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Real Estate Principles and Practices Chapter 21 Real Estate Math © 2014 OnCourse Learning Overview Square footage House or parcel of land Percentages Prorations Commission Taxation Subdivided property Capitalization Amortization Loan payments Discount Interest © 2014 OnCourse 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 © 2014 OnCourse Learning 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 © 2014 OnCourse 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 © 2014 OnCourse Learning 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 © 2014 OnCourse Learning 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 © 2014 OnCourse Learning 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 © 2014 OnCourse Learning 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 © 2014 OnCourse Learning 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 © 2014 OnCourse Learning 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 © 2014 OnCourse Learning 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’ © 2014 OnCourse Learning 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’ © 2014 OnCourse Learning 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 © 2014 OnCourse Learning 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 © 2014 OnCourse Learning 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 © 2014 OnCourse Learning 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 © 2014 OnCourse Learning 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% © 2014 OnCourse Learning 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 © 2014 OnCourse Learning 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% © 2014 OnCourse Learning 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 © 2014 OnCourse Learning 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 © 2014 OnCourse Learning 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 © 2014 OnCourse Learning 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 © 2014 OnCourse Learning 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 © 2014 OnCourse Learning 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 © 2014 OnCourse Learning 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 © 2014 OnCourse Learning 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 © 2014 OnCourse Learning Prorations Dividing expenses between buyer and seller Time is multiplied by the rate Taxes, rent, insurance, and interest charges © 2014 OnCourse Learning 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 © 2014 OnCourse Learning 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 © 2014 OnCourse Learning 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 © 2014 OnCourse Learning 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 © 2014 OnCourse Learning 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 © 2014 OnCourse Learning 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% © 2014 OnCourse Learning 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? © 2014 OnCourse Learning 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 © 2014 OnCourse Learning 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 © 2014 OnCourse Learning 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 © 2014 OnCourse Learning