Real Estate Principles and Practices Chapter 21 Real Estate Math © 2014 OnCourse Learning

Real EstateReal Estate Principles and Practices Principles and Practices

Chapter 21Chapter 21

Real Estate MathReal Estate Math

© 2014 OnCourse Learning


OverviewOverview

Square footageHouse or parcel of land

Percentages

Taxation

Subdivided property

Capitalization

AmortizationLoan payments

Discount

Interest

Prorations

Commission


Measurement ProblemsMeasurement Problems

Linear measureLinear measure12 in = 1 ft12 in = 1 ft

36 in = 3 ft or 1 yd36 in = 3 ft or 1 yd

Square measureSquare measure144 sq in = 1 sq ft144 sq in = 1 sq ft

9 sq feet = 1 sq yd9 sq feet = 1 sq yd

Cubic measure – calculating volumeCubic measure – calculating volume1 cubic ft = 1,728 cubic in1 cubic ft = 1,728 cubic in27 cubic ft = 1 cubic yd27 cubic ft = 1 cubic yd


Measurement ProblemsMeasurement Problems

link = 7.92 incheslink = 7.92 inches

chain = 66 ft or 4 rodschain = 66 ft or 4 rods

rod = 16 ½ feet or 1 perchrod = 16 ½ feet or 1 perch

mile = 5,280 feet or 8 furlongsmile = 5,280 feet or 8 furlongs

acre = 43,560 sq ft, 4,840 sq yds, or 160 sq rodsacre = 43,560 sq ft, 4,840 sq yds, or 160 sq rods

Section = 640 acres or 1 sq mileSection = 640 acres or 1 sq mile

Township = 36 sectionsTownship = 36 sections

Surveyor’s Measure


Square Footage and YardageSquare Footage and Yardage

Area = length X widthArea = length X width

Example: Example: room measures room measures 18’ long and 12’ wide18’ long and 12’ wide

A = 18’ (L) X 12’ (W)A = 18’ (L) X 12’ (W)

A = 216 sq ftA = 216 sq ft



Example: Example: compute the compute the square footage of the square footage of the househouse

A = 40’ X 28’ = 1,120 sq ftA = 40’ X 28’ = 1,120 sq ft

B = 2’ X 10’ = 20 sq ftB = 2’ X 10’ = 20 sq ft

C = 20’ X 10’ = 200 sq ftC = 20’ X 10’ = 200 sq ft

Total area = Total area = 1,3401,340

10”

AA

BB

CC



Example: Example: To find square yards, divide by 9To find square yards, divide by 9

Example: Example: Find the square yards of carpet Find the square yards of carpet needed to cover a 15’ X 18’ roomneeded to cover a 15’ X 18’ room

216 sq ft ÷ 9 = 216 sq ft ÷ 9 = 24 sq yards 24 sq yards

15’ X 18’ = 270 sq ft15’ X 18’ = 270 sq ft

270 sq ft ÷ 9 = 270 sq ft ÷ 9 = 30 sq yds30 sq yds



Area of a triangleArea of a triangle

Area = half the base X altitudeArea = half the base X altitude

Example: Example: base of 200’ and altitude base of 200’ and altitude of 150’ Find the area of 150’ Find the area

A = A = X 150X 150

A = 100 X 150 A = 100 X 150

200200 22

AA

BB CC DD

A = A = 15,000 sq ft15,000 sq ft



To compute the sq ft, add the 2 widthsTo compute the sq ft, add the 2 widths

40’ + 50’ = 90’ 40’ + 50’ = 90’

divide by 2 divide by 2

90’ ÷ 2 = 45’ 90’ ÷ 2 = 45’

45’ X 80’ = 45’ X 80’ = 3,600 sq ft3,600 sq ft

40’40’

80’80’

90°90°50’50’multiply by the lengthmultiply by the length


Cubic Footage and YardageCubic Footage and Yardage

L X W X H = cubic feetL X W X H = cubic feet

Example: Example: 20’ X 12’ X 8’ room20’ X 12’ X 8’ room

Example: Example: Driveway measures Driveway measures 60’ by 8’ by 3’ deep60’ by 8’ by 3’ deep

60’ X 8’ X ¼’ = 60’ X 8’ X ¼’ = 120 cubic ft 120 cubic ft

20’ X 12’ X 8’ = 20’ X 12’ X 8’ = 1,920 cubic ft 1,920 cubic ft

LengthLength

Wid

th

Wid

thH

eig

ht

He

igh

t


Cubic Footage and YardageCubic Footage and Yardage

Example: Example: Driveway is 54’ Driveway is 54’ long by 15’ wide and 4” deep. long by 15’ wide and 4” deep. At $30 per cubic yd, what is At $30 per cubic yd, what is the cost?the cost?

270 cubic ft ÷ 27 = 10 cubic yds 270 cubic ft ÷ 27 = 10 cubic yds

54’ X 15’ X 1/3’ = 270 cubic ft 54’ X 15’ X 1/3’ = 270 cubic ft LengthLength

Wid

th

Wid

thH

eig

ht

He

igh

t

10 X $30 = 10 X $30 = $300$300


Ratio and ProportionRatio and Proportion

Comparison of 2 related numbers

Ratios must always be equal or in Ratios must always be equal or in proportionproportion

Example: 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”?

441616

== 1144

772828

1144

==

Scale is ¼” = 1’Scale is ¼” = 1’



Example: Example: What is the measurement of a property 6” in length by 8” wide if the scale is 1/8 inch = 1 foot?

The measurement is 48’ X 64’The measurement is 48’ X 64’

If 1/8” to 1’ then 1” = 8’If 1/8” to 1’ then 1” = 8’

6 X 8’ = 48’6 X 8’ = 48’

8 X 8’ = 64’8 X 8’ = 64’



Example: 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?

511

==150150 XX

150150 XX

1155

XX

X = 30 SalesX = 30 Sales

==150150 5X5X

150150 55 = X= X



Example: Example: How many acres are there in Plot A if B contains 25 acres?

900900 XX

==1,3501,350 2525

900900 XX

25251,3501,350

XX = = 16 2/3 16 2/3 acresacres

== 22,50022,500 1,3501,350

900’900’ 1,350’1,350’



Example: 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?

40% of $3,000 40% of $3,000 = $1,200 = $1,200

4 + 6 = 10 parts4 + 6 = 10 parts

100% ÷ 10 = 10%100% ÷ 10 = 10%

4 X 10% = 40% and 6 X 10% = 60%4 X 10% = 40% and 6 X 10% = 60%


Capitalization and Other Capitalization and Other Finance ProblemsFinance Problems

II = income

RR = rate (interest)

VV = value

Example: Example: $140 is 3.5% of what amount?

$140 (I)$140 (I).035 (R).035 (R) = V= V

$140 ÷ .035 = $140 ÷ .035 = $4,000$4,000



Example: Example: Quarterly payments are $150 on a $12,000 loan. What is the interest rate?

$600 (I)$600 (I)$12,000 (R)$12,000 (R) = R= R

$600 ÷ $12,000 = $600 ÷ $12,000 = 5%5%

$150 X 4 = $600$150 X 4 = $600



Example:Example: What is a property’s value with a net income of $5,480 and annual return of 8%?

$5,480 (I)$5,480 (I) .08 (R).08 (R) = V= V

$5480 ÷ .08 = $5480 ÷ .08 = $68,500$68,500



Example: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?

$1,680 (I)$1,680 (I) $21,000 (V)$21,000 (V) = R= R

$1,680 ÷ $21,000 = $1,680 ÷ $21,000 = 8%8%

75% X $28,000 = $21,000 75% X $28,000 = $21,000

$140 X 12 = $1,680$140 X 12 = $1,680



Example:Example: If an investment’s value is $350,000 and returns 12% annually, what is the income produced?

$350,000 X 12% = $350,000 X 12% = $42,000 $42,000



Example:Example: The cap rate on a building that produces $20,000 annually is 10%. What is the value?

$20,000 (I)$20,000 (I) .10 (R).10 (R) = V= V

$20,000 ÷ .10 = $20,000 ÷ .10 = $200,000$200,000



Example:Example: What is the value of the same building with a cap rate of 5%?

$20,000 (I)$20,000 (I) .15 (R).15 (R) = V= V

$20,000 ÷ .05 = $20,000 ÷ .05 = $400,000$400,000

TheThe higher the rate, the lower the value higher the rate, the lower the value


Loan PaymentsLoan Payments

Amortized loan: equal payments consisting of principal and interest

Example: 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$45,000 X .0975 = $4,387.50

$4,387.50 ÷ 12 = $365.63$4,387.50 ÷ 12 = $365.63

$387.70 - $365.63 = $387.70 - $365.63 = $22.07 $22.07



To determine monthly payment: compute interest and add to principal

Example: 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 $30,000 X .09 = $2,700 ÷ 12 = $225

$200 (P) + $225 (I) =$200 (P) + $225 (I) = $425 P & I $425 P & I



Example:Example: Semiannual interest payments are $400 and the rate is 5% annually. What is the loan amount?

$400 X 2 = $800 $400 X 2 = $800

$800 ÷ .05 =$800 ÷ .05 = $16,000 $16,000


Loan-to-Value RatioLoan-to-Value Ratio

Loan is based on percentage of appraised value

Example: Example: Appraised value is $93,000 and the borrower puts down 20%. What is loan amount?

$93,000 X .80 = $93,000 X .80 = $74,400$74,400

Example: 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$115,000 X .90 = $103,500

$103,500 X .90 = $103,500 X .90 = $93,150$93,150


Discount PointsDiscount 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$25,000 X .97 = $24,250

$30,000 X .95 = $28,500$30,000 X .95 = $28,500

$52,750$52,750

$52,0750 X .035 = $52,0750 X .035 = $1,846.25$1,846.25


ProrationsProrations

Dividing expenses between buyer and seller

Time is multiplied by the rate

Taxes, rent, insurance, and interest charges



Example: 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 monthsMarch 1 – July 15 = 4½ months

$156 ÷ 12 = $13 $156 ÷ 12 = $13

$13 X 7 ½ = $13 X 7 ½ = $97.50$97.50



Example: 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$15,000 X .08 = $1,200 ÷ 12 = $100

Plus ½ for July Plus ½ for July

Total = Total = $150.00$150.00

Mortgage Interest ProrationMortgage Interest Proration



1. Insurance1. Insurance

July 15 – Dec. 5 =July 15 – Dec. 5 =

1 year, 4 months, 20 days1 year, 4 months, 20 days

$396 ÷ 36 = $11 X 19 = $209$396 ÷ 36 = $11 X 19 = $209

$11 ÷ 30 = .366 X 10 = $3.67$11 ÷ 30 = .366 X 10 = $3.67

$209 + $3.67 = $209 + $3.67 = $212.67 to Ms Lloyd$212.67 to Ms Lloyd

Prorating InsuranceProrating Insurance

16 months and 20 days used16 months and 20 days used

19 months and 10 days 19 months and 10 days not usednot used



2. Taxes2. Taxes

$982.80 ÷ 12 = $81.90$982.80 ÷ 12 = $81.90July 1 – Dec 5 = 5 mo., 5 daysJuly 1 – Dec 5 = 5 mo., 5 days

$81.90 X 5 = $409.50$81.90 X 5 = $409.50

$81.90 ÷ 30 = $2.73$81.90 ÷ 30 = $2.73$2.73 X 5 = $13.65 + 409.50 =$2.73 X 5 = $13.65 + 409.50 =

$423.15 due from Ms. Lloyd$423.15 due from Ms. Lloyd

$2.73 X 25 =$2.73 X 25 =

$68.25 due from Mr. Wiley $68.25 due from Mr. Wiley

Tax ProrationTax Proration


CommissionsCommissions

Example: 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 $23,000 X 6% = $1,300

100% - 35% = 65%100% - 35% = 65%

$1,380 X 65% = $1,380 X 65% = $897$897

Split CommissionSplit Commission



Example: 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 $50,000 X 6% = $3,000

$7,400 - $3,000 = $4,400$7,400 - $3,000 = $4,400

$160,000 - $50,000 = $110,000$160,000 - $50,000 = $110,000

$4,400 = what % of $110,000?$4,400 = what % of $110,000?

$4,400 (P) ÷ $110 (B) = .04 = $4,400 (P) ÷ $110 (B) = .04 = 4%4%

““Sliding Commission”Sliding Commission”



Example: 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?

Rent CommissionRent Commission


Deductions on Income TaxesDeductions on Income Taxes

Example: 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?

Deductions for Interest PaidDeductions for Interest Paid

$85,000 X .08 = $6,800$85,000 X .08 = $6,800

28% X 6,800 = 28% X 6,800 = $1,904$1,904



Example: 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?

Effective Monthly InterestEffective Monthly Interest

$1,904 ÷ 12 = $158.67$1,904 ÷ 12 = $158.67

$711.45 - $158.67 = $711.45 - $158.67 = $552.78$552.78



Example: Example: Adding both the interest and property tax savings, the Does’ effective monthly house payment is?

$158.67 + $65.33 = $224$158.67 + $65.33 = $224

$711.45 - $224 = $711.45 - $224 = $487.45$487.45

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Real Estate Principles and Practices Chapter 21 Real Estate Math © 2014 OnCourse Learning