‹#›
![](3D"master04_background.gif")
![](3D"master04_image005.gif")
July 08
Simplification of Real Estate Mathmatics
‹#›
![3D"Simplification](3D"slide0001_image006.gif")
July 08
Simplification of Real Estate Mathmatics
1
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
2
Mathematical Impact on Test
•=
Most
state tests have from five to fifteen mathematical
problems on any given test.
•=
The
Brokers’ test will tend to have a greater number
of mathematical problems.
•=
Regardless,
if you can gain three or four points by correctly answering mat=
h =
problems
it will be beneficial.
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
3
Your Mathematical Expertise
•=
You
may be very proficient at math, and that should be helpful to you fro=
m a
testing standpoint, and in actual practic=
e in
the business.
•=
Still,
real estate is not based on mathematics, but rather on sales,=
=
negotiation
and recognition of opportunities.
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
4
•=
If
you are limited in mathematics, this is not the
time to become a mathematician. I=
f you have
time try and learn the skill to answer a few
basic problems.
•=
Don’t
delay your test because you lack what you
might consider a competent mathematical ability.
=
•=
You
could, in fact, miss every math question and st=
ill
easily pass the sale or brokers test.
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
5
Calculators
=
A.No
“musical” calculators unless you can stop the music.
<=
span
style=3D'mso-special-format:"numbullet1\,1";position:absolute;left:-8.57%'=
>B.No
printing calculators.
<=
span
style=3D'mso-special-format:"numbullet1\,1";position:absolute;left:-7.84%'=
>C.Programmable
calculators are allowed.
<=
span
style=3D'mso-special-format:"numbullet1\,1";position:absolute;left:-8.57%'=
>D.No
alphanumeric calculators.
=
E.We
recommend that you use a simple, hand-held
calculator with large numbers.
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
6
The “Magic Circ=
le”
![](3D"slide0006_image007.gif")
![](3D"slide0006_image008.gif")
=
![](3D"slide0006_image009.gif")
Divide Line
![](3D"slide0006_image010.gif")
![](3D"slide0006_image011.gif")
Multiplication Line=
July 08
Simplification of Real Estate Mathmatics
‹#›
![](3D"slide0007_image012.gif")
July 08
Simplification of Real Estate Mathmatics
7
The Segments are Labeled
A
B
C
¸
X
¸
July 08
Simplification of Real Estate Mathmatics
‹#›
![](3D"slide0008_image015.gif")
July 08
Simplification of Real Estate Mathmatics
8
The Working Segments
![](3D"slide0008_image017.gif")
¸
X
A
C
Any number in this segment will be divid=
ed
by numbers in “B” or =
by
numbers in “C”. Giving the answer for the other.
Any number in B can be divide=
d into
A and give you C or Multiplied by
C and give you A
C and give you A
B
Any
number in C can
be divided into A = and
give you B or Multiplied
by B and give you = A
be divided into A = and
give you B or Multiplied
by B and give you = A
¸
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
9
Circle Diagram Rules
1. Percentage always goes in C.&=
#13;
2. Little number in “A”, Big nu=
mber
in “B”,
Where “C” is less than 100%. =
Where “C” is less than 100%. =
3. Little number in “B”, Big nu=
mber
in “A”,
Where “C” is greater than 100%.&#= 13;
Where “C” is greater than 100%.&#= 13;
<=
span
style=3D'mso-special-format:"numbullet3\,4";position:absolute;left:-7.95%'=
>4.“A” always gets divided =
by the
others.
<=
span
style=3D'mso-special-format:"numbullet3\,4";position:absolute;left:-8.57%'=
>5.Always
annualize figures.
<=
span
style=3D'visibility:hidden'>•
July 08
Simplification of Real Estate Mathmatics
‹#›
![](3D"slide0010_image018.gif")
July 08
Simplification of Real Estate Mathmatics
10
The Rules Visualized
A
¸
X
![](3D"slide0010_image020.gif")
C
B
¸
LESS than 100%
BIG number
Little Number
%
July 08
Simplification of Real Estate Mathmatics
‹#›
![](3D"slide0011_image021.gif")
July 08
Simplification of Real Estate Mathmatics
11
The Rules Visualized
A
¸
X
![](3D"slide0011_image023.gif")
C
B
¸
BIG number
MORE than 100%
Little Number
%
July 08
Simplification of Real Estate Mathmatics
‹#›
![](3D"slide0062_image024.gif")
July 08
Simplification of Real Estate Mathmatics
12
Capitalization Appraisal Problems<=
/div>
![](3D"slide0062_im=)
![](3D"slide0062_image026.gif")
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A
¸
X
C
B
¸
Little Number
Net Annual Income<= /span>
Net Annual Income<= /span>
LESS than 100%
CAP Rate
CAP Rate
BIG Number
Property Value
Property Value
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
13
Let’s Try a Typical Problem
=
1.The net income of an
apartment building went down $400 per mont=
h when
a freeway was built nearby. If investors demand a 12% capitalization rate=
in
this area, how much has the building lost in
value?
A. $3,333
B. $20,000
C. $36,000
D. $40,000
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
14
Rule 5 – Always Annualize Figures<=
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Slide 1
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Slide 1
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=
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Slide 1
•=
Rule
5 tells us to always annualize figures.
The problem gives us a rent loss =
of
$400 per month. The capitalization rate is 12%, as stated
it is already annualized.
•=
You
will have to annualize the monthly loss of
$400.
•$400 X =
12
Months =3D $4,800 a Year<=
/div>
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
15
Put Your Information In The Circle=
A
¸
X
C
B
¸
$4,800 Annual Loss
12%
Value Loss
%
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
16
The Reasoning
•We know that the percentage, the 12% capitalization
rate is less than 100% so the smaller
number will go in “A” – we can presume that $4=
,800
is the smaller number since it is the lost income, the
building value loss will be the greater
number.
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
17
The Calculation
A
¸
X
C
B
¸
$4,800 Annual Loss
12%
$40,000
%
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
18
The Circle Points Out
•<=
span
style=3D'font-family:"Times New Roman";mso-ascii-font-family:"Times New Ro=
man"'>The
circle tells us that we will divide the “C” segment, the 12%
capitalization rate into “A” the rent loss of $4,800,=
and
that will come to $40,000.
=
–$4,800 ¸ =
12% =3D $40,000
–The $40,000 answer is at D, so the
answer is D.
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
19
Mark The Correct Answer
=
1.The net income of an
apartment building went down $400 per mont=
h when
a freeway was built nearby. If investors demand a 12% capitalization rate=
in
this area, how much has the building lost in
value?
A. $3,333
B. $20,000
C. $36,000
• D. $40,000
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
20
Let’s Try Another
Capitalization Prob= lem
Capitalization Prob= lem
•Frederick, a typical real estate investor,
wants to purchase a 40 unit
apartment building that has an annual net income of
$174,000. If Frederick uses an =
8% capitalization rate how much will he be willing <=
/span>to pay?
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
21
Everything is Annualized
All
of the numbers in this problem are annualized, we don’t have to worry
about that.
=
The
percentage is less than 100%, so the smaller number will go in the “A”
segment of the circle.
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
22
Our Circle Looks Like This
A
¸
X
C
B
¸
$174,000 Net Operating Income
8%
Frederick’s Estimate of Value
%
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
23
The Circle Tells Us
=
1.We
need to find the answer for circle segment “B”.
<=
span
style=3D'mso-special-format:"numbullet3\,1";position:absolute;left:-8.57%'=
>2.We
will divide “C” into “A”.
3.We
will divide the 8% capitalization rate into
the $174,000 net operating income.
<=
span
style=3D'mso-special-format:"numbullet3\,1";position:absolute;left:-8.57%'=
>4.Our
answer will be $2,175,000.
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
24
The Finished Circle Looks Like This
A
¸
X
C
B
¸
$174,000
8%
$2,175,000
%
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
25
The Answer Is
•You were given several answers as
follows;
•
• A. $1,400,000
• B. $1,650,000
• C. $1,985,000
<=
span
style=3D'font-family:"Times New Roman";mso-ascii-font-family:"Times New Ro=
man"'> D. $2,175,000
•
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
26
This is Another Type
of Capitalization Question
of Capitalization Question
A small income property generates a monthly gross income of=
=
$1,000. Over the l=
ast
five years it has been vacant for three months. The annual
expenses are $3,000. If an apprai=
ser applies a 12% capitalization rate to this property, what wi=
ll the value of the building be?
A. $58,000
B. $65,000
C. $70.000
D. $90,000
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
27
Break The Problem Down
•The problem has been given to you with monthly
rent. That will have to be annualized. The second problem is that they have
given you a vacancy factor for a 5 year period. The third dilemma is the problem has <=
/span>assigned
an annual expense factor of $3,000. Finally,
the capitalization rate has been given to
you as an annual rate.
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
28
Make It Understandable
1.Annualize the rent.
$1,000 a month times 12 months would be $12,000 a year.
2.Figure the 5 year rent.
$12,000 a year times 5 years equals $60,000.
=
;
=
3.Subtract the five year vacancy factor. $60,000 less =
$3,000 equals $57,000.
4.Annualize the five year gross rents. $57,000 divided by 5 years equals $11,400 a year.
5.Subtract the annual $3,000 expense from the average =
annual rent. $11,4=
00
less $3,000 equals $8,400.
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
29
Place Your Adjusted
Information In the Magic Circle
Information In the Magic Circle
A
¸
X
C
B
¸
$8,400
12%
Estimated Value
%
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
30
The 1=
2%
Capitalization Rate has to go in segment “C”, the small number, the Net Operating Income will h=
ave
to go into “A”, you will divide “C” into “A” to find the
answer for “B”, the
estimated value of the building.
A
¸
X
C
B
¸
$8,400
12%
$70,000
%
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
31
You Apply Your Answer
=
A small income property generates a monthly gross income of $1,000. =
Over
the last five years it has been vacant for thr=
ee
months. The annual expenses are $3,000. If an
appraiser applies a 12% capitalization rate=
to
this property, what will the value of the buildi=
ng
be?
A. $58,000
B. $65,000
• C. $70.000
D. $90,000
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
32
Investment Problems
A
¸
X
C
B
¸
LITTLE Number
INCOME/PROFIT/YIEL= D
(Do not include return of original investment)
INCOME/PROFIT/YIEL= D
(Do not include return of original investment)
(Less than 100%=
)
RATE of RETURN
RATE of RETURN
BIG Number
Amount Invested
Amount Invested
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
33
Finding Invested Amount
How
much would an investor need to invest in order
to earn $75 per month from an investment which
produces a 5% Return?
A. $4,000
B. $9,000
C. $12,000
D. $18,000
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
34
Break The Problem Down
1.They
have given you a monthly return. =
Remember
everything has to annualized. So,
$75 X 12 Months =3D $900.00
2.The
5% Capitalization Rate is already annualized. We leave that at 5%.
<=
span
style=3D'mso-special-format:"numbullet3\,1";position:absolute;left:-8.17%'=
>3.We
need to find the amount invested.
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
35
A
¸
X
C
B
¸
$900
5%
Amount Invested
%
Apply The ‘Magic Circle” Rules
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
36
A
¸
X
C
B
¸
$900
5%
$18,000
%
Apply The ‘Magic Circle” Rules
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
37
Equity Profit Upon Sale
Joyce purchased a home for $125,000. She obtained a loan from the bank for 88% of
the purchase price, payable at $=
1,549
per month, including 12% interest.
Joyce sold the home for $139,750
before she even made the payment on the first loan. What w=
as her
equity at the time of the sale?
A. $12,000
B. $14,750
C. $29,750
D. $18,000
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
38
First Find The Loan
1.Initial Loan Amount equals
$125,000 X 88% =3D $110,000
original loan amount is $110,000.
$125,000 X 88% =3D $110,000
original loan amount is $110,000.
=
2.She has made no payments on the loan, so her =
=
loan balance has to be the same, $110,000.
3.Find the After Sale Equity. Sales Price less the =
loan amount equals the after sale equity.
•$139,750 - $110,000 =3D $29,750
•$29,750 will be Joyce’s Equity
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
39
Find The Loan Amount
Using The Circle
Using The Circle
A
¸
X
C
B
¸
Find The Loan Amount
88%
$125,000
Purchase Price
Purchase Price
%
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
40
A
¸
X
C
B
¸
$110,000
88%
$125,000
%
Fill in The Loan Amount
Purchase Price X Percent loan to value =3D Amount
of Loan
$125,000 X 88% =3D $110,00=
0
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
41
Finish The Problem
<=
span
style=3D'mso-special-format:"numbullet3\,1";position:absolute;left:-7.77%'=
>1.$125,000 X 88% =3D $110,000
<=
/div>
Slide 1
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Slide 1
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Slide 1
<=
span
style=3D'mso-special-format:"numbullet3\,1";position:absolute;left:-8.04%'=
>2.$139,500 - $110,000=
=3D $29,750
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<=
span
style=3D'visibility:hidden'>3.
<=
/div>
The equity at sale is $29,75=
0
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
42
Select The Proper Answer
Joyce purchased a home for $125,000. She obtained a loan from the bank for 88% of
the purchase price, payable at $=
1,549
per month, including 12% interest.
Joyce sold the home for $139,750
before she even made the payment on the first loan. What w=
as her
equity at the time of the sale?
A. $12,000
B. $14,750
• C. $29,750
D. $18,000
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
43
Returns on Discounted Notes
=
An investor purchased a $5,000 straight note for $4,500. (A straight note=
is
interest only) The note is =
=
due in one year. T=
he
note bears an interest rate of 6%. What rate of return, as a percentage, =
will
the investor receive at=
the
end of one year?
A. 6%
B. 12%
C. 17.8%
D. 20%
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
44
The Sequential Logic
1.Find the interest that will be earned in one year. $5,000 X 6% =
=3D $300
2.Find the money earned from the discount at the =
end of the year.
Face - Purchase Price= =3D Profit
Face - Purchase Price= =3D Profit
3.You have two profit sources.
The interest earned and the disc=
ount
gained when the loan is repaid. This means that the return will be the=
<=
span
style=3D'font-family:"Times New Roman";mso-ascii-font-family:"Times New Ro=
man";
font-size:88%'>interest earned plus the discount, or;
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
45
A
¸
X
=
C
B
¸
Return =3D Interest Plus Discount
Find % Return
Total Investment
%
Fill The Information as Follows
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
46
A
¸
X
=
C
B
¸
$300 + $500 =3D $800
??%
$4,500
%
Find the Percent Return
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
47
A
¸
X
=
C
B
¸
$800
17.78%
$4,500
%
Fill in The Loan Amount
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
48
Pick Your Answer
An investor purchased a $5,000 straight note for =
$4,500. (A straight note=
is
interest only) The note is =
due in one year. T=
he
note bears an interest rate of 6%. What rate of return, as a percentage, =
will
the investor receive at=
the
end of one year?
A. 6%
B. 12%
• C. 17.8%
D. 20%
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
49
Finance Problems
A
¸
X
C
B
¸
LITTLE Number
INTEREST
(Lender’s Profi= t)
INTEREST
(Lender’s Profi= t)
(Less Than
100%)
INTEREST RATE =
INTEREST RATE =
BIG Number
LOAN BALANCE
LOAN BALANCE
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
50
=
Mary
borrowed $256,500 using a straight note, for 20 ye=
ars
at an interest rate of 15% per annum. How =
much
interest will Mary pay during the term of the note?
=
A. $26,500
B. $79,500
C. $95,000
D. None of the above.
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
51
The Logic of This Problem
=
1.The note is a strai=
ght
note, so only interest is paid, no principal.
This means we can figure it easily with a simple
calculator.
<=
span
style=3D'font-size:88%'>2.The interest for one
year on this note will be the face value of the n=
ote,
multiplied by 15% or; $26,500 X 15% =3D $3,975.
Mary is paying $3,975 each year.&#=
13;
=
3.Mary has the loan f=
or
20 years, so she will have 20 Years X $3,975 =
=3D
$79,500,
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
52
Select The Answer That Matches
=
Mary
borrowed $26,500 using a straight note, for
20 years at an interest rate of 15% per annum.
How much interest will Mary pay during the term of the note?
=
A. $26,500
• B.<=
span
style=3D'mso-tab-count:2;width:7.12%'> $79,500
C. $95,000
D. None of the above.
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
53
Mary’s Problem has
Circle
Solutions – First F= ind The Interest
Solutions – First F= ind The Interest
A
¸
X
C
B
¸
Annual Interest
=
Interest Rate
Loan Amount
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
54
Mary’s Problem has
Circle
Solutions – First F= ind The Interest
Solutions – First F= ind The Interest
A
¸
X
C
B
¸
$3,975
15%
$26,500
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
55
Second Step of Prob=
lem
– Find The Total Interest Paid=
For
The Term
A
¸
X
C
B
¸
Total Interest Paid
=
Period of Time
Annual Interest
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
56
Second Step of Prob=
lem
– Find The Total Interest Paid=
For
The Term
A
¸
X
C
B
¸
$79,500 Total Interest Paid
=
20 Year
$3,975 Per Year
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
57
Select The Answer That Matches
=
Mary
borrowed $26,500 using a straight note, for
20 years at an interest rate of 15% per annum.
How much interest will Mary pay during the term of the note?
=
A. $26,500
• B.<=
span
style=3D'mso-tab-count:2;width:7.12%'> $79,500
C. $95,000
D. None of the above.
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
58
Second Finance Problem
•William is the beneficiary on a 10 year note. The annual inte=
rest
rate is 8.4%. If in five <=
/span>years
William has received $5,460 in interest, what
is the principle amount of the loan?
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
59
Approaching The Problem
1.We know that the interest for 5 years is $5,460.
2.Rule #5 of the Circle Rules tells us to annualize =
all figures. To
annualize this 5 year interest of $5,460 we will have=
to
divide that by 5 years.
3.$5,460 ¸ 5 Years =3D $1,092 a year.
4.The annual interest rate is 8.4%. We can conclude that 8.4% X some number =3D $1,092.
5. Little number in “A”, Big number in “B”,
Where “C” is less t= han 100%.
Where “C” is less t= han 100%.
<=
/div>
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
60
Place Numbers in Circle
A
¸
X
C
B
¸
$1,092 Annual Interest Earned
=
8.4%
Principle <=
/span>Amount of Note
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
61
Divide “C” Into “A” to Get “B”
A
¸
X
C
B
¸
$1,092 Annual Interest Earned
=
8.4%
$13,000
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
62
Apply The Answer
•William is the beneficiary on a 10
year note. The
annual interest rate is 8.4%. If =
in
five years William has received $5,460=
in
interest, what is the principle amount of t=
he
loan?
C. $13,000
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
63
Finance Problem #3
•John borrowed $20,000 from a bank to purc=
hase
a small piece of real estate. He paid 4 points to get the loan. The loan contained a 2% prepayment penalty, based upon the original =
loan amount. His m=
onthly
payment is $163.00 including interest at 8% per
year. Five years later John sold =
the
real estate and paid off=
the
loan. If the loan had an average =
balance of $18,500, during the five years John owned the property, what was the bank’s gross profit on this loan?=
3;
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
64
Analyzing The Question
•What the question is really asking you is=
how
much money has the lender
made. This is a flip from most <=
span
style=3D'font-family:"Times New Roman";mso-ascii-font-family:"Times New Ro=
man";
font-size:88%'>questions that ask how much has the borrower paid. Break the question
down.
•1. Total
Points Paid. =3D
$20,000 X 4% =3D $800&= #13;
$20,000 X 4% =3D $800&= #13;
•2. Total
Pre-payment penalty 2% =3D
$20,000 X 2% =3D $400
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$20,000 X 2% =3D $400
•3. They
give you an average balance so that you
can estimate the interest paid. <= /div>
can estimate the interest paid. <= /div>
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
65
You Would Then
Add The Three Areas= of Profit
Add The Three Areas= of Profit
Points =3D $ 800
=
Prepayment
Penalty =3D $ 400
Total
Interest =3D $7,400
=
Total
Earned $8,600
The
total that earnings by the bank on this loan,
with the information given is $8,600
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
66
Total Bank Earnings Problem #3
•John borrowed $20,000 from a bank to purc=
hase
a small piece of real estate. He paid 4 points to get the loan. The loan contained a 2% prepayment penalty, based upon the original =
loan amount. His m=
onthly
payment is $163.00 including interest at 8% per
year. Five years later John sold =
the
real estate and paid off=
the
loan. If the loan had an average =
balance of $18,500, during the five years John owned the property, what was the bank’s gross profit on this loan?=
3;
C. $8,600
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
67
The Magic Circle
•If
we use the “Magic Circle” on this problem it would have to be
implemented on all three of the questions. The Points would
involve one circle, the Pre-Payment Penalty would involve another cir=
cle,
and the interest would involve still a
third circle. You
would then add the three answers up and find the total 5 year earning=
s.
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
68
Find the Earnings From Points
A
¸
X
C
B
¸
$800 Earnings From Points
=
4%
$20,000
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
69
Calculating
The Pre-Payment Pen= alty
The Pre-Payment Pen= alty
A
¸
X
C
B
¸
$400 Pre-Payment Penalty
=
2%
$20,000
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
70
Estimate the Total Interest Paid
A
¸
X
C
B
¸
$1,480 Annual Interest
=
8%
$18,500
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
71
Add All The Income Sources
=
Finally, the annual interest has to be estimated for
the 5 year period.
the 5 year period.
• $1,480 =
X 5 Years =3D $7,400
=
=
Now
you will add the three sources of income or earnings;
1.Points =3D $ 800
2.Pre-Payment <=
/span>=3D $ 400
3.Earned Interest =3D =
$7,400
Total Earnings =3D $8,600
Total Earnings =3D $8,600
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
72
Commission Problems
A
¸
X
C
B
¸
Little Number
Commission
(Figure the total commission received by broker)
Commission
(Figure the total commission received by broker)
(Less Than 100%)
Commission Rate
Big Number<=
span
style=3D'font-family:"Times New Roman";mso-ascii-font-family:"Times New Ro=
man";
font-size:178%'>
Selling Price
Selling Price
July 08
Simplification of Real Estate Mathmatics
‹#›
July 08
Simplification of Real Estate Mathmatics
73
Commission Question #1
•Broker Bob and Broker Bill agreed to divi=
de a
4 ½% Commission equally =
on
the sale of a home, which sold for $=
162,500. Mary, the listing salesperson, works f=
or
Broker Bob on a 50-50
commission split. Mary would rece=
ive approximately how much commission as a result of the sale?
July 08
Simplification of Real Estate Mathmatics
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74
Logic of This Problem
=
1.First Broker Bob and
Broker Bill split a 41/2% commission. That i=
s a
50-50 split between the brokers.
=
2.After the split bet=
ween
the brokers Broker Bob and Mary further sp=
lit
the commission that Broker Bob got, 50-=
50,
or ½ each.
3.There are a number =
of
ways to figure a correct answer for this
problem.
July 08
Simplification of Real Estate Mathmatics
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75
Our Solution Today
•=
Today
we’ll first figure the total commission earned upon the close =
of escrow. That will be 4½% of $162,500.
• $162,500 =
X 4 ½% =3D $7,312.50
Each broker is to get ½ of t=
his
commission, or 50% each.
• $7,312.50=
X 50% =3D $3,656.25
July 08
Simplification of Real Estate Mathmatics
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Each Broker Now Has Their Half
•=
At
this point both brokers are getting $3,656.25.
•=
Mary
and Broker Bob are sharing this $3,656.25 ½ Each, or 50% each.=
3;
•Mary will get 50% of $3,656.25=
3;
• $3,656.25 X 50% =3D $1,828.125
• Mary’s share is $1,828.125
July 08
Simplification of Real Estate Mathmatics
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The Closes Answer Would Be
=
Broker Bob and Broker Bill agreed to divide a 4 ½% <=
/span>Commission equally on the sale of a home, which sold =
for $162,500. Mary=
, the
listing salesperson, works for Broker Bob on a 50-=
50
commission split. Mary would receive approximately how much commission as a =
result of the sale?
•=
A. $1,828
<=
span
style=3D'font-size:81%'>• B. $2,828
<=
span
style=3D'font-size:81%'>• C. $3,656
<=
span
style=3D'font-size:81%'>• D. $7,312
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Simplification of Real Estate Mathmatics
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Applying the Problem to the Circle=
A
¸
X
C
B
¸
$7,312.50
4 ½%
$162,500
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Simplification of Real Estate Mathmatics
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Second Part Is
Figure What Each Br= oker Gets
Figure What Each Br= oker Gets
A
¸
X
C
B
¸
$3,656.25 to Each Broker
=
50%
$7,312.50
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Simplification of Real Estate Mathmatics
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Third Part Is
What Do Mary & Broker Bill Get?
What Do Mary & Broker Bill Get?
A
¸
X
C
B
¸
$1,828.124 For Mary & Broker Bill
=
50%
$3,656.25
July 08
Simplification of Real Estate Mathmatics
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81
The Closes Answer Would Be
Broker Bob and Broker Bill agreed to divide a 4 ½% <=
/span>=
Commission equally on the sale of a home, which sold =
for $162,500. Mary=
, the
listing salesperson, works for Broker Bob on a 50-=
50
commission split. Mary would =
receive approximately how much commission as a result of the sale?
•=
A. $1,828
• B. $2,828
• C. $3,656
• D. $7,312
July 08
Simplification of Real Estate Mathmatics
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82
Commission Problem #2
=
2.Sam, a salesperson
working bro Broker Martha, received a 45% shar=
e of
a 6% commission. =
Sam’s share came to $8,100.
What was the selling price of the
property?
A. $100,000
B. $150,000
C. $250,000
D. $300,000
July 08
Simplification of Real Estate Mathmatics
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The First Part
is to Find the Total Commission
is to Find the Total Commission
A
¸
X
C
B
¸
$8,100
45%
Total Commission
=
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Simplification of Real Estate Mathmatics
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Simplification of Real Estate Mathmatics
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=
First =
Part
is to Find the Total Commission
is to Find the Total Commission
A
¸
X
C
B
¸
$8,100
45%
$18,000
July 08
Simplification of Real Estate Mathmatics
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=
2nd
Part Divide the Total Commission =
Commis=
sion
By 6% to Find the Sales Price.
A
¸
X
C
B
¸
$18,000
6%
Selling Price
July 08
Simplification of Real Estate Mathmatics
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86
=
2nd
Part Divide the Total Commission =
Commis=
sion
By 6% to Find the Sales Price.
A
¸
X
C
B
¸
$18,000
6%
$300,000
July 08
Simplification of Real Estate Mathmatics
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Selling Price Problems
A
¸
X
C
B
¸
(Little
Number)
Net Amount<= /span>
Net Amount<= /span>
(Less
than 100%)
100% Minus the Commission, cost of
sale, or discount<= /span>
100% Minus the Commission, cost of
sale, or discount<= /span>
(Big Number)
Selling Price
Selling Price
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Simplification of Real Estate Mathmatics
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88
Selling Price Problem One
=
Mark sold his home and carried back a $37,400 second trust deed. He
immediately sold the loan at a discount to an inve=
stor
and received a$24,310. What was the rate of discount?
A. 25%
B. 30%
C. 35%
D. None of the above
July 08
Simplification of Real Estate Mathmatics
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