Chapter 21: Real Estate Math Review

Question 1

How many square feet in an Acre

Answer 1

43,560

Question 2

How do you determine a rectangle’s square footage?

Answer 2

Multiply the length of one side by the length of the adjacent side.

Question 3

What is considered the front footage?

Answer 3

Th first number given in a set of dimensions.

Question 4

How is a sales commission calculated?

Answer 4

Multiply the selling price by the commission rate.

Question 5

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 5

Selling Price = Seller’s Net + Closing Costs divided by 100% - Commission %.
So $100,000 + $8,000 / 100%-10% or
$108,000 / 90% = $120,000.

Question 6

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 6

$100,000 x 5% = $5,000
$100,000 x 6% = $6,000
$135,300 x 7% = $9,471

TOTAL = $20,471

Question 7

What are the three approaches used when appraising real property?

Answer 7

Comparable Sales approach
Cost-Depreciation approach and
Income approach

Question 8

Describe the processes in the Cost depreciation approach.

Answer 8

Step 1: Reproduction Cost / Economic Life x Effective Age = Total Depreciation

Step 2: Reproduction Cost - Total Deprecation + Land value = Depreciated Value of the Property

Question 9

Describe the Income Capitalization Approach.

Answer 9

(I) Net Operating Income / (R) Capitalization Rate x (V)Value

Question 10

Describe the Gross Rent Multiplier Approach.

Answer 10

(V)Value / (R)Monthly Rental Income x (M)Multiplier

Question 11

What is Gross Income Multiplier Approach

Answer 11

A simple way of determining Value or Gross Annual Rental Income by using the VRM formula.

Question 12

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 12

$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 13

What is the formula for Amortization

Answer 13

I / (PRT)

Question 14

How do you figure out payment amortization?

Answer 14

1. Loan amount x Annual interest rate = Annual interest div by 12 = Monthly interest
2. Mortgage payment (principal & interest) – Monthly interest = Principal portion
3. Principal balance of loan – principal portion of payment = New loan balance

Question 15

How much is a Doc stamp on a deed?

Answer 15

.70 per $100 of the purchase price

Question 16

On a financed property, how much is the Doc stamp on the note?

Answer 16

.35 per $100 of the Mortgage note

Question 17

How do you calculate the intangible Tax on a new mortgage note?

Answer 17

The Intangible Tax is .002 (2 mills) on the new debt.

Question 18

How do you calculate prorated property taxes?

Answer 18

Figure out the number of days from January 1st to the date of the closing. Next divide the annual property taxes by 365 days and multiply that by the number of days from the first part.

Question 19

If a person is in a 32% tax bracket, which of the following represents the most desirable investment?

a. 22% Before Taxes
b. 20% Before Taxes
c. 18% After Taxes
d. 16% After Taxes

Answer 19

Step 1: Convert the before tax answers to after tax answers by subtracting their tax bracket (32%) from 100 to give you 68%.
Step 2: Multipy the Before tax % by their tax bracket to give you their After tax return %.
a. = .22 x 68% = 14.96% after taxes
b. = .20 x 68% = 13.6% after taxes
Step 3: Choose the highest after tax %.

c. 18% After Taxes

Question 20

A property is 300’ x 550’ and costs $150,000. What is the cost per front foot?

Answer 20

$150,000 / 300 = $500

Question 21

City taxes are 7 mills, County taxes are 6 mills and school taxes are 5 mills. If a non-homestead property is assessed for $365,000, how much are the total property taxes?

Answer 21

$6570

Question 22

Broker Bob has agreed to pay sales associate Sam 60% of the total commissions earned by Sam. Sam sold a property for $375,000 with an agreed upon commission of 7.5% of the sales price. What is Bob’s share of the commission?

Answer 22

$11,250

Question 23

How many acres are in the N ½ of the NE ¼ of the SW ¼ of Section 22?

Answer 23

640 acres (section) / 4 / 4 / 2 = 20

Question 24

A home sells for $185,000. The buyer assumes an existing first mortgage of $103,225 with the seller taking back a purchase money mortgage of $50,000. How much are the doc. stamps on the deed?

Answer 24

$185,000 / 100 = 1850 * .7 = $1295

Question 25

If a Building’s cost is $400,000, its chronological age is 7 years, economic life is 30 years, effective age is 3 years, and the value of the land is $80,000, what is the value of the property using the Cost-Depreciation Method?

Answer 25

$400,000 / 30yrs = 13,333.33333333333 * 3yrs = 40,000.

$400,000 - $40,000 + $80,000 = $440,000.

Question 26

Seller Sam notifies his broker that he wants to net $100,000 from the sale of his home. The seller’s closing costs will be $3,000 and the broker would like to earn a commission of 10%. How much does the property need to sell for in order to satisfy the seller and the broker?

Answer 26

Seller’s net + Closing cost / 100%-Broker commission.

$100,000 + $3,000 ($103,000) / 90% = $114,445

Question 27

The net income of a rental property is $15,000 and the overall cap rate is 12%, what is the value of the property?

Answer 27

I / (RV) = $15,000 / 12% = $125,000

Question 28

How many acres are contained in a rectangular property that measures 300 feet by 240 feet?

Answer 28

300 * 240 / 43560 = 1.65 acres

Question 29

A broker has a listing in which the seller has agreed to pay 8% commission on the first half of the sales price and 6% on the balance. If the property sells for $260,000, how much is the broker’s commission?

Answer 29

$18,200

Question 30

The city is going to pave your street at a cost of $50 per running foot and agreed to pay 40% of the cost. Your property measures 120’ x 145’. What is the amount of the special assessment for your property?

Answer 30

120 front footage * $50 * .60 = 3600 / 2 = $1800

Always assume there is someone across the street to pay half the cost.

Question 31

What is the principal balance of a $100,000 mortgage at 7% interest after the second monthly payment of $775.30?

Answer 31

$99,614.94

Question 32

An investment property was purchased for $400,000 and the buyer is investing $100,000 as a down payment. What is the loan to value ratio?

Answer 32

75%

Question 33

A property sells for $135,000 with the buyer borrowing $100,000. How much are the total transfer taxes (doc. stamps on deed, note, and intangible tax) due on this transaction?

Answer 33

$1495

Question 34

A developer purchased three lots that are 100’x 200’ each and cost $500 per front foot. He later subdivided the lots into five parcels and sold them for $40,000 each. What is the developer’s percentage of profit?

Answer 34

made / paid = 33%

Question 35

A property costs $130,000 based on $5.00 per square foot. How many acres are contained in the property?

Answer 35

43560 * $5 = 217,800. $130,000 / 217,800 = .59 acres