Real Estate Math

Owner pays annual property tax of $1,000. The tax rate is 15 mills. Assuming the owner gets the benefit of a $25,000 homestead exemption, what is the property's assessed value?
$66,667
$87,667
$158,334
$91,667
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Terms in this set (31)
Owner pays annual property tax of $1,000. The tax rate is 15 mills. Assuming the owner gets the benefit of a $25,000 homestead exemption, what is the property's assessed value?
$66,667
$87,667
$158,334
$91,667
$91,667

$1000 tax / .015 15 mills = 66,667 Tax value66,667 Tax value + 25,000 Homestead exemption = $91,667 Assessed value
The assessed value is $91,667. The tax rate is 15 mills. Assume that the owner gets the benefit of a $25,000 homestead exemption. What is the approximate property tax?
$1375
$900
$1000
$66,667
$1000

$91,667 Assessed value - $25,000 Homestead exemption = $66,667 Tax value
$66,667 Tax value x .015 (15 mills) = $1,000 property tax
Owner purchased a property for $100,000, putting 20% down and paying no interest or principal for one year. At the end of the year, Owner sells the property for a 25% gain. How much was Owner's profit per dollar invested?
$20,000
$125
$25,000
$1.25
$1.25

$100,000 Original value x 20% Down payment percentage = $20,000 Cash invested$100,000 Original value x 25% = 25,000 % Gain Profit$25,000 Profit / $20,000 Invested = $1.25 profit per dollar invested
An apartment building with a 30 year economic life is estimated to have a present value of $540,000 after 3 years of ownership. What was the original cost of the property?
$594,000
$700,000
$600,000
$794,000
$600,000

3 Age of building / 30 Economic life = 10% Depreciation %$540,000 Current value / 90% (100% - 10% depreciation) = $600,000 original cost
Charging 4 points increases the effective price of the mortgage by approximately:
1/16%
1/4%
1/2%
1/2%

1 Point = 1/8% Effective price increase4 Points = 4 X 1/8% (% per point) = 4/8%= 1/2% effective price increase
A sales associate earns a 40% commission. The listed property sells for $100,000. The commission is 5% on the first half and will be 7% on the second half. The sales associate's commission is:
$2800
$3000
$2400
$2000
$2400

Solution:$100,000 Sales price x 6% Average commission = $6,000 Total commission$6,000 Total commission x 40% Sales associate's share = $2,400 commission
Following are dimensions of 4 parcels of land. Which is an 8-acre tract?
660\' x 528\'
1320\' x 330\'
660\' x 1,320\'
660\' x 660\'
660\' x 528\'

43,560 Sq ft per acre x 8 Acres = 348,480 Sq ft in 8 acres660\' x 660\' = 435,600 square feet1320\' x 330\' = 435,600 square feet660\' x 1320\' = 871,200 square feet660\' x 528\' = 348,480 square feet
Loan-to-value ratio is 78%. What is the down payment required to purchase a $180,000 property?
$104,400
$39,600
$36,900
$140,400
$39,600

Solution:$180,000 * .78 = $140,400$180,000 - $140,400 = $39,600
Zoning restrictions on Jackson Avenue call for a 20 foot setback. Smith owns a lot on Jackson Avenue that measures 200' x 200'. How many square feet are available for construction of an improvement?
4000
40,000
32,400
36,000
36,000

Solution:200 (Total depth) - 20 (Setback) = 180 (Net build-able depth)180 (Net build-able depth) x 200 (Net build-able width) = 36,000 (square feet available)
XYZ Broker has an agreement in which 20% of the overall commission goes to the Listing Sales Associate and the remainder is split between the Broker and the Selling Sales Associate. How much does the Selling Sales Associate receive for a $70,000 sale at a 5.5% commission?
$3,850
$1,540
$3,080
$770
$1,540

Solution:$70,000 Sale price x 5.5% Commission rate = $3,850 Total commission$3,850 Total commission x 20% Listing sales associate = $770 Listing sales associate share$3,850 Total commission - $770 Listing sales associate share = $3,080$3,080 Split with broker /2 = $1,540 sales associate's commission
Craft Store is renting space in a retail strip center. Craft Store pays a base rent of $4,000 per month PLUS 3% of gross income. Last month the total rent payment was $6,500. How much was Craft Store's gross income? $216,667 $133,333 $83,333 $350,000$83,333 Solution:$6,500 (Total rent) - $4,000 (Base rent) = $2,500 (Percentage rent)$2,500 (Percentage rent) / 3% (Percentage rent rate) = $83,333 gross incomeBorrower obtained a short term loan of $70,000 at 5.5% interest. The total interest charge was $962.50. How many months did Borrower pay interest? 6 8 3 123 Solution:$70,000 (Loan amount) x 5.5% (Annual interest rate) = $3,850 (Annual interest)$962.50 (Interest charge) / $3,850 (Annual interest) = .25%12 (Months per year) x .25 (25%) = 3 (months interest)Using the income-capitalization approach, what is the value of the property with the following information: Gross income: $60,000 Operating expenses: $42,500 Cap rate: 4% $24,000 $1,500,000 $437,500 $1,062,500$437,500 Solution:$60,000 (Gross income) - $42,500 (Operating expenses) = $17,500 (Net operating income)I / R = V$17,500 (Net operating income (I)) / 4% (Cap rate (R)) = $437,500 (value (V))How many acres are contained in a parcel that measures 660\' x 330\' x 660\' x 330\'? 2.5 1.25 5 5005 Solution:660 (Side 1) x 330 (Side 2) = 217,800 sq ft217,800 Sq ft / 43,560 (Square feet per acre) = 5 acresAppraiser performing the cost-depreciation approach has estimated the land value to be $10,500 and the reproduction cost $65,000. Appraiser estimates that the depreciation rate is 8%. What is the value? $70,300 $59,800 $69,460 $49,300$70,300 Solution:65,000 Reproduction cost of improvement x 8% Depreciation rate = $5,200 Depreciation$65,000 Reproduction cost - $5,200 Depreciation = $59,800 Depreciated value of improvements + $10,500 Land value = $70,300 total valueBorrower is purchasing a property for $220,000. Terms of the transaction are a purchase money mortgage with a 75% loan-to-value ratio and an owner-held second mortgage for 67% of the balance. How much is Borrower's down payment? $18,150 $55,000 $72,600 $36,850$18,150 Solution:$220,000 (Purchase price) x 75% (LTV) = $165,000 Purchase money mortgage$220,000 - $165,000 (purchase price) = $55,000 (Down payment purchase money mortgage)$55,000 x 67% (Second mortgage %) = $36,850 (Second mortgage amount)$55,000 (Down payment purchase money mortgage) - $36,850 (Second mortgage amount) = $18,150 down paymentInvestor is trying to determine the value of an apartment building. Using the income approach, what is the value if the Effective Gross Income (EGI) is $144,000, the operating expense ratio is 45%, and the desired capitalization rate is 15%? $432,000 $528,000 $960,000 $972,000$528,000 Solution:$144,000 Gross Income- $64,800 (45% x 144,000)$79,200 Net Operating IncomeI/R = V$79,200 (I) / 15% (R)= $528,000 (V)ender's loan-to-value ratio is 90%. The purchase price is $65,000, but the appraisal is $60,000. What is the maximum loan? $65,000 $60,000 $54,000 $58,500$54,000 Solution:$60,000 < $65,000 (use whichever is less)$60,000 * .90 (90%) = $54,000Owner wishes to net $10,000 after the $15,000 mortgage and an additional 6% in expenses have been paid. What sale price will accomplish Owner's objectives? $26,596 $20,500 $23,500 $25,000$26,596 $10,000 (Net after expenses) + $15,000 (expenses) = $25,000 (Net plus expenses)$25,000 / 94% (Remainder %) = $26,596 Sale PriceBorrower obtained a $53,000 loan secured by a mortgage. Payments are interest-only non-compounded and are due quarterly. The first quarterly payment was $1,192.50. What was the interest rate? 0.1 0.11 0.09 0.08.09 $1,192.50 x 4 = $4,770$53,000 x rate = $4,770rate = $4,770 / $53,000rate = .09How many acres are contained in a parcel of land measuring 1,650 feet by 1,650 feet? 70 acres 62.5 acres 67.5 acres 50 acres62.5 acres Explanation: 1650 x 1650 = 2,722,500 square feet / 43,560 = 62.5 acresSales associate is to receive 2/3 of a 7% commission. How much does sales associate earn if she sells the N 1/2 of NW 1/4 of NE 1/4 for $2,500 per acre? $1,667 $2,333 $7,000 $3,5002,333 Explanation: 640/2/4/4 = 20 acres x 2,500 =$50,000 sales price x 7% = $3,500 x 2/3 (.6666) = $2,333Sales Associate earns 40% of the total commission. Broker's commission is computed as 6.5% of the first half of sales price and 5.5% of the second half. How much does Sales Associate earn for a $65,000 sale? $1,175 $3,900 $2,225 $1,560$1,560 Explanation: The average commission is 6%. $65,000 x 6% = 3,900 x 40% = $1,560Owner explained to Broker that they wanted to net $149,500 and that Broker could keep any amount over and above the net amount. If the customary and normal commission charged by Broker is 8%, what is the listing price? $162,500 $137,540 $167,000 $194,760$162,500 Explanation: $149,500 / 92% = $162,500A residential investment has $30,000 gross income, $12,000 operating expenses, and a 12% cap rate. What is the value? $135,000 $175,000 $125,000 $150,000$150,000 Explanation: $30,000 - $12,000 = $18,000 (I) / 12% (R) = $150,000 (V)3-month term loan of $5,000 at 13% interest. What is the total payment due at the end of the term? $4,982.75 $5,162.50 $4,765.88 $5,433.34$5,162.50 Explanation: 5,000 x 13% = 650 per year; 650 / 12 months =54.17 per month x 3 months = 162.50; 5,000 principal + 162.50 interest = $5,162.50Borrower obtained a straight-term loan at 7.5%. Over the 11 year term the borrower paid $7,177.50 interest. What was the principal amount of the loan? $7,800 $8,700 $8,350 $8,995$8,700 Explanation: $7,177.50 / 11 years = $652.50 interest per year / 7.5% rate = $8,700A home sold for $89,850. The buyer paid $13,000 cash down, assumed a mortgage with a balance of $38,710 by signing a new note, and gave a second mortgage to the seller for the balance of $38,140. What is the total of all documentary stamp and intangible tax related to this transaction? $898.80 $629.30 $1,244.03 $975.08$975.08 Explanation: Deed: 89,850 / 100 = 898.5 hundreds rounded up to 899 x $.7 = 629.30 tax on deed; Notes: 38,710 assumed / 100 = 387.1 hundreds rounded up to 388 x $.35 = $135.80 38,140 new / 100 = 381.4 hundreds rounded up to 382 x $.35 = $133.70 $135.80 + $133.70 = $269.50 total tax on new and assumed notes New mortgage: $38,140 x .002 = $76.28 intangible tax on new mortgage Total: $629.30 + $269.50 + $76.28 = $975.08The city has been petitioned to pave your street at a cost of $72 per running foot of property. The city has agreed to pay 45 percent of the cost. If your lot frontage on the street is 120 feet, what will your special assessment be for street paving? $8,640 $4,320 $2,376 $4,752$2,376 Explanation: 120 front feet x $72 = $8,640 x 55% (owner?s share) = $4,752 / 2 (sides of street) = $2,376Investor is performing an analysis of a 120 x 200 4 story industrial warehouse building. Investor estimates that 20% of the space will be unusable. How many 10 x 20 bins could be built? 200 units 48 units 96 units 384 units384 units 120 x 200 = 24,000 square feet x 80% (usable) = 19,200 square feet usable per floor; 10 x 20 = 200 square feet per unit; 19,200 / 200 = 96 units per floor x 4 floors = 384 unitsOwner paid $1,600 property tax. The local tax rate is $2.50 per $100 of assessed value. What is the assessed value of Owner's property? $68,000 $59,000 $64,000 $62,000$64,000 Explanation: 1,600 / 2.50 = 640 hundreds x 100 = $64,000