500.00 and sold for \$88,000.00, how much would the purchaser be permitted to borrow?

A. \$73,500.00
B. \$69,200.00
C. \$70,400.00
D. \$65,200.00
B. \$69,200.00

The loan value is based upon the appraised value, not the sale price. The appraised value is \$86,500.00; 80% of that amount is \$69,200.00. This would be the maximum the purchaser would be permitted to borrow.
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11. A property is valued at \$100,000 and is taxed at 45 mills. The assessment rate on the property is 35%. Calculate the yearly taxes.

A. \$1,575.00
B. \$4,500.00
C. \$15.75
D. \$157.50
A. \$1,575.00

To solve this problem, keep a simple formula in mind: take the appraised value (\$100,000) x the assessment rate (35%). This will give the assessed value (\$35,000). Next take the assessed value x the millage rate of 45; but remember to divide your answer by \$1,000, as a mill means dollars per thousand. \$100,000 x 35% x 45 / 1,000 = \$1,575
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12. An investor buys a single-family rental property with an initial basis of \$150,000. Assuming 30 year straight-line depreciation, what is the basis of the property after 10 years?

A. \$200,000
B. \$50,000
C. \$120,000
D. \$100,000
D. \$100,000

The annual depreciation would be \$5,000 (150,000 / 30), thus 10 years' depreciation would be \$50,000 (10 x 5,000). The basis after 10 years is 150,000 - 50,000 = \$100,000.
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13. A property has been renting for \$750 per month. Based on comparable, the GRM is 110. What is the indicated value of the property?

A. \$68,182
B. \$82,500
C. \$99,000
D. \$990,000
B. \$82,500

The indicated value using a GRM (Gross Rent Multiplier) is the montly rent x GRM. in this case, \$750 x 110 = \$82,500
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14. The salesperson earns a 6% commission on the first \$100,000 of the sales price and 3% of that portion of the sales price that exceeds \$100,000. The commission is \$7,050. What is the sales price?

A. \$141,000
B. \$153,000
C. \$135,000
D. \$154,500
C. \$135,000

This problem has to be broken into two segments. The first step is to calculate the value of the part of the commission that was earned at the 6% rate. Use the percentage formula.
P = % x W
P = .06 x \$100,000
P = \$6,000
Now we know that \$6,000 of the \$7,050 was earned at the 6% rate. Subract \$6,000 form \$7,050; the remaining \$\$1,050 of the commission was earned at the 3% rate. Use the percentage formula again, this time switching it around to isolate the unknow quantity. which now is the remaining portion of the sales price.
P / % = W
\$1,050 / .03 = W
\$35,000 = W
Finally, add the \$35,000 to the \$100,000, for a total sales price of \$135,000.
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15. A 10-year-old property was recetly appraised for \$257,000. It has depreciated 25% since it was new. What was it originally worth?

A. \$342,667
B. \$355,886
C. \$392,125
D. \$356,925
A. \$342,667

The first step is to subtract the rate of depriciation from 100%.
100% - 25% = 75%
This shows that the property is worth 75% of what it was originally worth. Now we can use the basic percentage formula to solve the problem. We know the "part," i.e., its recetly appraised value, and the percentage, so we need to isolate the "whole," which is its original value.
P = % x W
P / % = W
\$257,000 / .75 = W
\$342,666.67 = W
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16. The broker's commission is 7% of the sales price. What is the commission if the property sells for \$3.50 per square foot and its dimensions are 200' x 175'?

A. \$8,575
B. \$8,050
C. \$8,138
D. \$9,112
A. \$8,575

the first step is to calculate the area of the property. Use the area formula.
A = B x H
A = 200 x 175
A = 35,000
Now multiply 35,000 square feet by \$3.50 per square foot find the sales price.
35,000 x \$3.50 = \$122,500
Finally, use the percentage formula to calculate the amount of the commission.
P = % x W
P = .07 x \$122,500
P = \$8,575
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17. A convenience store occupied 30% of a 150'x200' lot. Ten percent of the lot was condemned for public use easement. How many square feet was left for parking after the easement was established?

A. 19,759
B. 18,000
C. 18,460
D. 21,346
B. 18,000

The first step is to find the total square footage of the lot. Use the area formula.
A = B x H
A = 150 x 200
a = 30,000 square feet
Next, we need to find what percentage of the lot can be used for parking. The store occupies 30% of the lot, and the easement occupied another 10%, for a total of 40%. Therefore, 60% of the lot remains for parking. Now we can use the percentage formula to find out how many square feet that represents.
P = % x W
P = .6 x 30,000
P = 18,000 square feet
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18. A property has a present depreciated value of \$36,900.00. What was its original cost if it had depreciated at the rate of 2-1/4\$ for the past 8 years (use straight line depreciation).

A. \$45,000.00
B. \$43,875.00
C. \$36,900.00
D. \$49,600.00
A. \$45,000.00

2-1/4% depreciation over past 8 years would be a total depreciation of 18%. Thus, the property has depreciated 18% form its original 100% value. If X is the original value, X multiplied by 82% (100% - 18% = 82%) \$36,900 divided by 82% equals \$45,000.00
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19. A property is appraised at \$150,000 and assessed for tax purpose at 35% value. Calculate semi-annual tax bill if the mills total is 80.

A. \$2,100.00
B. \$7,500.00
C. \$4,200.00
D. \$42.00
A. \$2,100.00

Don't forget to divide the answer by 2 as a final step. The formula for obtaining property taxes is as follows: take the appraised value of \$150,000 x the assessed rate of 35%, which will yield the assessed value. Next, take the assessed value x the millage of 80 and divide the answer by 1,000, as mills are \$1 per 1,000. This will give you an answer of \$4,200, but you must remember to divide by 2 since the questions asks for the semi-annual tax bill.
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20. A house is sold for \$500,000 with a \$50,000 down payment. The seller will pay 3 discount points and 1% loan origination fee. The brokerage fee is 6%. How much do the seller’s expense come up to?
\$48,000

*Calculate the loan amount (\$500,000 - \$50,000 = \$450,000) and then calculate the amount of the discount points and loan origination fee (which together are 4% of the loan amount, with 3% for discount points and 1% for loan origination fee) \$450,000 x .04 = \$18,000. Now calculate the brokerage fee (\$500,000 x .06 = \$30,000) then add the figure together for the seller’s expense (\$18,000 + \$30,000 = \$48,000)
21. An investor obtains a 90% loan to purchase a \$150,000 duplex. Given a choice between a loan at 8% interest with 2 discount points or a loan at 7% interest with 4.5 discount points, he chooses the loan with the lower interest rate. What is the minimum amount of cash he must bring to the transaction to cover the down payments and discount points?
\$21,075

*First is to find out the loan amount (\$150,000 x 90%= \$135,000) the amount of the down payment is \$15,000. (\$150,000 - \$135,000 = \$15,000) next, calculate the amount of discount points (\$135,000 x 4.5% = \$6,075) Add \$15,000 + \$6,075 = \$21,075
22. A seller sells his house at \$128,000. He takes back a mortgage from the buyer for \$63,000. He pays off \$43,000 balance on the existing loan and pays a 5.5% brokerage fee. What are his proceed from the sale?
\$14,960

*To determine the seller’s proceed, start with the selling price of (\$128,000) subtract the seller financing (\$63,000) subtract the existing loan balance payoff (\$43,000) and subtract the brokerage fee (\$128,000 x .055 = \$7,040) The result is \$14,960 (\$128,000 - \$63,000 - \$43,000 - \$7,040 = \$14,960. Note that “Proceeds” is generally understood to mean money actually taken away at closing. Money received over the years for the sell-financed mortgage is part of the check the seller gets on closing day, so it’s not considered proceeds
23. A small office building with measurements of 110’ x 90’ rents for \$11 per square foot annually. Smith signs a 10-year lease, with the first year’s rent waved by the landlord. If Smith makes monthly payments, what will the payments average over the 10-year period?
\$8,167.50

*110 x 90 = 9900 square feet. Now mulitiply \$11 x 9900 = \$108,900 (Annual Rent) multiply \$108,900 by nine years = \$980,100. Divide the total rent paid by 120 months (120 divided 12 = 10years the actual term of the lease, and the average monthly rent comes to \$8,167.50
24. P has applied for a loan to buy a house appraised at \$100,000. If the sale price of the house is \$102,500 and the bank's maximum LTV is 80%, what is the maximum amount the bank is willing to loan?
\$80,000

*A lender calculates LTV on the appraised value or sale price, which ever is lower. In this case, that would be the appraised value of \$100,000. Therefore the maximum the bank will loan is 80% of \$100,00 is \$80,000.
25. The seller wants to net at \$104,000. he pays a 7% commission. \$2,400 in discount points and \$1,500 in repairs. Approximaely how much should the seller ask for the property?
\$116.022

• *\$104,000 (desired net) + \$2,400 (commission) + \$1,500 (repairs) = \$107,900 (required net after commission but before settlement cost)
• *100%-7% (commssion) = 93%
• *\$107,900 divided by 93% = \$116,021.51 or \$116,022
26. How many square feet are in 3.5. acres?

A. 97,574,400
B. 152,460
C. 158,760
D. 2,240
B. 152,460

Multiply the number of square feet in an acre (43,560) by 3.5 (43,560 x 3.5 = 152,460).
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27. A buyer purchases a home for \$380,000 using a seller-financed straight loan. If he pays 50% down, makes montly payments on the balance at 11% interest, and pays an extra \$19,000 towards the principal before the end of each year, how much does the seller receive during the first year?

A. \$39,900
B. \$250,800
C. \$60,800
D. \$229,900
D. \$229,900

First calculate the amount of the downpayment (\$380,000 x .50 = \$190,000). The balance of the purchase price is the loan amount (\$380,000 - \$190,000 = \$190,000), which is used to calculate the interest paid over the course of the year (\$190,000 x .11 = \$20,900). Add the downpayment, the interest payments, and the prepaid \$19,000 together, to find that the seller receives \$229,900 during the first year (\$190,000 + \$20,900 + \$19,000 = \$229,900).
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28. Brian purchases two parcels of lands, one measuring one square mile and the other containing five acres. If paid \$2,000 an acre, what was his total purchase price?

A. \$1,290,000
B. \$1,208,000
C. \$1,280,000
D. \$1,209,000
A. \$1,290,000

One square mile equals 640 acres. 640 acres + 5 acres = 645 acres. 645 x \$2,000 = \$1,290,000
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29. A rental property produces a 10% rate return. The net income on the property is \$1,100 per month. Using the income approach to value, what is the property's market value?

A. \$132,000
B. \$155,000
C. \$99,500
D. \$187,500
A. \$132,000

Multiply the monthly income by 12 to find the annual net income. \$1,100 x 12 = \$13,200. Then divide the net income by the rate of return (10%) to find the value. \$13,200 / .10 = \$132,000.
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30. A property sells for \$100,000. The commission is 6%. The selling broker and listing broker split the commission 60/40. Each of the brokers then splits his share of the commission evenly with his salesperson. How much is the listing salesperson's share of the commission?

A. \$3,600
B. \$1,200
C. \$6,000
D. \$2,400
B. \$1,200

The total commission amount is \$6,000 (\$100,000 x .06 = \$6,000.) If the brokers split it 60/40, the selling broker will receive \$3,600 (\$6,000 x .6 = \$3,600) and he listing broker will receive \$2,400 (\$6,000 x .4 = \$2,400). The listing salesperson's share will be \$1,200 (\$2,400 / 2 = \$1,200).
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31. A borrower agrees to pay 3 discount points on a \$150,000 loan, How much do the discount points cost?

A. \$3,000
B. \$1,500
C. \$9,000
D. \$4,500
D. \$4,500

Each discount points is 1% of the loan amount so 3 discount points is 3% of \$150,000. \$150,000 x .03 = \$4,500.
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32. The direct sales comparison approach indicates that a single-family residence's market value is \$75,000. The property's reproduction cost is \$85,000. The property was just sold by the seller as part of bankruptcy proceedings for \$70,000. The best estimate of the property's value is

A. \$75,000
B. \$85,000
C. \$80,000
D. \$70,000
A. \$75,000

The best appraisal method for estimating the value of a single-family residence is the direct sales comparison approach, so the likeliest value is \$75,000. Reproduction cost and liquidation value would be best less relevant
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33. The J's have a 25-year loan at 8.5% interest, with a current principal balance of \$149,000. How much will their next monthly payment of \$1,200 reduce the principal balance?

A. \$144.58
B. \$148.59
C. \$1,055.42
D. \$1,067.81
A. \$144.58

Multiply the loan balance by the annual interest rate to get the annual interest (\$149,000 x 8.5% = \$12,665). Divide the annual interest by 12 montsh (\$12,665 / 12 = \$1,055.42). Subtract the monthly interest from the total payment (\$1,200 - \$1,055.42 = \$144.58) to get the principal reduction amount
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34. An individual has an income-producing property for sale that generates \$64,250 in gross earnings. The property has \$24,360 in operating expenses and credits and vacancy losses. With a 10% capitalization rate, how much could an investor afford to pay for the property.

A. \$298,900
B. \$202,700
C. \$390,500
D. \$402,400
A. \$298,900

\$64,250 - \$24,360 = \$39,890 (net income). Divide \$39,890 by the 10% capitalization rate for a value of \$398,900.
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35. A property with no outstanding lien sold. The seller paid \$2,450 in discount points, \$1,236 in other closing cost, and a 6% commission. She received a closing check for \$112,000. What was the selling price?

A. \$118,720
B. \$125,250
C. \$122,405
D. \$123,070
D. \$123,070

Add the settlement cost to the seller's net: \$112,000 + \$3,686 (settlement cost of \$2,450 + \$1,236) = \$115,686. This amount is 94% of the sales price (100% - 6% commission = 94%). \$115,686 / 94% = \$123,070.21 (sales price)
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36. M is interested in selling a parcel of land that measures 110' x 297'. Similar property recently solf for \$20,000 per acre. What is M likely to get for his land?

A. \$15,000
B. \$20,000
C. \$32,670
D. \$35,000
A. \$15,000

110' x 297' = 32,670 square feet. Divide 32,670 by 43,560 (the number of square feet in an acre) to get .75 acres. Multiply .75 acres by \$20,000 to get \$15,000
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37. A borrower secures a mortgage loan in the amount of \$95,000, with semiannual interest payments of \$4,275. What was the interest rate charged by the lender?

A. 9%
B. 8.5%
C. 7.75%
D. 8%
A. 9%

Mulitiply the semiannual payments by two to get the annual interest (\$4,275 x 2 = \$8,550). Divide the annual interest by the loan amount to get the interest rate (\$8,550 / \$95,000 = .09, or 9%).
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38. An eight-yeal-old property was recently appraised at \$125,000. It has depreciated 35% since it was built. What was it originally worth?

A. \$168,750
B. \$192,308
C. \$175,456
D. \$199,119
B. \$192,308

\$125,000 (current value) / 65% (100% less 35%) = \$192,307.69
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39. A property with no outstanding liens sold. The seller paid \$2,450 in discount points, \$1,236 in other closing costs, and a 6% commission. She received a closing check for \$112,000. What is the selling price?

A. \$125,250
B. \$118,720
C. \$123,070
D. \$122,405
C. \$123,070

Add the settlement costs to the seller's net: \$112,000 + \$3,686 (settlement costs of \$2,450 + \$1,236) = \$115,686. This amount is 94% of the sales price (100% - 6% commission = 94%). \$115,686 / 94% = \$123,070.21 (sale price)
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40. A house has dimensions of 60 x 20'. The attached garage is 12' x 20'. What is the total square footage of the house plus garage?

A. 300
B. 1,440
C, 2,560
D. 2,880
B. 1,440

Multiply the house's lenght times the width (60' x 20' = 1,200 square feet). Then multiply the garage's lenght times the width (12' x 20' = square feet). Add the two areas together to total 1,440 square feet.
41. A borrower secure a mortgage loan in the amount of \$95,000, with semiannual interest payments of \$4,275. What was the interest rate charged by the lender?

A. 8.5%
B. 7.75%
C. 9%
D. 8%
C. 9%

Multiply the semiannual payments by two to get the annual interest (\$4,275 x 2 = \$8,550). Divide the annual interest by the loan amount to get the interest rate (\$8,550 / \$95,000 = .09, or 9%)
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42. A one-story house had original dimensions of 60' by 30'. However, a new addition, measuring 24' by 20', was recently added by the owners. The house's total square footage is now:

A. 1,800
B. 2,280
C. 5,040
D. 1,320
B. 2,280

The original part of the house measures 1,800 square feet (60' x 30' = 1,800). The new addition is 480 square feet (24 x 20 = 480). Add the two together, for a total of \$2,280 square feet (1,800 / 480 = 2,280)
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43. A parcel occupies the NW 1/4 of the SE 1/4, and the S 1/2 of the SW 1/4 of the NE 1/4 of section 4. How many acres is this parcel?

A. 100
B. 60
C. 80
D. 40
B. 60

A section is 640 acres, so a quarter-section is 160 acres (640 / 4 = 160) and a quarter-quarter section, like the NW 1/4 of the SE 1/4, is 40 acres (160 / 4 = 40). Half of a quarter-quarter section, like the S 1/2 of the SW 1/4 of the NE 1/4 is 20 acres (40 / 2 = 20). Add the two parts together to find the parcel is 60 acres (40 + 20 = 40).
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44. The owner of a lot that is 99' by 110' would like to sell it. Similar properties sell for \$180,000 per acre. What is the likely selling price for this property?

A. \$45,000
B. \$60,000
C. \$54,450
D. \$90,000
A. \$45,000

First, find the square footage of the lot (99 feet x 110 feet = 10,890 square feet). Convert that to acreage (10,890 square feet / 43,560 square feet per acre = 0.25, or one quarter of an acre). Multiply that by the price per acre to find the selling price (\$180,000 x 0.25 = \$45,000)
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45. A 100' x 100' unimproved lot is listed for sale. The listing price is \$200 per front foot, and the listing broker will collect a 7% commission on the sale. If the lot sells for the asking price, what will the broker's commission be?

A. \$1,400
B. \$20,000
C. \$200
D. \$140,000
A. \$1,400

To find the listing price, multiply \$200 by lot's front footage of 100' (\$200 x 100' = \$20,000). The broker's commission is 7% of \$20,000 (\$20,000 x .07 = \$1,400).
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46. A property produces a 12% rate of return. The property's net income is \$10,500 per month. Using the capitalization method, what is the property's market value?

A. \$2,000,000
B. \$1,050,000
C. \$1,512,000
D. \$875,000
B. \$1,050,000

The first step is to determine the annual income (\$10,500 per month x 12 = \$126,000 per year). Divide that by the capitalization rate to find the property's value (\$126,000 / 0.12 = \$1,050,000).
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47. Bob's property has a fair market value of \$190,000. It is in a county where properties are assessed at 50% of value, and tax rate is \$55 per \$1,000 of assessed value. What's Bob's annual property tax?

A. \$5,225.00
B. \$10,450.00
C. \$7,837.50
D. \$2,612.50
A. \$5,225.00

The first step in calculating a tax problem is t find its assessed value (\$190,000 x 0.5 = \$95,000). Divide the assessed value by \$1,000 t find the number of increments (\$95,000 / \$1,000 = 95) and then multiply by the tax rate to find the annual tax bill (95 x \$55 = \$5,225)
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48. Art sold his house, which was not encumbered with a mortgage. Closing expenses were \$5,264, and he paid a commission of 7% of the selling price. He received a check at closing for \$372,316. What did the house sell for?

A. \$404,260
B. \$406,000
C. \$411,100
D. \$398,000
B. \$406,000

This is a seller's net problem. The first step is to add the costs of the sale to the seller's net (which in this case is the actual net, not a desired net). Add \$5,264 to \$372,580. Divide that by the commission rate subtracted from 100 (100% - 7% = 93%). \$377,580 divided by 0.93 equals \$406,000
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49. A property is sold for \$340,000. There is a remaining mortgage balance of \$68,000, and other closing costs will be \$6,400. The seller also must pay a brokerage fee of 6.5%. What will the seller net?

A. \$243,500
B. \$254,320
C. \$237,100
D. \$243,916
A. \$243,500

This is a seller's net problem, except backwards, starting with the sales prices. Start by finding the amount of commission (\$340,000 x 0.065 = \$22,100) and then subtract the commission from the price paid (\$340,000 - \$22,100 = \$317,900). Subtract the other costs that must be paid to find the seller's net (\$317,900 - \$68,000 - \$6,400 =\$243,500).
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 Author: happyedi253 ID: 8146 Card Set: Real Estate Math Updated: 2010-05-02 21:10:13 Tags: Washington Real Estate Math License Folders: Description: Real Estate Math from Pearson Vue and Rockwell Institute Show Answers: