Linear Measure

12 inches = 1 ft
3 ft = 1 yd
5,280 ft = 1 mile
640 acres = 1 sq mile
1 sq mile = 1 section
36 sections = 1 township

Square Measure

144 sq inches= 1sq ft
9 sq ft = 1 sq yd
43,560 sq ft = 1 acre

Cubic Measure

27 cubic feet = 1 cubic yard

Tax Valuation

X Dollars Per $100 AV = X/100 = Tax Rate

Divide the AV by 100, then multiply by X Dollars

X Mils Per $1 AV

Divide the AV by 1000,
then multiply by X Mils

Area Formulas

Formula for rectangles: Area = length x width
Formula for square: Area = side x side
Formula for triangle: Area = base x height x 0.5

MATHEMATICS Percentages

To use a percentage in an arithmetic calculation, change the percentage to its decimal equivalent. The rule for changing a percentage to a decimal is to remove the percent sign and move the decimal point two places to the left (or divide the percentage by 100). Examples of converting a percentage to a decimal are:

98% = 0.981 1/2% = 1.5% = 0.015
1.42% = 0.01421 1/4% = 1.25% = 0.0125
0.092% = 0.000923/4% = 0.75% = 0.0075

To change a decimal or a fraction to a percentage, simply reverse the procedure. Move the decimal point two places to the right and add the percent sign (or multiply by 100). Some examples of this operation are:

1.00 = 100%1/2 = 1 ÷ 2 = 0.5 = 50%
0.90 = 90%3/8 = 3 ÷ 8 = 0.375 = 37.5%
0.0075 = 0.75%2/3 = 2 ÷ 3 = 0.667 = 66.7%

Commission Problems

Problems involving commissions are readily solved by the Formula: sales price X rate of commission = total commission

Sales

  1. A real estate broker sells a property for $90,000. Her rate of commission is 7%. What is the amount of commission in dollars?

Product Missing = multiply
Solution Step 1 – sales price x rate = commission
Calculation
$90,000 x 0.07 = $6,300
Answer: $6,300 commission

  1. A real estate broker earns a commission of $6,000 in the sale of a residential property. His rate of commission is 6%. What is the selling price?

Factor Missing = Divide
Solution Step 1 – sales price = commission dollars divided by commission rate
Calculation
$6000/.06 = $100,000
Answer: $100,000 sales price

  1. A real estate broker earns a commission of $3,000 in the sale of property for $50,000. What is her rate of commission?

Factor missing = divide
Solution Step 1 – commission dollars divided by sales price = rate of commission
Calculation
$3,000/50,000 = 6%
Answer = 6% commission rate

Rentals

  1. A real estate salesperson is the property manager for the owner of a local shopping center. The center has five units, each renting for $24,000 per year. The center has an annual vacancy factor of 4.5%. The commission for rental of the units is 9% of the gross rental income. What is the commission for the year?

Solution Step 1 — Actual Occupancy Rate = 100% – Vacancy Rate
Calculation – 100% – 4.5 % = 95.5% = Actual Occupancy Rate

Solution Step 2 — Actual Rent Dollars = Potential Gross Rent x Occupancy Rate
Calculation = $120,000 x 95.5% = $114,600

Solution Step 3 – Actual Rent x Commission Rate = Commission Dollars
Calculation — $114,600 x 9% = $10,314 = Commission Dollars
Answer: $10,314 commission

Commission Splits

  1. A real estate broker sells a property for $65,000. The commission on this sale to the real estate firm with whom the broker is associated is 7%. The broker receives 60% of the total commission paid to the real estate firm. What is the firm’s share of the commission in dollars?

Solution Step 1 Selling Price x Commission Rate = Commission Dollars
Calculation – $65,000 x 7% = $4,550

Solution Step 2 — Total Commission x Firm Share Percentage = Firm Share Dollars
Calculation – $4,550 x 40% = $1,820
Answer: $1,820

Estimating Partial Sales of Land

  1. A subdivision contains 400 lots. If a broker has sold 25% of the lots and his sales staff has sold 50% of the remaining lots, how many lots are still unsold?

Solution Step 1 — Original Number of Lots x Percentage Sold by Broker = Number of Lots Remaining
Calculation — 400 x 25% = 100 lots. 400 Lots minus 100 Lots = 300 Lots

Solution Step 2 — Remaining Lots x % Sold by Sales Force = Number of lots Sold by Agents
Calculation — 300 x 50 % = 150 Lots

Solution Step 3 Add the number of lots sold
Calculation — 100 + 150 = 250

Solution Step 4 — Original Number of Lots less the Number of Lots Sold = Number of Lots Remaining
Calculation — 400 — 250 = 150
Answer: 150 lots still unsold

Profit/Loss on Sale of Real Estate

The formula for profit is: investment X percent of profit = dollars in profit

The formula for loss is: investment X percent of loss = dollars lost

  1. Mr. Wong buys a house for investment purposes for $48,000. He sells it six months later for $54,000 with no expenditures for fix-up or repair. What is Mr. Wong’s percentage of profit?

Solution Step 1 — Sales Price less Original investment = Profit Dollars
Calculation = $54,000 – $48,000 = $6,000

Solution Second Step — Profit Dollars divided by Original Investment Dollars = % Profit
Calculation = $6,000/$48,000 = 12.5%
Answer: 12.5% Profit

  1. Ms. Clary purchases some property in 1987 for $35,000. She makes improvements in 1988 costing her $15,500. In 1990 she sells the property for $46,000. What is her percentage of loss?

Solution Step 1 — Purchase Price Plus Improvements = Current Investment
Calculation = $35,000 + $15,500 = $50,500

Solution Step 2 — Investment less Selling Price = Loss
Calculation = $50,500 – $46,000 = $4,500 loss

Solution Step 3 = Loss divided by Investment = Percent Loss
Calculation = $4,500/$50,500 = 8.91%
Answer: 8.91%