Upload
aubrie-hensley
View
222
Download
4
Embed Size (px)
Citation preview
Real EstateReal Estate Principles and Practices Principles and Practices
Chapter 21Chapter 21
Real Estate MathReal Estate Math
© 2014 OnCourse Learning
© 2014 OnCourse Learning
OverviewOverview
Square footageHouse or parcel of land
Percentages
Taxation
Subdivided property
Capitalization
AmortizationLoan payments
Discount
Interest
Prorations
Commission
© 2014 OnCourse Learning
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
© 2014 OnCourse Learning
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
© 2014 OnCourse Learning
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
© 2014 OnCourse Learning
Square Footage and YardageSquare Footage and Yardage
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
© 2014 OnCourse Learning
Square Footage and YardageSquare Footage and Yardage
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
© 2014 OnCourse Learning
Square Footage and YardageSquare Footage and Yardage
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
© 2014 OnCourse Learning
Square Footage and YardageSquare Footage and Yardage
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
© 2014 OnCourse Learning
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
© 2014 OnCourse Learning
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
© 2014 OnCourse Learning
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’
© 2014 OnCourse Learning
Ratio and ProportionRatio and Proportion
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’
© 2014 OnCourse Learning
Ratio and ProportionRatio and Proportion
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
© 2014 OnCourse Learning
Ratio and ProportionRatio and Proportion
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’
© 2014 OnCourse Learning
Ratio and ProportionRatio and Proportion
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%
© 2014 OnCourse Learning
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
© 2014 OnCourse Learning
Capitalization and Other Capitalization and Other Finance ProblemsFinance Problems
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
© 2014 OnCourse Learning
Capitalization and Other Capitalization and Other Finance ProblemsFinance Problems
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
© 2014 OnCourse Learning
Capitalization and Other Capitalization and Other Finance ProblemsFinance Problems
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
© 2014 OnCourse Learning
Capitalization and Other Capitalization and Other Finance ProblemsFinance Problems
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
© 2014 OnCourse Learning
Capitalization and Other Capitalization and Other Finance ProblemsFinance Problems
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
© 2014 OnCourse Learning
Capitalization and Other Capitalization and Other Finance ProblemsFinance Problems
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
© 2014 OnCourse Learning
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
© 2014 OnCourse Learning
Loan PaymentsLoan Payments
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
© 2014 OnCourse Learning
Loan PaymentsLoan Payments
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
© 2014 OnCourse Learning
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
© 2014 OnCourse Learning
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
© 2014 OnCourse Learning
ProrationsProrations
Dividing expenses between buyer and seller
Time is multiplied by the rate
Taxes, rent, insurance, and interest charges
© 2014 OnCourse Learning
ProrationsProrations
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
© 2014 OnCourse Learning
ProrationsProrations
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
© 2014 OnCourse Learning
ProrationsProrations
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
© 2014 OnCourse Learning
ProrationsProrations
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
© 2014 OnCourse Learning
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
© 2014 OnCourse Learning
CommissionsCommissions
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”
© 2014 OnCourse Learning
CommissionsCommissions
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
© 2014 OnCourse Learning
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
© 2014 OnCourse Learning
Deductions on Income TaxesDeductions on Income Taxes
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