Real Estate Math Questions
Mary has purchased a home for $120,000 and obtained a loan from a local bank for 75% of the purchase price. She agreed to pay 2 discount points. Mary has placed $2,500 earnest money with the broker. How much money will Mary need at closing to complete the transaction? A. $31,800 B. $30,000 C. $29,900 D. $29,300
$120,000 x .75 = $90,000 Loan Amount. $90,000 x .02 = $1,800 in Points (Every Point is 1% of Loan Amount). $120,000 x .25 = 30,000 Down Payment $30,000 Down Payment + $1,800 in Points = $31,800 - $2,500. Earnest Money = $29,300 Total to Bring to Closing
Mr. Smith is blind, owns a home assessed at $150,000, and has lived in Florida for 6 years. The city millage rate is 8 mills, the county rate is 9 mills, and the school rate is 8 mills. What are his property taxes for the year? A. $2462.50 B. $2,500 C. $2,687.50 D. $2,987.50
$150,000 - $25,500 = $124,500 ($500 additional for blind exemption). $124,500 x .025 = $3,112.50 (city .008/county .009/school .008 = .025) Amount exempt from city and county taxes $25,000 x .017 = $425 (The additional $25,000 homestead exemption only applies to city and county taxes) $3,112.50 - $425 = $2,687.50
An investor assumes a first mortgage loan of $88,000 at 8% and the seller takes back a second mortgage of $19,000 at 11%. The overall rate on both mortgages would be: A. 8.5% B. 9.0% C. 9.5% D. 10%
$88,000 (1st mortgage) x .08 (8%) = $7,040 (1st mortgage interest). $19,000 (2nd mortgage) x .11 (11%) = $2,090 (2nd mortgage interest). $7,040 + $2,090 = $9,130 (total interest on both loans). $88,000 (1st) + $19,000 (2nd) = $107,000 (total loan amount). $9,130 interest ÷ $107,000 loan amount = .085 or 8.5%
Types of Questions
(1) Percentage questions include commission, net listing, profit or loss, principal and interest, or interest only computations. (2) Square footage questions include how many lots or what size lot can be developed, and replacement costs. (3) Formula questions include memorizing formulas. They can be comparable sales appraisal questions or specific formulas for IRV, or taxable values.
Ad Valorem Tax: A blind widow has a homestead exemption on a property with an assessed value of $48,000. If the total millage rate is 22 mills, her annual taxes would be: A. $484 B. $586 C. $756 D. $1,056
A. Annual taxes = Taxable value x Millage rate. $25,000 (basic) + $500 (widow) + $500 (blind) = $26,000 (total exemptions). $48,000 (assessed value) ‐ $26,000 (exemptions) = $22,000 (taxable value). $22,000 (taxable value) x .022 (22 mills) = $484 (annual tax amount) Additional Exemptions - $500 for Widows. - $500 for Blind People. - $5,000 for Veterans.
Mrs. Smith sold two 60‐acre tracts for $2,000 per acre. Profit on one sale was 20%; loss on the other sale was 20%. What was her loss or gain? A. $10,000 B. $20,000 C. $30,000 D. $40,000
A. $2,000 x 60 = $120,000 Sale Price for each Tract. $120,000 ÷ 1.20 = $100,000 Originally Paid for Tract with 20% Profit $120,000 ‐ $100,000 = $20,000 Profit. $120,000 ÷ .80 = $150,000 Originally Paid for Tract with 20% Loss $120,000 ‐ $150,000 = ($30,000) Loss. $20,000 ‐ $30,000 = ($10,000) Net Loss
Nonhomestead property with an assessed value of $137,500 is sold and the closing takes place on April 12th. If the day of closing is charged to the buyer, how is the proration for taxes listed on the closing statement under the 365 day method if the millage rate is 24 mills? A. $913.15 debit to the seller and $913.15 credit to the buyer. B. $913.15 credit to the seller and $913.15 debit to the buyer. C. $2286.85 debit to the seller and $913.15 credit to the buyer. D. $3,300 debit to the seller and $913.15 credit to the buyer.
A. Nonhomestead = no exemptions. $137,500 (assessed value) x .024 (24 mills) = $3,300 (Total tax). $3,300 ÷ 365 days = $9.0411 (daily tax amount). 31 (Jan) + 28 (Feb) + 31 (Mar) + 11 (Apr) = 101 seller days. $9.0411 (daily tax) x 101 (seller days) = $913.15 debit to seller and $913.15 credit to buyer
An apartment complex has 3 apartments rented for $400 each, 6 apartments rented for $360 each, and 6 apartments rented for $350 each. All apartments are rented on a monthly basis with rental payments due on or before the first of each month. If the gross rent multiplier is 55, what is the value of the property? A. $275,000 B. $300,300 C. $305,000 D. $325,000
B. $400 x 3 = $1,200 $360 x 6 = $2,160 $350 x 6 = $2,100 = $5,460 total monthly rent. $5,460 x 55 GRM = $300,300 property value.
Real Estate Commission: A real estate sales associate's agreement with their broker gives the sales associate 60% of all commissions earned by the firm. If a property sells for $145,000 and the firm earns a 6% commission, what would be the sales associate's share? A. $3,480 B. $5,220 C. $8,700 D. $9,870
B. $145,000 x 0.6 commission = $8,700. 60% of $8,700 = $5,220.
A building rents for $20 per square foot based on a CPI (rent index) of 1.5. If the CPI increases to 1.8, what would be the new rent per square foot? A. $22 B. $24 C. $26 D. $28
B. $20 (rent per sq. ft.) ÷ 1.5 (old CPI) = $13.3333 $13.3333 x 1.8 (new CPI) = $24 (new rent per sq. ft.)
A lot measures 240' x 660' and costs $21,780 per acre. What is the cost per square foot? A. $0.30 B. $0.50 C. $1.00 D. $5.00
B. $21,780 per acre ÷ 43,560 sq. ft. per acre = $.50
Principal & interest with amortized or level payment loan: How much of the second loan payment would apply to principal if the loan was originally $175,000 at 6% over 30 years with a monthly payment of $1,049.21? A. $174.21 B. $175.08 C. $874.13 D. $875
B. Formula: Principal x Rate x Time (in months) = Interest. $175,000 (initial loan) x 6% (interest) = $10,500 (12 mo. interest) $10,500 ÷ 12 = $875 (1st month interest) $1,049.21 (payment) ‐ $875 (interest part) = $174.21 (1st mo. principal part). $175,000 (original balance) ‐ $174.21 (principal paid) = $174,825.79 (new loan balance) $174,825.79 (balance at start of 2nd mo.) x 6% = $10,489.55 (12 mo. interest) $10,489.55 ÷ 12 = $874.13 (2nd month interest) $1,049.21 (payment) ‐$874.13 (interest part) = $175.08 (2nd mo. principal part)
A property has a potential gross income of $450,000. Fixed and variable operating expenses have been calculated at $112,000 annually. The property is being operated at a vacancy rate of 2% with $4,000 being held in reserve for replacements. If the property sells for $2 million, what is the capitalization rate? A. 14.25% B. 15.65% C. 16.25% D. 17.65%
C. PRI - V&C + OI ----------- = EGI - OE ----------- = NOI Stack formula: $450,000 (PGI) x .02 (V&C rate) = $9,000 (V&C) $450,000 (PGI) - $9,000 (V&C) = $441,000 (EGI) $441,000 (EGI) - $112,000 (OE) - $4,000 (R) = $325,000 (NOI) IRV formula: $325,000 (NOI) ÷ $2,000,000 (Value) = .1625 or 16.25% (cap rate)
Jane has hired Gold Star Realty to sell her house. She has closing costs and expenses of $4,200. She must net $150,000 from the sale. Jane agreed to pay Gold Star a 6% commission. At what price must the house sell for Jane to achieve her goals? A. $159,574.74 B. $163,452 C. $164,042.55 D. $167,455
C. $150,000 Net + $4,200 Closing Costs and Other Expenses = $154,200 Total $154,200 ÷ .94 = $164,042.55 (Commission is 6% so Jane's share of the sale is 94%)
Size of lot after a setback: A lot measures 165 feet by 165 feet. If there are setbacks on all four sides of 10 feet, what square footage could be developed on this lot? A. 18,500 B.. 19,525 C. 21,025 D. 23,025
C. 165 ft. (side length of lot) ‐ 20 ft. (10 ft. setback x 2 for each end of side) = 145 ft. (usable side length). 145 ft. x 145 ft. = 21,025 sq. ft (available for development)
A house is valued at $65,000. The monthly rent is $500, monthly debt service is $375, and annual taxes are $840. If there are no other expenses, what is the gross rent multiplier (GRM)? A. 75 B. 80 C. 130 D. 175
C. GRM = Sales Price ÷ Monthly Rent GRM = $65,000 ÷ $500
An income-producing property has an gross income of $30,000 and expenses of $12,000. The rate of return expected is 12%. What is the value of the property? A. $250,000 B. $100,000 C. $150,000 D. $75,000
C. Income = Rate x Value $18,000 = 0.12 x V V = $150,000
IRV Formula: If the net operating income is $65,000 and the capitalization rate is 6%, which of the following would represent the value of this property? A. $756,733 B. $853,067 C. $1,083,333 D. $1,115,986
C. Income = Rate x Value $65,000 = .06 x Y Y = $1,083,333
Tax Proration Questions
Credit to the buyer. Debit to the seller. ALWAYS.
# Lots for a parcel of land: A developer purchases a 65 acre tract to develop into lots of 8,500 square feet each. How many lots could be developed if roads total 900 feet in length and 30 feet in width and there is a common area of 400,000 square feet? A. 250 B. 260 C. 272 D. 282
D. 65 acres x 43,560 sq. ft. per acre = 2,831,400 sq. ft. 900 ft. x 30 ft. = 27,000 sq. ft (roads) 2,831,400 sq. ft. (total) - 27,000 sq. ft. (roads) - 400,000 sq. ft. (common) = 2,404,400 sq. ft. (available for lots) 2,404,400 sq. ft. (available) ÷ 8,500 sq. ft. (each lot size) = 282.87 or 282 lots Round down for the number of full lots
Profit or Loss: A property was purchased for $140,000 and later sold for $156,500. Which represents the profit percentage earned in this transaction? A. 5% B. 8% C. 10% D. 12%
D. Divide what is made by what is paid. $156,500 (purchase price) - $140,000 (sales price) = $16,500 (amount made). $16,500 (amount made) ÷ $140,000 (amount paid) = .117857 or 12%
Net listing: A seller wants to net $50,000 after paying off a loan of $65,000 and a real estate commission of 5%. Which list price would give the seller his or her net? A. $106,500 B. $120,750 C. $120, 950 D. $121, 053
D. $50,000 (seller's net) + $65,000 (loan payoff amount) = $115,000 (total) 100% - 5% (commission rate) = 95% (or .95) $115,000 (total) ÷ .95 = $121,052.63 (listing price)
Interest only loans: If an interest only loan has monthly payments of $825 and an interest rate of 5%, what was the original loan balance? A. $156,000 B. $165,000 C. $178,000 D. $198,000
D. $825 (monthly payment) x 12 months = $9,900 (1 year of payments) $9,900 ÷ .05 (5% interest) = $198,000 (original loan balance)
If you purchased property for 60% of the asking price and later resold the property for 100% of the original asking price, what is your profit? A. 20% B. 33.33% C. 40% D. 66.66%
Made ÷ Paid = Profit Margin 40% ÷ 60% = 66.66%
