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% | = | 0.98 | 1 | 1/2% | = | 1.5% | = | 0.015 |
| 1.42% | = | 0.0142 | 1 | 1/4% | = | 1.25% | = | 0.0125 |
| 0.092% | = | 0.00092 | 3/4% | = | 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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%
