Math Test

Question 1

A lot measuring 20 and 2/3 acres must be divided equally between four heirs. How much will each heir receive? a. 5 1/3 acres b. 5 1/6 acres c. 2 2/3 acres d. 5 acres

Answer 1

b

Question 2

A Realtor sells 7/8 of an acre for $40,000, and receives a 7% commission. If she splits with her broker 50-50, what did she receive per square foot?

a. $.037 / SF b. $.074 / SF c. $.028/ SF d. $.058 / SF

Answer 2

a $.037 / SF

Question 3

A home appreciated 5 ¼% one year, then 6 2/3% the next year, then 7.2% the third year. What was the average appreciation over the 3-year period expressed as a decimal?

a. 6.37% b. 6 1/3% c. 19.12% d. 6 2/3 %

Answer 3

a. 6.37%

Question 4

A survey finds that agents in a particular region, on the average, receive 60% of ½ of 7% commissions on an average home sale price of $234,000. What is an agent’s average commission in dollars?

a. $16,380 b. $3,276 c. $9,828 d. $4,914

Answer 4

d

Question 5

Lots in the St. Cloud subdivision are selling for approximately $.50 / SF. The Andersons want to build a 2,500 SF home on a 1.5 acre corner lot. The custom builder can build the home for $135 / SF. What will the completed property cost the Andersons?

a. $369,170 b. $370,170 c. $32,670 d. $371,070

Answer 5

b

Question 6

Andre owned a ¼ acre lot. He wanted to construct a 120’ x 80’ tennis court on the lot. What approximate percentage of the lot will be left over, if any, when he has completed the construction?

a. 12% b. 88% c. 3% d. 15%

Answer 6

a

Question 7

A developer wants to develop a 20-acre subdivision. He figures that the streets and common area will take up about 25% of this overall area. If the minimum lot size is to be 10,000 SF, how many lots can the developer have on this property?

a. 64 b. 653 c. 65 d. 87

Answer 7

c

Question 8

Jeannie leased an office building to a tenant under a 3-year lease for $20 / SF. Her commission is 4% of the rent payable over the lease term. If she received a $15,000 commission, how big was the office building?

a. 18,750 SF b. 2,500 SF c. 6,250 SF d. 5,000 SF

Answer 8

c

Question 9

9. A homeowner wants to insulate the new recreation room in her basement. She has been told that 4” of insulation would do the job. The walls are all 8’ high and respectively measure 15’, 15’, 17’, and 17’ in length. How many rolls will she need if each roll measures 4” x 2’ x 50’?
   a. 6 b. 50 c. 5 d. 3

Answer 9

a. 6

First, the requirement = 2(15’x 8’) +2 (17’x 8’) =512 SF. Each roll is 2’x 50’, or 100 SF. Thus she will need 6 rolls.

Question 10

Kinza plans to mulch the flower area around her house. The house measures 40’ x 30’, and she figures she’ll mulch an area 8’ in width to form a big rectangle all around the perimeter. She also figures 4” of depth should be sufficient. If a landscaper quotes Kinza that mulch costs $20 / cubic yard, how much will she spend?

a. $918 b. $1,019 c. $260 d. $340

Answer 10

d. $3
First figure the area to be mulched. If the home is 40 x 30, the flower area adds 8’ to each side of the house. Thus the outside perimeter of the flowered area is (40+8+8) by (30+8+8), or 46’ by 56’. The area of the flowered area is (46’ x 56’) minus the house area of 1,200 SF. Thus the flowered area is 1,376 SF. Second, figure the volume of the mulch: 1,376 SF x 4” = 459 cubic feet. Since there are 27 cubic feet in a cubic yard, she will need 459 / 27 cubic yards, or 17. Thus she will spend $340.

Question 11

Jamie Spiffup advised her clients they needed to paint their living room before showing the property. The walls of these rooms were all 8’ high. The wall lengths were 14’, 18’, 16’, and 18’. The job required two coats of paint. If a gallon of paint covers 200 SF, how many whole gallons would the homesellers have to buy?

a. 3 b. 4 c. 5 d. 6

Answer 11

d.

Question 12

A rancher has a rectangular 350 acre piece of property fronting a highway. He wants to put a barbed-wire fence along his road frontage. How much fence does he need if his property depth is 3,000’?

a. 3,904’ b. 5,082’ c. 508’ d. 1,852’

Answer 12

b. 5,082’

Question 13

An investor just purchased a rectangular 2-acre retail lot for $250 a frontage foot. If she paid $100,000 total, what was the depth of the lot?

a. 400’ b. 250 c. 871’ d. 218’

Answer 13

d. 218’

Since the investor paid $100,000 total, and that equals $250 per frontage foot, there are 400 frontage feet (100,000 / 250). If the property is two acres, it totals 87,120 SF. Dividing this by 400 produces a lot depth of 217.8’.

Question 14

A boat dock runs 80% of the length of a property’s seawall. If the property is a rectangular ¼ acre lot with 80’ of depth between the street and the seawall, how long is the dock?

a. 136’ b. 109 c. 64’ d. 124’

Answer 14

b. 109
First, the lot is ¼ acre, or 43,560 SF / 4, or 10,890 SF. If the lot is 80’ deep, divide the depth into the lot area to calculate the length of the seawall: 10,890 / 80 = 136.12’. Multiply this length times 80% to derive the length of the dock: .80 x 136’ = 109’.

Question 15

A homeowner paid $185,000 for a house three years ago. The house sells today for $239,000. How much has the property appreciated?

a. 23 % b. 77 % c. 29 % d. 123 %

Answer 15

c. 29%
Appreciation as a per cent can be estimated by (1) subtracting the estimated current market value from the price originally paid (239,000 - 185,000 = 54,000) and (2) dividing the result by the original price (54,000 / 185,000 = . 29 or 29%). >appreciation 1<

Question 16

A property sells for $180,000 one year after it was purchased. If the annual appreciation rate is 10%, how much did the original buyer pay for it?

a. $162,000 b. $163,636 c. $180,000 d. $198,000

Answer 16

b. $163.636
The selling price is 110% of the purchase price. Therefore, the purchase price is the selling price divided by 1.1 (110%). $180,000 / 1.1 = $163,636. >appreciation 2<

Question 17

Yvonne bought a home in Biltmore Estates 3 years ago for $250,000. She obtained an 80% loan. Over the past three years, the total appreciation rate has been 18%, and she has paid down her loan by $4,000. What is Yvonne’s equity after this period?

a. $45,000 b. $99,000 c. $95,000 d. $54,000

Answer 17

b. $99,000

Equity = Market value – loan balance. Her loan was .8 x $250,000, or $200,000. Her initial equity was 20% x $250,000, or $50,000. The home has appreciated 18%, or (.18 x $250,000), or 45,000. Plus she has paid down her loan $4,000. Her equity is therefore ($295,000 market value – 196,000 loan), or $99,000.

Question 18

The roof of a property cost $10,000. The economic life of the roof is 20 years. Assuming the straight-line method of depreciation, what is the depreciated value of the roof after 3 years?

a. $10,000 b. $8,500 c. $7,000 d. $1,500

Answer 18

b. $8,500
First derive the annual depreciation which is the cost divided by the economic life. Then multiply annual depreciation times the number of years to identify total depreciation. Remember to subtract depreciation from the original cost if the question asks for the ending value. Thus, ($10,000 / 20 years x 3 years) = $1,500 total depreciation. The ending value is $10,000 – 1,500, or $8,500. >depreciation 1<

Question 19

The Kruteks obtain a fixed-rate amortized 30-year loan for $280,000 @ 6.25% interest. If the monthly payments are $1,724, how much interest do the Kruteks pay in the second month of the loan?

a. $1,748.33 b. $1,456.95 c. $1,458.33 d. $1724.00

Answer 19

b. $1,456.95

(principal x interest)/12=interest paid
Subtract principal then remaining principal x interest/12= interest paid in second month

Question 20

The loan officer at FirstOne Bank tells Amanda she can afford a monthly payment of $1,300 on her new home loan. Assuming this is an interest-only loan, and the principal balance is $234,000, what interest rate is Amanda getting?

a. 6.67% b. 5% c. 8.25% d. 6%

Answer 20

a. 6.67%
The equation for the interest rate is (annual payment / loan amount) = interest rate. Thus ($1,300 x 12) / $234,000 = 6.67%. >rates, payments 3<

Question 21

A borrower obtains a 30-year, amortized mortgage loan of $200,000 at 8%. What is the balloon payment at the end of the loan term if her PI payment is $1,466?

a. 20,800 b. $1,733 c. $1,466 d. Zero

Answer 21

d. Zero

If a loan is fully amortizing, its loan balance is zero at the end of the loan term. >rates, payments 4<

Question 22

A $300,000 loan has monthly interest-only payments of $2,000. Its annual interest rate is:

a. 4% b. 6% c. 8% d. 10%

Answer 22

c.  8%
Remember that (Principal x Rate) = Annual Payment.  If you know 2 of the 3 quantities, you can solve for the third.  To solve for the interest rate, change the formula to (Rate = Annual Payment /  Principal).  Thus ($2,000 x 12 months) / $300,000 = .08, or 8%.  >rates, payments 5<

Question 23

A lender offers the Amerines two alternative loan packages for their $60,000 home equity application. One option is an interest-only loan for 5 years @ 6.5% interest with no points, and the second, a 6.25% interest-only loan for 5 years with 1 point to be paid at closing. Which loan will cost the Amerines less total interest, and by how much?

a. The first option, by $150. b. The second option, by 150. c. The second option, by $750. d. Both options charge the same amount of interest.

Answer 23

b. The second option, by 150.

The first option’s interest total is (6.5% x $60,000) x 5 years, or $19,500. The second option will charge (6.25% x $60,000) x 5 years, plus $600, or a total of $19,350. The 2nd option is $150 cheaper. >rates, payments 7<

Question 24

Carrie Creative pays $650 per month for her mortgage. One day she sells her home under a contract for deed. Her bargain price is set at 90% of the appraised value, and Carrie offers to give the buyers an 80% interest-only loan for 7% with a 4-year balloon. If the appraisal came in at $300,000, and the bank allows her to keep her underlying loan, what is Carrie’s monthly net profit?

a. $1,260 b. $610 c. $650 d. $750

Answer 24

b. $610
Carrie sold her home for (90% x $300,000), or $270,000. The loan she gave the buyer is for ($270,000 x 80%), or $216,000. The monthly payments on this are ($216,000 x 7%) / 12, or $1,260. Therefore she is making a profit of ($1,260 – 650), or $610. >rates, payments 8<

Question 25

Amortization Calculation
Formulas: Month 1: Principal paid = Monthly payment - (Loan amount x
Rate ÷ 12)
Month 2: New loan amount = (Previous month principal -
Principal paid)
Principal paid = Monthly payment - (New loan
amount x Rate ÷ 12)
Example: A borrower obtains a 30-year $100,000 amortized loan @ 7% with
a $665.31 monthly payment. What is the principal paid in the
second month?
Month 1: Principal paid = $665.31 - ($100,000 x 7% ÷ 12) =
$665.31 - (583.33 interest paid) = $81.98
Month 2: New loan amount = $100,000 previous month
beginning loan amount - $81.98 principal paid =
$99,918.02
Principal paid = $665.31 - ($99,918.02 x 7% ÷ 12) =
$665.31 - (582.86 interest paid) = $82.45

Answer 25

Amortization Calculation

Question 26

A property produces an income of $10,000 per year. Management expenses are $700 annually. Monthly heating costs are $92. If the property is valued at $80,000, what is the owner’s approximate overall capitalization rate?
a. 7% b. 8% c. 10% d. 14%

Answer 26

c. 10%

Question 27

The potential gross monthly rent on an apartment building is $5,380. In July, operating expenses were $1,500. A tenant whose monthly rent is $550 failed to pay rent in July. If the property manager’s commission is 5% of the rental income, the management fee for July was:
a. $322.80 b. $194.00 c. $269.00 d. $241.50

Answer 27

d. $241.50

Question 28

A management agreement between an owner and a broker states that the management fee will be 7% of the first $15,000 of the monthly gross collected rent and 8% of the collected rent that exceeds that amount. If last months rent collection totaled $18,500 what will the average annual management fee be, assuming it will be the same each month?
a. $1,330 b. $12,600 c. $15,540 d. $15,960

Answer 28

d. $15,960

Question 29

If a licensee is paid a salary of $600 per month plus one-half of the office’s 6% fee on all sales, what must the licensee’s monthly sales be for the licensee to receive a total monthly income of $2,200?
a. $27,000 b. $37,000 c. $54,000 d. $74,000

Answer 29

c. $54,000

Question 30

A commercial building that occupies an area 52 feet X 28 feet can be replaced at a cost of $34.90 per square foot. The total accrued depreciation on the building is estimated at 25% of the replacement cost. Current value of the land on which the building stand is $6,300. According to the cost approach, the indicated value of the property is approximately how much?
a. $42,836. b. $44,411. c. $50,814 d. $57,114

Answer 30

b. $44,411

Question 31

A broker and an owner agree to list a residential property at a selling price of $50,000 with a commission of eight percent. On June 1, after the owner makes a monthly mortgage payment of $500 that includes 8.5% interest, and mortgage balance of $28,500 remains. Taxes are based on an assessed value of $20,000, at 8.75%, payable in advance on January 1 of each year. The buyer’s cost of title insurance is 1.5% of the selling price. The broker subsequently sells the property to a buyer for $48,500 and the closing is to take place August 15. For test purposes there are 12 months in each year and 30 days in each month.

48. After the owner makes the August 1 mortgage payment, the principal balance remaining on the mortgage is how much?
    a. $27,902 b. $28,033 c. $28,182 d. $28,202

Answer 31

a. $27,902

Question 32

A broker and an owner agree to list a residential property at a selling price of $50,000 with a commission of eight percent. On June 1, after the owner makes a monthly mortgage payment of $500 that includes 8.5% interest, and mortgage balance of $28,500 remains. Taxes are based on an assessed value of $20,000, at 8.75%, payable in advance on January 1 of each year. The buyer’s cost of title insurance is 1.5% of the selling price. The broker subsequently sells the property to a buyer for $48,500 and the closing is to take place August 15. For test purposes there are 12 months in each year and 30 days in each month.
What is the cost to the buyer for title insurance PLUS their share of taxes on this property for the year?
a. $728 b. $1,095 c. $1,256 d. $1,384

Answer 32

d. $1,384

Question 33

If two lots, each 75 feet wide by 105 feet deep, cost $30,000 in total, what is their APPROXIMATE cost per square foot?
a. $1 b. $2 c. $3 d. $4

Answer 33

b. $2

Question 34

Title insurance on a property is $174.90. The fee for title search is $75; the cost of preparing papers is $15, and other miscellaneous fees amount to $6.10. If the seller pays 60% of the total charge and the buyer pays the balance, to the nearest dollar, how much MORE will the seller pay than the buyer?
a. $49. b. $53. c. $54 d. $56

Answer 34

c. $54

Question 35

Which of the following credit terms maybe included in an advertisement for real estate without further disclosure?

a. “10% annual percentage rate”
b. “5 years to repay”
c. “$5,000 down payment”
d. “$300 monthly payment”

Answer 35

a. “10% annual percentage rate”

Question 36

An apartment project with 320 units has 16 vacancies. The vacancy ate is:
a. 5% b. 8% c. 92% d. 20%

Answer 36

a. 5%

Question 37

End of Payment Interest at 10% Principal Unpaid balance Year required of unpaid balance retirement at end of year 1 $263.80 $100.00 $163.80 $836.20 2 $263.80 $ 83.62 $180.18 $656.02 3 $263.80 $ 65.60 $198.20 $457.82 4 $263.80 $ 45.78 $218.02 $239.80 5 $263.80 $23.98 $239.80 $ 00 Total retired: $1,000

70. The chart above illustrates the monthly repayment schedule for which type of loan:
    a. An adjustable rate mortgage.
    b. A reverse annuity mortgage.
    c. A fixed rate mortgage fully amortized.
    d. A graduated payment mortgage.

Answer 37

c. A fixed rate mortgage fully amortized

Question 38

If the quarterly real estate tax on a property with an assessed value of $70,000 is $491, approximately what percent of the assessed value is the annual real estate tax?
a. .7% b. 2.8% c. 3.8% d. 5%

Answer 38

b. 2.8%

Question 39

A buyer purchases a $100,000 home with an 80% loan. There was a real estate commission of 8% and a loan origination fee of $100. The buyer’s attorney charged them $75. The credit report was $35. If the loan discount points were 2% of the loan, what was the total of the buyer closing costs?
a. $210 b. $2,210 c. $8,610 d. $1,810

Answer 39

d. $1,810

Question 40

What should the maximum purchase price for a small shopping center be in total annual rentals are $75,000, total annual expenses are $9,000 and an annual return on investment of 12% is desired?

a. $550,000
b. $625,000
c. $792,000
d. $900,000

Answer 40

a. $550,000

Question 41

A house that sold for $72,500 has been assessed at 60% and the taxes are $2.50 per $100. How much are the annual taxes?
a. $109 b. $261 c. $1,088 d. $1,813

Answer 41

c. $1,088

Question 42

Chuck has owned his home for one year. His records show the following: $650 property insurance; $720 property taxes; $1,000 general maintenance; $1,180 amortization payments; $3,675 mortgage interest; $1,500 straight line depreciation; $800 property improvements. What is the total amount that Chuck can deduct on his federal income tax return?
a. $4,395. b. $3,675. c. $5,575 d. $5,895

Answer 42

a. $4,395.

Question 43

An investor bought a tract of land one-year ago for $960 per acre. His annual expenses are $100 per acre. If he wants to sell a 2 acre tract at a profit of 9% he should sell it for a minimum of:
a. $1,155 b. $2,080 c. $2,202 d. $2,311

Answer 43

d. $2,311

Question 44

An investor purchased a rental home for a price of $36,000. He added $13,000 in improvements by remodeling. The purchase was financed with a $30,000 first mortgage loan. A $10,000 second mortgage loan financed part of the improvements. Cumulative line depreciation taken over the holding period was $8,000. Using the services of a broker, the investor sold the home for $67,500. The investor paid commission and closing costs of $3,000. How much gain did the investor realize on the sale?
a. $15,000. b. $18,500 c. $23,500 d. $26,500

Answer 44

c. $23,500

Question 45

The Wilson’s earn $32,500 per year. They own a house valued at $70,000 but want to buy a larger home. If a lender’s requirements include buyer qualification at 2.5 times their annual income, and if the Wilson’s will net $42,000 from the sale of their present home, what would be the most expensive home they could afford to buy?
a. $74,500 b. $81,250 c. $123,250 d. $185,250

Answer 45

c. $123,250

Question 46

A farmer purchased the NE ¼ and the E ½ of the SE ¼ of a section for $360,000. How many acres did he purchase and how much did he pay per acre? (Remember: a section is 640 acres.)

a. 160 acres at $2,250 per acre
b. 320 acres at $1,135 per acre
c. 240 acres at $1,500 per acre
d. 120 acres at $3,000 per acre

Answer 46

c. 240 acres at $1,500 per acre

Question 47

A $100,000, 30 year fully amortized, fixed rate loan is made for 9.5% annual interest. The monthly principal and interest payment is $840.87. Calculate the principal balance owing after the second monthly payment has been made.

a. $98,318.26
b. $98,416.66
c. $99,901.21
d. $99,950.80

Answer 47

c. $99,901.21

Question 48

How many acres is 348,480 square yards?

a. 2.66 b. 8 c. 24 d. 72

Answer 48

: 1 acre = 43,560 square feet. 9 sure feet = 1 square yard

d. 72

Question 49

A buyer obtained a $50,000 loan with a 9% interest rate. The loan was amortized over 30 years with a monthly payment of $403. Which of the following statements is true?

a. The total amount of interest paid over the term was $145,080.
b. The total amount of interest paid over the term was $135,650
c. The amount of principal in the first month’s payment was $129.00.
d. The amount of principal in the first month’s payment was $28.00.

Answer 49

d. The amount of principal in the first month’s payment was $28.00.

Question 50

An office building rents for $600,000, has expenses of $400,000, and a cash flow of $100,000. The prevailing gross rent multiplier is 8. Using the GRM, what is the value of the building?
a. $800,000 b. $1,600,000 c. $3,200,000 d. $4,800,000

Answer 50

d. $4,800,000

Question 51

A borrower earns $3,000/month and makes credit card and car note payments of $500. A conventional lender requires a 27% income ratio. What monthly amount for housing expenses (principal, interest, taxes, insurance) will the lender allow this person to have in order to qualify for a conventional mortgage loan?
a. $810 b. $675 c. $972 d. $1,040

Answer 51

a. $810

Question 52

A $250,000 interest-only loan carries a 7% rate. Monthly payments are a. $1,750. b. $1,458. c. $17,500.
d. Cannot be determined without loan term data.

Answer 52

b. $1,458

Question 53

A lender is charging 2.75 points on a $240,000 loan. How much must the borrower pay for points?
a. $550. b. $5,500. c. $6,600. d. $660.

Answer 53

c. $6,600

Question 54

Mary Bright bought a home for $80,000, paying $10,000 down and taking a mortgage loan of $70,000. The following year she had a new roof put on, at a cost of $2,000. What is Mary’s adjusted basis in the house if she now sells the house for $100,000?
a. $12,000 b. $72,000 c. $18,000 d. $82,000

Answer 54

d. $82,000

Question 55

An office building has a potential income of $500,000 and vacancy of 10%. Its cash-paid bills total $300,000, and annual depreciation is $5,000. Payments on the loan total $100,000. What is the property’s pre-tax cash flow? a. $45,000 b. $50,000 c. $150,000 d. $155,000

Answer 55

b. $50,000

Question 56

A property is purchased for $200,000. Improvements account for 75% of the value. Given a 39-year depreciation term, what is the annual depreciation expense? a. $3,846 b. $5,128 c. $6,410 d. $8,294

Answer 56

a. $3,846

Question 57

An income property is bought for $500,000. Gross income is $100,000, and net operating income is $60,000. Cash flow is $10,000. What is the return on investment (ROI)?
a. 2.00% b. 12% c. 10.00% d. 60.00%

Answer 57

b. 12%

Question 58

The village of Parrish has an annual budget requirement of $20,000,000 to be funded by property taxes. Assessed valuations are $400,000,000, and exemptions total $25,000,000. What must the tax rate be to finance the budget?
a. 4.70% b. 5.33% c. 5.00% d. 11.25%

Answer 58

b. 5.33%

Question 59

A canal dredging project is to cost $100,000. There are 40 properties along the canal, and 40 others across the street from the canal. The total canal footage to be dredged is 2,500 feet. How much will the assessment be for a 150-foot property on the canal?
a. $1,250 b. $2,500 c. $3,000 d. $6,000

Answer 59

d. $6,000