Real Estate Principles and Practices Chapter 21 Real Estate Math © 2009 by South-Western, Cengage Learning

Overview Square footage House or parcel of land Percentages Taxation Subdivided property Capitalization Amortization Loan payments Discount Interest Prorations Commission

© 2009 by South-Western, Cengage Learning 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

© 2009 by South-Western, Cengage Learning Measurement Problems 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 Surveyor’s Measure

© 2009 by South-Western, Cengage Learning 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

© 2009 by South-Western, Cengage Learning Square Footage and Yardage Example: compute the square footage of the house A = 40’ X 28’ = 1,120 sq ft B = 2’ X 10’ = 20 sq ft C = 20’ X 10’ = 200 sq ft Total area = 1,340 10” A B C

© 2009 by South-Western, Cengage Learning Square Footage and Yardage Example: To find square yards, divide by 9 Example: Find the square yards of carpet needed to cover a 15’ X 18’ room 216 sq ft ÷ 9 = 24 sq yards 15’ X 18’ = 270 sq ft 270 sq ft ÷ 9 = 30 sq yds

© 2009 by South-Western, Cengage Learning Square Footage and Yardage Area of a triangle Area = half the base X altitude Example: base of 200’ and altitude of 150’ Find the area A = X 150 X 150 A = 100 X ABCD A = 15,000 sq ft

© 2009 by South-Western, Cengage Learning Square Footage and Yardage To compute the sq ft, add the 2 widths 40’ + 50’ = 90’ divide by 2 divide by 2 90’ ÷ 2 = 45’ 45’ X 80’ = 3,600 sq ft 40’80’ 90° 50’ multiply by the length

© 2009 by South-Western, Cengage Learning Cubic Footage and Yardage L X W X H = cubic feet Example: 20’ X 12’ X 8’ room Example: Driveway measures 60’ by 8’ by 3’ deep 60’ X 8’ X ¼’ = 120 cubic ft 20’ X 12’ X 8’ = 1,920 cubic ft Length Width Height

© 2009 by South-Western, Cengage Learning Cubic Footage and Yardage Example: Driveway is 54’ long by 15’ wide and 4” deep. At $30 per cubic yd, what is the cost? Example: Driveway is 54’ long by 15’ wide and 4” deep. At $30 per cubic yd, what is the cost? 270 cubic ft ÷ 27 = 10 cubic yds 54’ X 15’ X 1/3’ = 270 cubic ft Length Width Height 10 X $30 = $300

© 2009 by South-Western, Cengage Learning Ratio and Proportion Comparison of 2 related numbers Ratios must always be equal or in proportion 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”? = = Scale is ¼” = 1’

© 2009 by South-Western, Cengage Learning Ratio 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’ If 1/8” to 1’ then 1” = 8’ 6 X 8’ = 48’ 8 X 8’ = 64’

© 2009 by South-Western, Cengage Learning Ratio 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? 51 = 150 X 150 X15 X X = 30 Sales = 150 5X 5X = X

© 2009 by South-Western, Cengage Learning Ratio and Proportion Example: Example: How many acres are there in Plot A if B contains 25 acres? 900 X = 1, X 1,350 X = 16 2/3 acres acres = 22,500 1,350 1,350900’1,350’

© 2009 by South-Western, Cengage Learning Ratio 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 = $1, = 10 parts 100% ÷ 10 = 10% 4 X 10% = 40% and 6 X 10% = 60%

© 2009 by South-Western, Cengage Learning Capitalization and Other Finance Problems I I = income R R = rate (interest) V V = value Example: Example: $140 is 3.5% of what amount? $140 (I).035 (R) = V $140 ÷.035 = $4,000

© 2009 by South-Western, Cengage Learning Capitalization and Other Finance Problems Example: Example: Quarterly payments are $150 on a $12,000 loan. What is the interest rate? $600 (I) $600 (I) $12,000 (R) = R $600 ÷ $12,000 = 5% $150 X 4 = $600

© 2009 by South-Western, Cengage Learning Capitalization and Other Finance 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 $5480 ÷.08 = $68,500

© 2009 by South-Western, Cengage Learning Capitalization and Other Finance 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 $1,680 ÷ $21,000 = 8% 75% X $28,000 = $21,000 $140 X 12 = $1,680

© 2009 by South-Western, Cengage Learning Capitalization and Other Finance Problems Example: Example: If an investment’s value is $350,000 and returns 12% annually, what is the income produced? $350,000 X 12% = $42,000

© 2009 by South-Western, Cengage Learning Capitalization and Other Finance 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 $20,000 ÷.10 = $200,000

© 2009 by South-Western, Cengage Learning Capitalization and Other Finance 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 $20,000 ÷.05 = $400,000 The higher the rate, the lower the value

© 2009 by South-Western, Cengage Learning Loan 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 $ How much is applied against principal after the 1 st payment? $45,000 X.0975 = $4, $4, ÷ 12 = $ $ $ = $22.07

© 2009 by South-Western, Cengage Learning Loan 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 $200 (P) + $225 (I) = $425 P & I

© 2009 by South-Western, Cengage Learning Loan Payments Example: 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

© 2009 by South-Western, Cengage Learning Loan-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 = $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 $103,500 X.90 = $93,150

© 2009 by South-Western, Cengage Learning Discount Points I ncrease 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

© 2009 by South-Western, Cengage Learning Prorations Dividing expenses between buyer and seller Time is multiplied by the rate Taxes, rent, insurance, and interest charges

© 2009 by South-Western, Cengage Learning Prorations 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 months $156 ÷ 12 = $13 $13 X 7 ½ = $97.50

© 2009 by South-Western, Cengage Learning Prorations 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 Plus ½ for July Total = $ Mortgage Interest Proration

© 2009 by South-Western, Cengage Learning Prorations 1. Insurance July 15 – Dec. 5 = 1 year, 4 months, 20 days $396 ÷ 36 = $11 X 19 = $209 $11 ÷ 30 =.366 X 10 = $3.67 $209 + $3.67 = $ to Ms Lloyd Prorating Insurance 16 months and 20 days used 19 months and 10 days not used

© 2009 by South-Western, Cengage Learning Prorations 2. Taxes $ ÷ 12 = $81.90 July 1 – Dec 5 = 5 mo., 5 days $81.90 X 5 = $ $81.90 ÷ 30 = $2.73 $2.73 X 5 = $ = $ due from Ms. Lloyd $2.73 X 25 = $68.25 due from Mr. Wiley Tax Proration

© 2009 by South-Western, Cengage Learning Commissions 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, % - 35% = 65% $1,380 X 65% = $897 Split Commission

© 2009 by South-Western, Cengage Learning Commissions Example: Example: Tom Lyons earns 6% on the 1 st $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% “Sliding Commission”

© 2009 by South-Western, Cengage Learning Commissions 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 1 st year with a $50 increase per month each succeeding year. What is Mr. Jones commission? Rent Commission

© 2009 by South-Western, Cengage Learning Deductions 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 Paid $85,000 X.08 = $6,800 28% X 6,800 = $1,904

© 2009 by South-Western, Cengage Learning Deductions on Income Taxes Example: Example: Assuming a mortgage is for 20 years, the payments would be 8.37 per 1000 borrowed, or $ per month. How much will the monthly payments be lowered to? Effective Monthly Interest $1,904 ÷ 12 = $ $ $ = $552.78

© 2009 by South-Western, Cengage Learning Deductions on Income Taxes Example: Example: Adding both the interest and property tax savings, the Does effective monthly house payment is? $ $65.33 = $224 $ $224 = $487.45