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Math Help

 

Dividing by a Percentage

Dividing by a Whole Number

Calculating Interest

Converting a Decimals to Percentages

Multiplying by Percentages

Calculating Commission

"Stepped" Commission

Commission Split

Interest & Loan Balance

Tax Per Day – “Per Diem”

Calculating Principal

Finding One Month's Interest

Calculating Square Footage

Calculating Square Feet in Acres

Square Footage

Finding Side of Rectangle

Calculating Area in Triangle

 

 

Dividing by a Percentage

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A seller tells you that he/she wants to net a certain selling price AFTER paying the real estate commission.

Example:

Kitty is selling her house. She wants to net $40,000 for her house after Broker Tom is paid 6% commission. Broker Tom needs to know what the sale price would have to be in order for Kitty to net $40,000 after paying his commission.

The first step is to calculate seller Kitty’s percentage of the net sales price.

This is easy if you think of it this way:

Broker Tom gets 6% of the selling price, so seller Kitty gets 94% of the selling price.

100% (of the full selling price) minus the broker's __% leaves _______% for the seller.

In this case:

100% (of $40,000) minus the broker’s 6% leaves 94% for the seller.

40,000 ÷ 94 % = 42,553.19

Remember to DIVIDE. The sales price would have to be HIGHER than the net amount. In order to arrive at a higher number, you would divide the whole number (net sale price) by the percentage (94%.)

Example:

Broker Tom sells the property for  $42,553.19. He is paid a commission of 6%, which means that Kitty gets 94% of the selling price.

42,553.19 x 94 % = 40,000

When a whole number is divided by a percentage, you will get a larger number than you started with.

Example:

100,000 ÷ 10% = 1,000,000

10% is less than one, so when you divide by a number less than one, you get a larger number.

It takes 1,000,000 dimes make $100,000 dollars!

There are ten dimes in a dollar, so DIVIDE 1/10 into 100,000 (100,000 ÷ .10) to get 1,000,000.

 Percentage means "parts per 100".

So, 15% is 15 parts per 100 or 15/100's.

 

Dividing by a Whole Number:

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When you divide a smaller number by a larger number, your answer will be a “percentage”. A “percentage” is a number that is less than one.

Example:

 15 ÷ 30 = .5

If you have to divide 15 apples between 30 people, it is obvious that each person would have to receive less than one apple.

In this case, each of the 30 people would get 1/2 or 50% of an apple.

 

Calculating Interest

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Interest is usually a “percentage”, or a number less than one.

Total Interest ÷ Loan Amount = ___% of interest

Example:

Sam pays $6,000 interest in one year on a $50,000 loan balance. His interest rate is 12%.

6,000 ÷ 50,000 = .12 or 12%.

 

Converting a Decimals to Percentages

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To convert a decimal into a percentage:

 move the decimal point two places to the right and add a %

Or

multiply the decimal by 100 and add a %.

Example

.869 is 86.9%.
(Multiply .869 x 100 = 86.9)

.14 is 14%
(multiply .14 x 100 = 14%)

.01 is 1%
(multiply .01 x 100 = 1%)

But what if there are not two places to the right of the decimal point?

Example

.5

In this case, just add an extra zero as shown below:


.50 x 100 = 50%

.5 is 50.0%

 

Multiplying by Percentages

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Example:

What is nine percent of $133,000?

a. $1,197
b. $11,790
c. $11,970   
d. $1,477
 

The answer is c. $11,970


 Look out! Answer b. $11,790 has the same numbers as the right answer!
 
 
Most calculators have a Percentage Key marked with a "%" sign. If you know how to use this key, it makes doing percentage problems easier.

Multiply $133,000 by 9%:  (use the % key)
133,000 x 9% =
11,970

Or, if you do not use the % key, calculate:

133,000 x .09 = 11,970

Example

Lenny wants to calculate 5% of 60,000 without using the percentage key. He would need to change 5% into a decimal:

.05 x 60,000 = 3,000

If he used the percentage key, he would enter this into the calculator:

5 x 60000 % = 3,000

Lenny would not need to convert the 5% into a decimal because the calculator does it for him when he used the "%" key.

Try these examples:

5.55% of 75,000 = ___

5.55 x 75000 % = 4,162.5

74.3% of 3,333 = ___

74.3 x 3333 % = 2,476.419

Exercise:

Solve each of the above using the calculator's percentage key. Develop a habit of using this key to simplify your calculations and avoid making keystroke mistakes.

The same principles apply when you divide by a percentage. Using the % key on your calculator will make your calculations much easier.

To divide 53,000 by 9% using the percentage key, you would enter:

53000 ÷ 9 % = 588,888.88

If you do not use the % key, enter:

53000 ÷ .09 = 588,888.88

 

Calculating Commission

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The Franklin’s want to get $198,500 for their house after the real estate broker is paid a 5% commission. In order to get this amount, at what price must the house have to sell?

a. $208,947.36
b. $208,425.00
c. $188,575
d. $280,947
 $280,425

The answer is: a. $208,947.36
d. $280,947 is WRONG. Look out for similar numbers in wrong order!

1. Divide 198,500 by 95%
   198,500 ÷ 95% =
208,947.36

Or if you do not use the "%" on your calculator:

198,500 ÷ .95 = 208,947.36

 

 

How much is the commission on a $363,500 sale if the house is listed at a 7 3/4% commission:

a. $27,262.50
b. $27,844.10
c. $28,171.25
d. $26,680.90

The answer is c. $28,171.25
 

1. Multiply 363,500 by 7.75%
   363,500 x 7.75% =
28,171.25

Or if you do not use the "%" Key on your calculator:

363,500 x .775 = 28,171.25

 

"Stepped" Commission

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The commission on a sale is 6% of the first $100,000, 5% of the next $100,000 and 2% on any amount over this. The house sold for $500,000. What was the commission on the sale:

$17,000
b. $16,000
c. $170,000
d. $160,000
e. $15,000

The answer is:  a. $17,000

The house sold for $500,000


1. To calculate the commission on the first $100,000:

100,000 x 6% = 6,000

2. Find the commission on the next $100,000
100,000 x 5% = 5,000

3.   Find the commission on the remaining $300,000
300,000 x 2% = 6,000

4.   Add the "stepped" commission amounts:

$6,000 1st  $100,000
$5,000 2nd $100,000
$6,000 bal. $300,000
$17,000

 

Commission Split

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Listing Agent Janet lists a property at 6% commission.  Selling Agent Chris brings a buyer and property sells $100,500. According to their agreement, the Listing Broker is to receive 2% of the sales price and the Selling Broker is to get got 4% of the sales price. Selling Agent Chris, is licensed with Selling Broker Dana on a 50% split. In this case, how much money did Selling Agent Chris make?

a. $6,030
b. $3,015
c. $2,010
d. $4,020

The answer is: c. $2,010

1.      Find out how much the selling sales associate's broker received.

4% (was received by the selling broker)


2.  Divide the 4% in half (the selling sales associate got half of what her broker received)
4% ÷ 2 = 2%


3.  Multiply 2% by the sale's price of the house

            2% x 100,500 = $2,010

 

Interest & Loan Balance

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The annual interest rate on a loan is 8%. Six months interest is $12,000. How much is the loan balance?

a. $300,000
b. $96,000
c. $960,000
d. $150,000
 

The answer is: a. $300,000

1.  Find out what one month's interest is:
(Divide $12,000 by 6 months to get one month's interest)

12,000 ÷ 6 = 2000

2.  Multiply $2000 times 12 months to get a year's interest (You want to figure interest per year or per annum)
12 x 2000 = 24,000


3.  Divide the interest rate (8%) into the yearly interest ($24,000) to find the loan balance
24,000 ÷ 8% =
300,000

 

On a $50,000 loan, 7 months interest equaled $3,500. What is the interest rate of the loan:

a. 12%
b. 12.5%
c. 11.5%
d. 9.125%
e. 12.75%

The answer is: a. 12%

1.  Find out what one month's interest is:
(Divide $3,500 by 7 months to get one month's interest in dollars)

3500 ÷ 7 = 500


2. Multiply $500 times 12 months to get a year's interest (You want to figure interest per year or per annum)
12 x 500 = 6,000
3.  Divide the loan amount ($50,000) into the yearly interest ($6,000) to find the annual interest rate

6,000 ÷ 50,000 = 0.12

0.12 equals 12%

 

Tax Per Day – “Per Diem”

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The taxes on a property are $855 a year. How much is this a day:(Use a 360 day year like they will on the OREC exam)

a. $2.34
b. $2.38
c. $2.73
d. $2.43

The answer is: b. $2.38

1. Divide $855 by 360 days:
    855 ÷ 360 = 2.375
    Round up to 2.38

Hint: This is a question to see if you can follow instructions and use a 360-day year as shown in question.

Calculating Principal

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David pays his first monthly payment of $600 on a new loan of $88,000, which is amortized at 8% interest. How much of this $600 payment was applied towards the principal balance?

a.   $13.33
b. $586.67
c. $26.66
d. $39.99

 The answer is: a. $13.33

1.  Find out what one year's interest is on an $88,000 loan at 8% interest:

$88,000 x 8% = $7,040 a year

2.  Divide $7,040 by 12 months to get one month's interest:
7040 ÷ 12 = $586.6666

Round up to $586.67

3.  Subtract the interest due from the total monthly payment to get the amount that went towards principal:

$600 - $586.67 = $13.33

Hint: You probably didn’t need a calculator to do this because you were asked to find the first month's principal.

Finding One Month's Interest

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Tony’s loan balance is $188,000. If the interest rate on his loan is 12.5%, how much is one month's interest?

a. $1,253.33
b. $1,504.00
c. $1,958.33
d. $2,350.00
e. $1,598.33

The answer is: c. $1,958.33
 e. $1,598.33 is WRONG. Look out for transposed numbers

1.  Find out what one year's interest is:

Multiply $188,000 by 12.5%

188,000 x 12.5% = $23,500

2. Next: divide $23,500 (a year's interest) by 12 to find one month's interest.

$23,500 ÷ 12 = $1,958.33

 

Calculating Square Footage

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A lot measures 250 feet x 350 feet. How many square feet are in the lot?

a. 87,500
b. 875,000
c. 8,750
d. 85,700
 
The answer is:

a. 87,500    A lot measures 250 feet by 350 feet. How many square feet are in the lot:

d. 85,700 is WRONG!! Look out for answers with the same numbers as the right answer

1. Multiply 250 by 350
    250 x 350 = 87,500

To get the area of a rectangle multiply the short side by the long side. If all sides are the same length (for example, a square), then multiply any side by any other side.

Calculating Square Feet in Acres

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There are 43,560 square feet in an acre. If a lot has 4,465,000 square feet, how many acres is it?

975.58
b. 97.56
c. 1,025.02
d. 102.502

The answer is: d. 102.502       c. is 1,025.02 WRONG. Look out for the decimal place!
1.
Divide 4,465,000 by 43,560
    4,465,000 ÷ 43,560 = 102.502

An acre can be any shape, but it consists of 43,560 square feet. SO, an area 2 feet wide and 21,780 feet long is an acre. (2 x 21,780 = 43,560).

Or, a lot that is 200 feet by 217.8 feet (200 x 217.8 = 43,560) is also an acre.

Square Footage

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How many square feet are there in a rectangular lot that measures 1000' by 2300'?

a. 23,000,000
b. 2,300,000
c. 230,000
d. 5,280,000
 

The answer is: b. 2,300,000

a. is 23,000,000 WRONG!! Look out for decimal point placement!
 
 1. Multiply 1000 by 2300
    1000 x 2300 = 2,300,000

To get the area of a rectangle multiply the short side by the long side. If all sides are the same length (for example, a square) then multiply any side by any other side.

Finding Side of Rectangle

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If a lot is a rectangle and it has 30 acres in it and the short side is 726 feet long, how long is the long side: (Remember an acre is 43,560 square feet)

a. 413
b. 2178
 c. 180.37
d. 1800

The answer is: d. 1800

1. Calculate square feet in 30 acres.

30 acres multiplied by 43,560 (the square feet in an acre). 30 x 43,560 = 1,306,800
 

2. Divide 1,306,800 by 726 (the known side of the rectangle)

3. Multiply one side times the other side. This will equal the square footage of the rectangle.

1,306,800 ÷ 726 = 1,800

To find the area of a rectangle multiply the short side by the long side. If all sides are the same length (for example, a square) then multiply any side by any other side.

Calculating Area in Triangle

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A lot forms a right triangle. The north/south side is 400 feet long and the east/west side is 600 feet long. You don't know how long the diagonal side is. How many square feet are in the lot?

a. 75,000
b. 240,000
c. 120,000
d. 150,000

The answer is: c. 120,000

1. Calculate the square feet in 400 x 600 foot lot:
Multiply 400 by 600
400 x 600 = 240,000
2. Divide 240,000 by 2 (a right triangle is one half of the area of the rectangle)
240,000 ÷ 2 = 120,000

A right triangle is really just one half the area of a rectangle.

To calculate the area of this right triangle

Find the area of the rectangle and divide it in half.
    400 x 600 = 240,000 ÷ 2 = 120,000.

 

A+ Institute, by Dixie Randock, Copyright 1997 - 2007. All rights reserved. Registered students of A+ Institute, who have paid full tuition/fees may copy portions of this material for their own non-commercial study use. Any other use or reproduction is forbidden.

 

 

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Revised: 07/12/07.