Real Estate
Principles and Practices
Chapter 21
Real Estate Math
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Overview
Square footage
House or parcel of land
Percentages
Prorations
Commission
Taxation
Subdivided property
Capitalization
Amortization
Loan payments
Discount
Interest
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Measurement Problems
Linear measure
12 in = 1 ft
36 in = 3 ft or 1 yd
Square measure
144 sq in = 1 sq ft
9 sq feet = 1 sq yd
Cubic measure – calculating volume
1 cubic ft = 1,728 cubic in
27 cubic ft = 1 cubic yd
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Measurement Problems
Surveyor’s Measure
link = 7.92 inches
chain = 66 ft or 4 rods
rod = 16 ½ feet or 1 perch
mile = 5,280 feet or 8 furlongs
acre = 43,560 sq ft, 4,840 sq yds, or 160 sq rods
Section = 640 acres or 1 sq mile
Township = 36 sections
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Square Footage and Yardage
Area = length X width
Example: room measures
18’ long and 12’ wide
A = 18’ (L) X 12’ (W)
A = 216 sq ft
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Square Footage and Yardage
Example: compute the
square footage of the
house
40”
10’
28’
20’
30’
2’
A = 40’ X 28’ = 1,120 sq ft
B = 2’ X 10’ = 20 sq ft
10”
A
C
C = 20’ X 10’ = 200 sq ft
B
Total area = 1,340
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Square Footage and Yardage
Example: To find square yards, divide by 9
216 sq ft ÷ 9 = 24 sq yards
Example: Find the square yards of carpet
needed to cover a 15’ X 18’ room
15’ X 18’ = 270 sq ft
270 sq ft ÷ 9 = 30 sq yds
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Square Footage and Yardage
Area of a triangle
Area = half the base X altitude
A
Example: base of 200’ and altitude
of 150’ Find the area
A =
200
X 150
2
A = 100 X 150
A = 15,000 sq ft
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B
C
D
Square Footage and Yardage
To compute the sq ft, add the 2 widths
40’
40’ + 50’ = 90’
divide by 2
80’
90’ ÷ 2 = 45’
multiply by the length
45’ X 80’ = 3,600 sq ft
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90°
50’
Cubic Footage and Yardage
L X W X H = cubic feet
Height
Example: 20’ X 12’ X 8’ room
20’ X 12’ X 8’ = 1,920 cubic ft
Example: Driveway measures
60’ by 8’ by 3’ deep
60’ X 8’ X ¼’ = 120 cubic ft
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Length
Cubic Footage and Yardage
Height
Example: Driveway is 54’
long by 15’ wide and 4” deep.
At $30 per cubic yd, what is
the cost?
54’ X 15’ X 1/3’ = 270 cubic ft
Length
270 cubic ft ÷ 27 = 10 cubic yds
10 X $30 = $300
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Ratio and Proportion
Comparison of 2 related numbers
Ratios must always be equal or in
proportion
Example: What is the scale of a
house plan if a room is 16’ X 28’ and
is shown on the scale of 4” X 7”?
4
=
16
1
4
7
=
28
Scale is ¼” = 1’
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1
4
Ratio and Proportion
Example: What is the measurement
of a property 6” in length by 8” wide
if the scale is 1/8 inch = 1 foot?
If 1/8” to 1’ then 1” = 8’
6 X 8’ = 48’
8 X 8’ = 64’
The measurement is 48’ X 64’
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Ratio and Proportion
Example: In 9 months, a salesperson
sells to 1 of every 5 purchasers.
How many sales would she make in
3 months if she showed property to
150 people?
5
150
=
1
X
150
1
150
X
=
X
5
5X
150
= X
5
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X = 30 Sales
Ratio and Proportion
Example: How many acres are there
in Plot A if B contains 25 acres?
900’
900
=
X
900
25 =
X
X
1,350
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1,350’
1,350
25
22,500
= 16 2/3
1,350
acres
Ratio and Proportion
Example: The ratio of a salesperson’s
commission to the broker’s is 4:6.
What does the salesperson earn from
a $3,000 commission?
4 + 6 = 10 parts
100% ÷ 10 = 10%
4 X 10% = 40% and 6 X 10% = 60%
40% of $3,000 = $1,200
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Capitalization and Other
Finance Problems
I = income
R = rate (interest)
V = value
Example: $140 is 3.5%
of what amount?
$140 (I)
= V
.035 (R)
$140 ÷ .035 = $4,000
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Capitalization and Other
Finance Problems
Example: Quarterly
payments are $150 on
a $12,000 loan. What is
the interest rate?
$150 X 4 = $600
$600 (I)
= R
$12,000 (R)
$600 ÷ $12,000 = 5%
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Capitalization and Other
Finance Problems
Example: What is a
property’s value with a
net income of $5,480 and
annual return of 8%?
$5,480 (I)
= V
.08 (R)
$5480 ÷ .08 = $68,500
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Capitalization and Other
Finance Problems
Example: Buyer has a 75%
loan on a home valued at
$28,000. What is the interest
rate if the payments are $140
per month?
75% X $28,000 = $21,000
$140 X 12 = $1,680
$1,680 (I)
= R
$21,000 (V)
$1,680 ÷ $21,000 = 8%
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Capitalization and Other
Finance Problems
Example: If an investment’s
value is $350,000 and
returns 12% annually, what
is the income produced?
$350,000 X 12% = $42,000
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Capitalization and Other
Finance Problems
Example: The cap rate on a
building that produces
$20,000 annually is 10%.
What is the value?
$20,000 (I)
= V
.10 (R)
$20,000 ÷ .10 = $200,000
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Capitalization and Other
Finance Problems
Example: What is the value
of the same building with a
cap rate of 5%?
$20,000 (I)
= V
.15 (R)
$20,000 ÷ .05 = $400,000
The higher the rate, the lower the value
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Loan Payments
Amortized loan: equal payments
consisting of principal and interest
Example: Ms. Morley buys a home with
a $45,000 mortgage at 9 ¾% interest.
Monthly payments are $387.70. How
much is applied against principal after
the 1st payment?
$45,000 X .0975 = $4,387.50
$4,387.50 ÷ 12 = $365.63
$387.70 - $365.63 = $22.07
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Loan Payments
To determine monthly payment:
compute interest and add to principal
Example: Mr. Winslow gets a $30,000
loan with payments of $200 per month
at 9% interest. What is the payment?
$30,000 X .09 = $2,700 ÷ 12 = $225
$200 (P) + $225 (I) = $425 P & I
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Loan Payments
Example: Semiannual interest
payments are $400 and the rate is
5% annually. What is the loan
amount?
$400 X 2 = $800
$800 ÷ .05 = $16,000
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Loan-to-Value Ratio
Loan is based on percentage of appraised value
Example: Appraised value is $93,000 and the
borrower puts down 20%. What is loan amount?
$93,000 X .80 = $74,400
Example: Buyer pays $115,000
for a home that appraised for
10% less. With 10% down what
is the loan amount?
$115,000 X .90 = $103,500
$103,500 X .90 = $93,150
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Discount Points
Increase the lenders yield at closing
1 point = 1% of the loan amount
Example: Mr. Corkle buys a $55,000 home with FHA
financing. He puts down 3% on the first $25,000
and 5% on the balance. The lender charges 3.5
discount points. How much is paid in points?
$25,000 X .97 = $24,250
$30,000 X .95 = $28,500
$52,750
$52,0750 X .035 = $1,846.25
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Prorations
Dividing expenses between buyer and
seller
Time is multiplied by the rate
Taxes, rent, insurance, and interest
charges
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Prorations
Example: Mr. Howard sells his
home with closing set for July
15. Ms. Stucky assumes the
loan and insurance policy
which was paid March 1 for 1
year at $156. How much is the
credit to Mr. Howard?
March 1 – July 15 = 4½ months
$156 ÷ 12 = $13
$13 X 7 ½ = $97.50
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Prorations
Mortgage Interest Proration
Example: Ms. Stucky is assuming the $15,000
mortgage with an interest rate of 8%. The interest
is paid to June 1. Mr. Howard is liable for the
interest until date of closing. How much interest
does he owe?
$15,000 X .08 = $1,200 ÷ 12 = $100
Plus ½ for July
Total = $150.00
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Prorations
Prorating Insurance
1. Insurance
July 15 – Dec. 5 =
1 year, 4 months, 20 days
16 months and 20 days used
19 months and 10 days not used
$396 ÷ 36 = $11 X 19 = $209
$11 ÷ 30 = .366 X 10 = $3.67
$209 + $3.67 = $212.67 to Ms Lloyd
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Prorations
Tax Proration
2. Taxes
$982.80 ÷ 12 = $81.90
July 1 – Dec 5 = 5 mo., 5 days
$81.90 X 5 = $409.50
$81.90 ÷ 30 = $2.73
$2.73 X 5 = $13.65 + 409.50 =
$423.15 due from Ms. Lloyd
$2.73 X 25 =
$68.25 due from Mr. Wiley
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Commissions
Split Commission
Example: A salesperson receives 35% of the
total commission from his broker. What is the
broker’s share if the property sold for $23,000
and the commission is 6%?
$23,000 X 6% = $1,300
100% - 35% = 65%
$1,380 X 65% = $897
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Commissions
“Sliding Commission”
Example: Tom Lyons earns 6% on the 1st
$50,000 of a $160,000 sale. The total
commission is $7,400, what % was paid on the
remainder?
$50,000 X 6% = $3,000
$7,400 - $3,000 = $4,400
$160,000 - $50,000 = $110,000
$4,400 = what % of $110,000?
$4,400 (P) ÷ $110 (B) = .04 = 4%
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Commissions
Rent Commission
Example: Mr. Jones, a real estate broker,
leases a property to Ms. Whitney for 5 years.
Mr. Jones will receive 5% commission. The
rent will be $300 per month for the 1st year
with a $50 increase per month each
succeeding year. What is Mr. Jones
commission?
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Deductions on Income Taxes
Deductions for Interest Paid
Example: Jane and John Doe
file a joint tax return and pay
28% income tax on their
earnings. If they have a
$85,000 mortgage at 8%, how
much is their tax savings?
$85,000 X .08 = $6,800
28% X 6,800 = $1,904
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Deductions on Income Taxes
Effective Monthly Interest
Example: Assuming a mortgage
is for 20 years, the payments
would be 8.37 per 1000
borrowed, or $711.45 per month.
How much will the monthly
payments be lowered to?
$1,904 ÷ 12 = $158.67
$711.45 - $158.67 = $552.78
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Deductions on Income Taxes
Example: Adding both the
interest and property tax
savings, the Does’ effective
monthly house payment is?
$158.67 + $65.33 = $224
$711.45 - $224 = $487.45
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