Math

Question 1

1. A broker keeps 60 percent of sales commissions and pays the sales associate the other 40 percent. A sales associate sells 50 acres of land at $900 per acre with a gross sale commission of 10 percent of the sale price. What is the broker’s commission?

a) $1,800
b) $2,700
c) $4,500
d) $4,700

Answer 1

1. b) $2,700

How to do it: 50 acres × $900 per acre = $45,000 total sale price; $45,000 sale price × .10 commission = $4,500 total commission; $4,500 × .60 broker’s share = $2,700 broker’s commission

Question 2

2. A broker earned a $3,120 commission for selling a residential lot at $52,000. What was the sale commission rate?

a) .06
b) .08
c) .60
d) 16.67

Answer 2

2. a) .06 or 6 percent

How to do it: $3,120 commission ÷ $52,000 sale price = .06 rate or 6 percent

Question 3

3. What is the annual premium for an insurance policy in the amount of $25,000 if the cost is $.60 per $100?

a) $15
b) $150
c) $416
d) $500

Answer 3

3. b) $150

How to do it: $.60 ÷ $100 = .006 premium rate; .006 × $25,000 policy = $150 premium

Question 4

4. A developer is subdividing a 12-acre tract into lots measuring 80’ × 110’. Each lot has a perimeter of 380 feet and a sale price of $4,500. She has allowed 126,720 square feet for required streets, sidewalks, and recreational facilities. How many salable lots are there?

a) 14.4
b) 59.4
c) 45
d) 116.6

Answer 4

4. c) 45

How to do it: 43,560 square feet per acre × 12 acres = 522,720 total square feet – 126,720 square feet for streets, sidewalks, etc. = 396,000 available square feet; 80 feet × 110 feet = 8,800 square feet per lot; 396,000 available square feet ÷ 8,800 = 45 lots

Question 5

5. Mr. Garcia’s monthly mortgage payment for principal and interest is $264.60. If his annual property taxes are $780 and his homeowner’s insurance premium is $198, what is his total monthly payment, including taxes and insurance?

a) $329.60
b) $346.10
c) $379.10
d) $527.60

Answer 5

5. b) $346.10

How to do it: $780 ÷ 12 months = $65.00 taxes per month; $198 per year ÷ 12 months = $16.50; $264.60 principal and interest payment + $65.00 + $16.50 = $346.10

Question 6

6. An investor is considering the purchase of a duplex for $215,500 cash. She wants an investment that will produce a first-year 12 percent net return on investment. How much net income must the duplex generate during the first year to produce this investor’s required return on investment?

a) $9,625
b) $11,550
c) $12,500
d) $25,860

Answer 6

6. d) $25,860

How to do it: .12 net return × $215,500 purchase price = $25,860 net income

Question 7

7. You have sold a residential property for $98,500. Your employment contract specifies that you receive 55 percent of the total sale commission for properties you sell. If the rate of commission is 8 percent, what amount will you receive?

a) $3,546
b) $3,940
c) $4,334
d) $7,880

Answer 7

7. c) $4,334

How to do it: $98,500 sale price × .08 commission rate = $7,880 total commission; $7,880 total commission × .55 sales associate’s share = $4,334 commission due sales associate

Question 8

8. A buyer has made an earnest money deposit of $7,000 on a home selling for $139,900. A bank has agreed to lend the buyer 80 percent of the sale price. How much additional cash must the buyer furnish to pay the total required down payment?

a) $7,000
b) $11,920
c) $20,980
d) $27,980

Answer 8

8. c) $20,980

How to do it: $139,900 sale price × .80 = $111,920 loan; $139,900 sale price – $111,920 loan = $27,980 down payment; $27,980 – $7,000 earnest money deposit = $20,980

Question 9

9. Mr. Jones borrowed $85,000 at 7.5 percent interest per year and paid a total of $3,187.50 in interest. How long was the term of this loan?

a) Two months
b) Three months
c) Four months
d) Six months

Answer 9

9. d) Six months

How to do it: $85,000 loan × .075 interest rate = $6,375 interest per year; $6,375 interest ÷ 12 months = $531.25 per month; $3,187.50 ÷ $531.25 = 6 months

Question 10

10. A seller received $52,000 from the sale of his home. He paid $2,500 in settlement costs in addition to an 8 percent commission. What is the selling price of the home? (Round to the nearest dollar.)

a) $54,500
b) $56,522
c) $58,860
d) $59,239

Answer 10

10. d) $59,239

How to do it: $52,000 sale proceeds + $2,500 settlement costs = $54,500; $54,500 ÷ .92 = $59,239.13 or $59,239 sale price

Question 11

11. The loan-to-value ratio offered by a local financial institution is 75 percent. If a buyer wishes to acquire a property selling for $129,500, what will her down payment need to be?

a) $1,727
b) $5,180
c) $32,375
d) $97,125

Answer 11

11. c. $32,375

How to do it: $129,500 sale price × .75 LTV = $97,125 loan; $129,500 sale price – $97,125 loan = $32,375 down payment

Question 12

12. A property has an assessed value of $125,500. What is the property tax based on a rate of 25 mills?

a) $313.75
b) $3,125
c) $3,137.50
d) $3,150

Answer 12

12. c) $3,137.50

How to do it: $125,500 × .025 property tax rate = $3,137.50

Question 13

13. The city is proposing to pave the streets in your neighborhood at a cost of $40 per foot of frontage. The city will absorb 25 percent of the cost. Your lot has footage on the street of 130 feet. Assuming there are homes on both sides of the street, what is the amount of your paving assessment?

a) $1,950
b) $2,600
c) $3,900
d) $5,200

Answer 13

13. a) $1,950

How to do it: $40.00 × .75 homeowner’s share = $30.00 homeowner’s cost per foot of frontage; $30.00 × 130 feet of footage = $3,900 ÷ 2 = $1,950

Question 14

14. The N½ of the NE¼ of the SW¼ and the S½ of the SE¼ of a section contains how many acres?

a) 2.5
b) 20
c) 80
d) 100

Answer 14

14. d) 100

How to do it: 640 acres ÷ 4 ÷ 2 = 80 acres; 640 acres ÷ 4 ÷ 4 ÷ 2 = 20 acres; 80 + 20 = 100 acres

Question 15

15. A duplex is scheduled to close on September 10. The seller collected rent for September on the first of the month amounting to $950. According to the sale contract, the buyer is due the rental income for the day of closing. What is the proration?

a) $285 debit to seller, $285 credit to buyer
b) $633.33 credit to seller, $633.33 debit to buyer
c) $665 debit to seller, $665 credit to buyer
d) $665 credit to seller, $665 debit to buyer

Answer 15

15. c) $665 debit to seller, $665 credit to buyer

How to do it: $950 ÷ 30 days = $31.666667/day; $31.666667 × 21 days = $665.00; Seller has collected the rent in advance; Seller owes buyer; Debit seller and credit buyer

Question 16

If you are given the dimensions only (e.g. 300’ x 200’), the first number is considered to be the _____ footage

Answer 16

“front”

Question 17

A parcel of land measures 400’ x 400’ (square). How many acres are contained in this parcel?

Answer 17

3.6731 acres

400’ x 400’ = 160,000 square feet

160,000 sq. ft. ÷ 43,560 = 3.6731 acres

Question 18

A parcel of land is 7.5 acres. How many square feet are in the parcel?

Answer 18

326,700 sq. ft.

43,560 x 7.5 = 326,700 sq. ft.

Question 19

Seller Alexa notifies her broker that she wants to net $100,000 from the sale of her home. The seller’s closing costs will be $8,000 and the broker must earn a commission of 10%. How much should the property sell for so that both the seller and broker receive the amount of money they want?

Answer 19

$120,000

Selling Price = Seller’s Net + Closing Costs
(divided by)
100% - Commission %

$100,000 + $8,000 = 108,000

(100% - 10% = 90%)

$108,000 (divided by) 90% = $120,000

Question 20

A broker list a property for $259,000 and agrees to accept a 5% commission on the first $100,000 of the selling price, 6% of the next $100,000, and 7% on the portion over and above $200,000. How much is the broker’s total commission on a sales price of $335,300?

Answer 20

$20,471

$100,000 x 5% = $5,000

$100,000 x 6% = $6,000

$135,300 x 7% = $9,471

TOTAL = $20,471

Question 21

Comparable Sales Approach Example:

Comp. #1 sold for $180,000. Comp #1 is identical to the subject in all aspects except that Comp #1 has a fireplace and the subject does not. If a fireplace is worth $5,000, what is the adjusted value of Comp #1?

Answer 21

$180,000 - $5,000 = $175,000 adjusted value

Question 22

Cost-Depreciation Approach:

Determining the value of a property using the cost-depreciation approach, a two-step math process is followed:

Answer 22

Step One:

Reproduction Cost
÷ Economic Life
x Effective Age
=======================
Total Depreciation

Step Two:

Reproduction Cost
- Total Depreciation (calculated from Step One)
+ Land Value
==================================
Depreciated Value of the Property

Question 23

Cost-Depreciation Approach Example:

If a building is valued at $300,000, it has an economic life of 20 years and an effective age of 4 years, what is the value of the property if the lot is worth $40,000?

Answer 23

$280,000

Step One:

$300,000
÷ 20
x 4
================
$60,000

Step Two:

$300,000
- 60,000
+ 40,000
================

$280,000

Question 24

Income Capitalization Approach:

The income capitalization approach formula is:
I
–(divided by)—
R X V

Answer 24

I = Net Operating Income
R = Capitalization Rate
V = Value

When you know the value of two of the letters, you can determine the value of the third letter by properly dividing or multiplying.

Question 25

Income Capitalization Example:

If Net Operating Income is $40,000, and the capitalization rate is 10%, what is the value of the property?

Answer 25

$400,000

R X V

R

$40,000 / 10% = $400,000

Question 26

Gross Rent Multiplier Approach:

The Gross Rent Multiplier (GRM) is an easy calculation to determine the value of a property if the monthly rent is the same each month. The formula is:

R X M

Answer 26

V = Value
R = Monthly Rental Income
M = Multiplier

If you know the value of two of the letters, you can determine the value of the third letter by properly dividing or multiplying.

Question 27

Gross Rent Multiplier Example:

If the monthly rent is $900 and the Gross Rent Multiplier is 94, what is the value of the property?

Answer 27

$84,600

R X M

R X M

Question 28

Gross Income Multiplier Approach:

The Gross Income Multiplier (GIM) is an easy calculation to determine the value of a property when analyzing the property’s income for the entire year. The formula is:

R X M

Answer 28

V = Value
R = Annual Rental Income 
M = Multiplier

If you know the value of two of the letters, you can determine the value of the third letter by properly dividing or multiplying.

Question 29

Gross Income Multiplier Example:

If the value of a property is $720,000 and the annual rental income is $60,000, how much is the gross income multiplier?

Answer 29

12

R X M

$720,000 / $60,000 = 12

Question 30

Discount Points:

Discount points are pre-paid interest. For every point that a lender charges, their yield increases 1/8 of one percent. When a lender charges points, they are paid at closing by the borrower.

Answer 30

One point is calculated as one percent of the loan amount; two points, two percent; etc.

Question 31

Discount Points Example:

Shifty Savings and Loan is making a $90,000 loan with an annual interest rate of 7%. If the lender charges 4 discount points at closing to make the loan, what is the yield to the lender and how much will the points cost the borrower?

Answer 31

$90,000 x 4% = $3,600 cost of points

Four points adds 4/8 or ½ of a percent to the lender’s yield

Question 32

Amoritization Example:

$80,000 loan for 30 years at an annual interest rate of 8% with monthly principal and interest payments of $587.01:

Answer 32

$80,000 x .08 = $6,400 (annual interest) ÷ 12 = $533.33 (monthly interest) $587.01 (P&I) - $533.33 (I) = $53.68 (P)

$80,000 - $53.68 = $79,946.32 new principal balance after the 1st payment.

$79,946.32 x .08 = $6,395.71 ÷ 12 = $532.98 $587.01 - $532.98 = $54.03

$79,946.32 - $54.03 = $79,892.29 new principal balance after the 2nd payment.

Question 33

OFFICE BUILDING SQUARE FOOTAGE

Sometimes the student is asked to calculate how many offices will fit in a multi-floor office location.

Answer 33

FIRST: FIGURE OUT HOW MUCH SQUARE FOOTAGE IS AVAILABLE FOR ONE FLOOR.

SECOND: CALCULATE HOW MANY OFFICES CAN BE FITTED ON ONE FLOOR.

THIRD: MULTIPLY THE NUMBER OFFICES ON ONE FLOOR BY THE NUMBER OF FLOORS

Question 34

Square Footage / Office Building Example:

Donald wants to rent out 3 floors of a bank building that measure 55,000 square feet each. On each floor, 30% of the square footage must be set aside for hallways, elevators, stairs, and other common areas. Donald decides that each office needs to be at least 1,400 square feet. How many offices can Donald fit if he rents out all 3 floors?

Answer 34

81 offices

1) Determine how much square footage is available for offices on one floor
55,000 x 70% = 38,500 square feet
2) Divide the number of available square feet by the size of each office
38,500 ÷ 1,400 = 27.5 offices. NEVER ROUND UP AT THIS STAGE. Therefore there are 27 offices on one floor
3) Multiply the number of offices by the number of floors to be rented
27 X 3 = 81 offices

Question 35

Your seller just lost his job and is unable to stay in his home. He makes the decision to sell his home to move to a smaller house and contacts you to list the property. Within a few days, you have a fully signed contract and are moving into the closing.

The contract states that the purchase price of the property is $215,000. The seller agrees to pay a 5.5% commission and $1,500 towards closing costs for the buyer. The seller’s payoff amount is $201,500. He will receive a credit at closing for taxes at $543 and a credit for HOA dues at $250.

Question: Based on the information above, would the seller be required to bring money to closing?

Answer 35

Answer: No. And here’s why:

(Subtract) Commission: $215,000 x 0.055 = $11,825

(Subtract) Seller paid closing costs = $1,500

(Subtract) Seller’s payoff = $201,500

(Add) Credit for Taxes = $543

(Add) Credit for HOA dues = $250

Total = $215,000 – $11,825 – $1,500 – $201,500 + $543 + $250 = $968 that the seller would receive back at closing.