1. ©2011 Cengage Learning

2. California Real Estate Principles
Chapter 6
Practical Real Estate Mathematics
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3. Chapter 6
To solve problems related to investment, discounting notes, appraisal, commissions, interest and loans, buyer costs and seller expenses, square footage and area, prorations and taxes.
Use amortization and other tables to simplify real estate mathematical computations
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4. SOLVING MATH PROBLEMS Read The Question Write Down the Formula
Substitute
Calculate
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5. CONVERTING FRACTIONS INTO DECIMALS1 4
1/4
3/4
4 1
1  4 = .25
Divide the Bottom number (Denominator) into the Top number (Numerator) 3 4
.25
.75
3  4 = .75
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6. Converting % to Decimals
Remove the percentage sign,
Move the decimal point 2 places to the left.
8% converts to .08
25% converts
9.5% converts
100% converts
105% converts
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7. Variables Made (I) = % ( R) x Paid (V) Made (I) / Paid (V) = % ( R)
Made (I) / % ( R) = Paid (V)
(I) Made = (V) Paid x ( R) %
1.Income earned Amount invested % return
2.Commission Sales Price Rate of comm
3. Doc transfer tax Taxable equity Transfer tax rate
4. Monthly rent Invested amount Rate of return
5. Annual NOI Property value Cap rate
6. Interest Principal Rate x Time
7. Discount amount Loan balance Rate of discount
8. Area of property Length Width
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8. CAPITALIZATION Income = Rate x Value
What is the maximum price to pay if the
investor wants a 9% investment rate?
$500 per month x 3 apartments = $1500
month
$1500 per month x 12 months = $18,000
year
$18,000 = 9% R x $?
$18,000
.09 = $200,000 = Value
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9. Commission PERCENTAGE I = % x Sales Price
If $9,900 was a 6% commission, what was the sales price of the house?
$9,900 = 6% x SP
$9,900 ÷ .06 = $165,000
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10. INTEREST Interest = Rate x Principal
If you borrowed $8,000 for one year and paid $640 interest,
what rate of interest did you pay?
$640 = $8,000 x ?%
640
8000
= 8%
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11. PROFIT (or LOSS) % x VB = VA
A house sold for $60,000 for a 20% profit. What was the original purchase price?
Value After = (100% + 20%) of
Value Before
120% x $ ? VB= $60,000
60,000
1.20
= $50,000
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12. SQUARES, RECTANGLES AND PARALLELOGRAMS
Area = One side (length/base) x the other One Side
(Width/Height)
Square
55’
One side (Height)
55’ One side (Base)
Rectangle
20’ One side (Height)
55’One side
(Base)
Parallelogram
20’One side (Height)
40’ One Side (Base)
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13. TRIANGLES Area = ½ One side x the other One side
55’ One side (Height)
55’ One side (Base)
= ½ 55 x 55
Or =55 x ½ 55
55’One side (Height)
90’One side (Base)
=1/2 55 x 90
Or = ½ 90 x 55
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14. ODD SHAPES
Divide the shape into triangles, squares, and rectangles, and calculate their areas
60 ft
40 ft
125 ft
50ft
70 ft
175 ft
110
110 70 65 60 50
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15. Add their areas together to get the area of the odd shaped whole.
ODD SHAPES (cont.)
Add their areas together to get the area of the odd shaped whole.
3500
Smallest box = 50 x 70 =
Larger box = 60 x 110 =
Triangle area = 110 / 2 X 65 =
6600
3575
13,675 square feet
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16. Prorations: Equitable division of costs
Every month = 30 Days
Every Year = 360 Days
# of Days x Rate Per Day = Share of Expense
Common items prorated: association dues, interest, taxes, insurance & prepaid rent
Credit is an Entry Made in Favor of the Party
Debit is an Entry to be Paid by the Party
(Note: Deeds record at 8 a.m.)
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17. PRORATION of Rent (Closing Statement Example)
$900 per month rent paid in advance
Paid on first of the month
Escrow closes on tenth of month
Calculate:
The amount per day and
Debit or Credit for Buyer and
Debit or Credit for Seller
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18. Proration When was the item (rent) last paid? lst of the month
Paid to whom? Collected by the Seller for 30 day period
Period the item paid for? From lst day of this month to the first day of next month.
Paid in advance to seller. Some portion is due to buyer for the balance of this month, until the next rent is due.
$900 {÷} 30 {=} $30 per day
1, 2, 3, 4, 5, 6, 7, 8, 9 = seller owns the property for 9 days
10, 11, 12, 13, = buyer owns the property for 21
$30 {x} 21 days {=} $630
Answer: $630 credit to buyer $630 debit to seller
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19. TAXES
I = R x V
How much will be owed on a home valued at $174,000 if the annual property tax rate is 1.05%?
I = x $174,000
I = $1,827
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20. I = R x V
V (Paid) x R (%) = I (Made) I (Made) ÷ V (Paid) = R (%) I (Made) ÷ R (%) = V (Paid) V (Paid) I (Made) R (%)
Sales Price Commission Comm Rate
Principal amt Return on Invest Rate of Return of Loan
Future Market Interest Interest Rate Value of Property Dividend Rate of Profit
Cost Net Income Cap Rate
Profit
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21. Review Quiz Chapter 6
1. A lot is sold for $180,000, making a 20% profit over cost. What was the cost? a. $136,000 b. $144,000 c. $148,000 d. $150,000
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22. Review Quiz Chapter 6
2. To settle the estate of the deceased, a probate sale is held on a mobile home. The first court bid is $30,000; the next minimum bid must be for at least:
a. $31,000
b. $32,000
c. $33,000
d. $31,750
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23. Review Quiz Chapter 6
3. An investor wants to acquire income property that will generate a 10% cap rate. A 6-unit apartment complex rents for $950 per unit per month. Vacancies are 5% of gross rents and operating expenses total $20,500 per year. What is the maximum the investor should offer for this property? (round to nearest $1,000) a. $684,000 b. $573,000 c. $445,000 d. $403,000
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24. Answers to Chapter 6 Review Quiz
1. (d) $180,000  1.20 = $150,000 cost 2. (b) $10,000  10% = $1,000; $20,000  5% = 1,000; $30, , ,000 = $32, (c) $950  6  12 = $68,400 − 5% = $64,980 − 20,500 = 44,480  .10 = $444,800 (rounded $445,000)
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