Chapter 17 - Math
A driveway will be installed, 115 feet by 20 feet. The paving cost is $0.065 per square foot. What will be the minimum cost to pave the new driveway?
Answer: $1,495 Step 1 - Length x Width = area Calculation = 115 * 20 = 2,300 square feet Step 2 - Cost of paving driveway - $0.65 per square foot - Area * Cost/sq = price Calculation = 2,300 * .65 per square foot = $1,495
If the assessed value of the property is $80,000 and the tax value is 100% of the assessed value, what is the annual tax if the tax rate is $1.50 per $100 and the equalization factor is 1.5?
Answer: $1,800 annual taxes Step 1 - Assessed value x equalization factor = Equalized assessed value Calculation = $80,000 x 1.5 = $120,000 = Equalized assessed value Step 2 - Equalized assessed value times $1.50/100 = Tax Bill Calculation = $120,000 * $1.50 = $180,000/100 = $1,800
If the assessed value of property is $68,000 and the annual tax paid is $1,105 and the equalization factor is 1.3, What is the tax rate?
Answer: $1.25 per $100 of tax value Step 1 - Assessed value * equalizer Calculation = $68,000 x 1.3 = $88,400 Step 2 - Tax dollars divided by the equalized assessed value x 100 = Tax rate Calculation = $1,105/$88,400 = $1.25 per $100 of tax value
A real estate salesperson is the property manager for the owner of a local shopping center. The center has five units, each renting for $24,000 per year. The center has an annual vacancy factor of 4.5 %. The commission for rental of the units is 9% of the gross rental income. What is the commission for the year?
Answer: $10,314 Step 1 - Actual occupancy rate = 100 % - vacancy Calculation = 100% - 4.5% = 95% = Actual occupancy rate Step 2 - Actual rent dollars = potential gross rent x occupancy rate Calculation = $120,000 x $95.5% = $114,600 Step 3 - Actual rent x commission rate = commission dollars Calculation = $114,600 x 9% = $10,314
A real estate broker earns a commission of $6,000 in the sale of a residential property. His rate of commission is 6%. What is the selling price?
Answer: $100,000 Factor missing = divide Step 1 - sales price = commission dollars divided by commission rate Calculation = $6000/.06 = $100,000
A property sold for $125,000. The purchaser assumed a mortgage on the property of $37,450. What is the total amount of the transfer tax?
Answer: $132 total amount of transfer tax Classroom method Step 1 $125,000 - $37,450 = $87,550 round up to closest $500 = $88,000 The first two numbers equal the amount of the state tax. $88 the first two numbers divided by 2 equal the county taxes add the two together to get total. Step 1 - Sales price minus assumed mortgage = taxable amount Calculation = $125,000 - $37,450 = $87,550 Step 2 - Taxable units = Each 500 and then any fraction of 500 Calculation = $87,500/500 = 175 plus another unit for the $50 left over = 176 units Step 3 - State Tax = Number of Units * $0.50 Calculation = 176 * $0.50 = $88.00 Step 4 - County tax = Number of units x $0.25 Calculation = 176 * $0.25 = $44 Step 5 = Total transfer tax = State plus county tax Calculation = $88 + $44 = $132
A loan of $15,000 is repaid in full, one year after the loan is made. If the interest on the loan is 12.5%, what amount of interest is owed?
Answer: $1875 interest Step 1 - Principle * interest rate = interest dollars Calculation = $15,000 x 12.5% = $1,875
A real estate broker sells a property for $65,000. The commission on this sale to the real estate firm with whom the broker is associated is 7%. The broker receives 60% of the total commission paid to the real estate firm. What is the firm's share of the commission in dollars?
Answer: $2,730 Step 1 - Selling price x commission rate = commission dollars Calculation - $65,000 x 7% = $4,550 Step 2 - Total commission x share percentage = share dollars Calculation - $4,500 x 60% = $2,730
In preparing a statement for a closing to be held August 14, a real estate broker determines that the annual property taxes in the amount of $360 have not been paid. What will the broker put in the buyer's statement as her entry for real property taxes?
Answer: $224 buyer credit Step 1 - Determine the monthly tax amount Calculation = $360/12 = $30 per month Step 2 - Determine the daily tax amount Calculation = $30/30 = $1 per day Step 3 - Determine the total monthly taxes owed Calculation = $30 x 7 (through July) = $210 Step 4 - Determine the total monthly taxes for the month of closing Calculation = $1 * 14 = $14 Step 5 - Add the total tax amount Calculation = $210 + 14 = $224 buyer credit
On October 1, a mortgagor makes a $300 payment or her mortgage, which is at the rate of 10%. Of the $300 total payment for principal and interest, the mortgagee allocates $200 to the payment of interest. What is the principal balance due on the mortgage on the date of the payment?
Answer: $24,000 mortgage balance on date of payment Step 1 - Monthly interest x 12 = Annual interest Calculation = $200 x 12 = $2,400 Step 2 - Annual interest dollars divided by interest rate = principal Calculation = $2400/10% (.10) = $24,000
A house measures 28 feet wide by 52 feet long and sells for $64,000. What is the price per square foot?
Answer: $43.96/sq ft Step 1 - Length * Width = Area Calculation 28 * 52 = 1,456 sq ft Step 2 - Area * price per sf = selling price Step 3 - Price per sq ft = selling price/sf Calculation = $64,000/1,456 = $43.96 = price per sf
If the market value is $70,000, the tax rate is 120 mills, and the equalization factor is 1.5 and the assessment is 80%, what is the semiannual tax bill? (To get mills, divide by 1000).
Answer: $5,040 Semiannual tax bill Step 1 - Market Value * Assessment rate = Assessed Value Calculation - $70,000 * .8 = $56,000 Step 2 - Assessed value * equalizer = equalized assessed value Step 3 - Equalized assessed value divided by 120 mills/$1000 = Annual tax bill Calculation = $84,000/1000 = 84 84 * 120 = $10,080 Step 4 - Annual tax bill/2 = Semiannual tax bill Calculation = $10,080/2 = $5,040 Semiannual tax bill
A triangular lot measures 200 feet along the street and 500 feet in depth on the side perpendicular to the front lot line. If the lot sells for 10 cents per square foot, what is the selling price?
Answer: $5000 Step 1 = Area of a triangle = Length * Width divided by 2 Calculation - (200 * 500)/2 = 50,000 square feet Step 2 - Area x Price per square foot = sales price Calculation = 50,000 * $0.10 = $5000 = sales price
A real estate broker sells a property for $90,000. Her rate of commission is 7%. What is the amount of commission in dollars?
Answer: $6,300 Step 1 - sales price x rate = commission Calculation = $90,000 x 0.07 = $6,300
A property sells at the assessed value. The annual real property tax is $706.56 at a tax rate of $1.15 per $100 of tax value, with an equalization factor of 1.2. The property is taxed at 80% of assessed value. What is the selling price?
Answer: $64,000 Step 1 - assessed value = taxes/tax rate Calculation = 706.56/$1.15/$100 = $706.56 * 100/$1.15 = $61,440 Step 2 - Assessed value divided by the equalization factor = Equalized Assessed Value Calculation = $61,440/1.2 = $51,200 = Equalized assessed value Step 3 - Equalized Assessed value divided by the Assessment rate = selling price Calculation = $51,200/.8 = $64,000 = selling price
Mr. Wong buys a house for investment purposes for $48,000. He sells it six months later for $54,000 with no expenditures for fix up or repair. What is Mr. Wong's percentage of profit?
Answer: 12.5% profit Step 1 - Sales price less original investment = profit dollars Calculation = $54,000 - $48,000 = $6000 Step 2 - Profit dollars divided by original investment dollars = profit Calculation = $6000/$48,000 = 12.5%
An acre of land has a width of 330 feet. If this acre of land is rectangular in shape, what is its length? (Each acre contains 43,560 square feet)
Answer: 132 foot long lot Step 1 - An acre has 43,560 square feet Step 2 - if length x width = area, then length = area/width Calculation = Length = 43,560/330 = 132"
A subdivision contains 400 lots. If a broker has sold 25% of the lots and his sales staff has sold 50% of the remaining lots, how many lots are still unsold?
Answer: 150 lots still unsold Step 1 - Original number of lots x percentage sold by broker = number of lots remaining Calculation = 400 x 25% = 100 lots 400 - 100 lots = 300 Step 2 - Remaining lots x % sold by sales force = Number of lots sold by agents Calculation = 300 x 50% = 100 lots Step 3 - Add the number of lots sold Calculation = 100 + 150 = 250 Step 4 - Original number of lots less the number of lots sold = number of lots remaining Calculation = 400 - 250 = 150
A rectangular lot measures 185' x 90'. How many square feet does this lot contain?
Answer: 16,650 square feet Step 1 = Length x Width = area Calculation = 185 * 90 = 16,650 square feet
A room measures 15' x 21'. We want to install wall to wall carpeting and need to calculate the exact amount of square yards of carpeting required.
Answer: 35 square yards Step 1 - Carpeting sold by square yard, so need to answer in square yards Step 2 - Calculate are of carpet in square feet length x width = area Calculation = 15 x 21 = 315 square feet Step 3 - Convert square feet to square yards - 9 square feet in a square yard ( 3 x 3) Calculation = 315 square feet/9 = 35 square yards
A real estate broker earns a commission of $3,000 in the sale of property for $50,000. What is her rate of commission?
Answer: 6% commission rate Factor missing = divide Calculation = $3000/50,000 = 6%
If a parcel of land contains 32,670 square feet, what percent of an acre is it?
Answer: 75% of an acre Step 1 - 43,560 in an acre Step 2 - part of area divided by the total area = % area Calculation = 32,670 square feet/ 43,560 = 75%
Ms. Clary purchases some property in 1987 for $35,000. She makes improvements in 1988 costing her $15,500. In 1990 she sells the property for $46,000. What is her percentage of loss?
Answer: 8.91% Step 1 - Purchase price plus improvements = current investment Calculation =$35,000 + $15,500 = $50,500 Step 2 - Investment less selling price = loss Calculation = $50,500 - $46,000 = $4500 loss Step 3 - loss divided by investment = percent loss Calculation = $4,500/$50,500 = 8.91%
