GENERAL MATH PROBLEM CATEGORIES AND ILLUSTRATED SOLUTIONS MEASUREMENT STANDARDS WHICH MUST BE MEMORIZED FOR THE BROKER TEST


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1 Chapter 17 Math Problem Solutions CHAPTER 17 GENERAL MATH PROBLEM CATEGORIES AND ILLUSTRATED SOLUTIONS MEASUREMENT STANDARDS WHICH MUST BE MEMORIZED FOR THE BROKER TEST Linear Measure 12 inches = 1 ft 3 ft = 1 yd 5,280 ft = 1 mile 640 acres = 1 sq mile 1 sq mile = 1 section 36 sections = 1 township Square Measure 144 sq inches= 1sq ft 9 sq ft = 1 sq yd 43,560 sq ft = 1 acre Cubic Measure 27 cubic feet = 1 cubic yard Tax Valuation X Dollars Per $100 AV = X/100 = Tax Rate Divide the AV by 100, then multiply by X Dollars X Mils Per $1 AV Divide the AV by 1000, then multiply by X Mils Area Formulas Formula for rectangle: Formula for square: Formula for triangle: MATHEMATICS Percentages a r e a a r e a a r e a === = l e n g t h x w i d t h = s i d e x s i d e = base X height X 0.5 To use a percentage in an arithmetic calculation, change the percentage to its decimal equivalent. The rule for changing a percentage to a decimal is to remove the percent sign and move the decimal point two places to the left (or divide the percentage by 100). Examples of converting a percentage to a decimal are: 98% = / 2 % = 1.5% = % = / 4 % = 1.25% = % = / 4 % = 0.75% =
2 Chapter 17 Math Problem Solutions To change a decimal or a fraction to a percentage, simply reverse the procedure. Move the decimal point two places to the right and add the percent sign (or multiply by 100). Some examples of this operation are: 1.00 = 100% 0.90 = 90% = 0.75% 1 / 2 = 1 2 = 0.5 = 50% 3 / 8 = 3 8 = = 37.5% 2 / 3 = 2 3 = = 66.7% Commission Problems Problems involving commissions are readily solved by the Formula: sales price X rate of commission = total commission Sales 1. A real estate broker sells a property for $90,000. Her rate of commission is 7%. What is the amount of commission in dollars? Product Missing = multiply Solution Step 1  sales price x rate = commission Calculation $90,000 x 0.07 = $6,300 Answer: $6,300 commission 2. 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? Factor Missing = Divide Solution Step 1  sales price = commission dollars divided by commission rate Calculation $6000/.06 = $100,000 Answer: $100,000 sales price 3. A real estate broker earns a commission of $3,000 in the sale of property for $50,000. What is her rate of commission? Factor missing = divide Solution Step 1  commission dollars divided by sales price = rate of commission Calculation $3,000/50,000 = 6% Answer = 6% commission rate Rentals 1. 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? Solution Step 1 Actual Occupancy Rate = 100%  Vacancy Rate Calculation  100% % = 95.5% = Actual Occupancy Rate Solution Step 2 Actual Rent Dollars = Potential Gross Rent x Occupancy Rate Calculation = $120,000 x 95.5% = $114,600 Solution Step 3  Actual Rent x Commission Rate = Commission Dollars 444
3 Chapter 17 Math Problem Solutions Calculation $114,600 x 9% = $10,314 = Commission Dollars Answer: $10,314 commission Commission Splits 1. 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? Solution Step 1 Selling Price x Commission Rate = Commission Dollars Calculation  $65,000 x 7% = $4,550 Solution Step 2 Total Commission x Share Percentage = Share Dollars Calculation  $4,550 x 60% = $2,730 Answer: $2,730 Estimating Partial Sales of Land 1. 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? Solution Step 1 Original Number of Lots x Percentage Sold by Broker = Number of Lots Remaining Calculation 400 x 25% = 100 lots. 400 Lots minus 100 Lots = 300 Lots Solution Step 2 Remaining Lots x % Sold by Sales Force = Number of lots Sold by Agents Calculation 300 x 50 % = 150 Lots Solution Step 3 Add the number of lots sold Calculation = 250 Solution Step 4 Original Number of Lots less the Number of Lots Sold = Number of Lots Remaining Calculation = 150 Answer: 150 lots still unsold Profit/Loss on Sale of Real Estate The formula for profit is: investment X percent of profit = dollars in profit The formula for loss is: investment X percent of loss = dollars lost 1. Mr. Wong buys a house for investment purposes for $48,000. He sells it six months later for $54,000 with no expenditures for fixup or repair. What is Mr. Wong's percentage of profit? Solution Step 1 Sales Price less Original investment = Profit Dollars Calculation = $54,000  $48,000 = $6,000 Solution Second Step Profit Dollars divided by Original Investment Dollars = % Profit Calculation = $6,000/$48,000 = 12.5% Answer: 12.5% Profit 445
4 Chapter 17 Math Problem Solutions 2. 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? Solution Step 1 Purchase Price Plus Improvements = Current Investment Calculation = $35,000 + $15,500 = $50,500 Solution Step 2 Investment less Selling Price = Loss Calculation = $50,500  $46,000 = $4,500 loss Solution Step 3 = Loss divided by Investment = Percent Loss Calculation = $34,500/$50,500 = 8.91% Answer: 8.91% AREA CALCULATIONS Acreage 1. 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.) Solution Step 1 An Acre has 43,560 square feet Solution Step 2 If Length x Width = Area then Length = Area/Width Calculation = Length = 43,560/330 = 132 feet Answer: 132 foot long lot 2. If a parcel of land contains 32,670 square feet, what percent of an acre is it? Solution Step 1 43,560 square feet in an Acre Solution Step 2 Part of Area divided by the Total Area = % area Calculation 32,670 square feet / 43,560 = 75% of an acre Answer: 75% of an acre Square Footage 1. A rectangular lot measures 185 feet by 90 feet. How many square feet does this lot contain? Solution Step 1 = Length x width = Area Calculation = 185 x 90 = 16,650 square feet Answer: 16,650 sq ft area 2. A room measures 15 feet by 21 feet. We want to install walltowall carpeting and need to calculate the exact amount of carpeting required. Solution Step 1 Carpeting sold by square yard, so need answer expressed in square yards Solution Step 2 Calculate Area of Carpet in square feet Length X Width = Area Calculation 15 x 21 = 315 square feet. Solution 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 Answer: 35 square yards 3. A new driveway will be installed, 115 feet by 20 feet. The paving cost is $0.65 per square foot. What will be the minimum cost to pave the new driveway? Solution Step 1 Length X Width Area Calculation 115 x 20 = 2,300 square feet Solution Step 2 Cost of paving driveway  $0.65 per square foot Area X Cost/SF = Price Calculation 2,300 x.65 per square ft = $1,495 Answer: $1,
5 Chapter 17 Math Problem Solutions 4. A house measures 28 feet wide by 52 feet long and square foot? Solution step 1 Length X Width = Area Calculation 28 x 52 = 1,456 square feet Solution Step 2  Area x Price per sf = Selling Price Solution Step 3  Price per sq. ft. = Selling Price/sf Calculation  $64,000/1,456 = $43.96 = Price per sf Answer: $43.96/sq per ft sq ft sells for $64,000. What is the price per Cost/Size 5. 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? Solution Step 1  Area of a Triangle = Length X Width divided by 2 Calculation (200 x 500)/2 = 50,000 square feet Solution Step 2 Area x Price per sq ft. = Sales Price Calculation 50,000 x $0.10 = $5,000 = Sales Price Answer: $5,000 Sales Price Tax Problems 1. 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? Solution Step 1 Assessed Value X Equalization Factor = Equalized Assessed Value Calculation  $80,000 x 1.5 = $120,000 = Equalized Assessed Value Solution Step 2 Equalized Assessed Value times $1.50/100 = Tax Bill Calculation  $120,000 x $1.50 = $180,000/100 = $1,800 Tax Bill Answer: $1,800 annual taxes 2. A property sells at the assessed value. The annual real property tax is $ 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? Solution Step 1  assessed value = taxes/tax rate Calculation X = $706.56/$1.15/$100 = $ x 100/$1.15 = $61,440 Solution Step 2 Assessed value divided by the equalization factor = Equalized Assessed Value Calculation  $61,440/1.2 = $51,200 = Equalized Assessed Value Solution Step 1 Equalized Assessed value divided by the Assessment Rate = Selling Price Calculation  $51,200/.8 = $64,000 = Selling Price Answer: $64,000 is selling price 3. 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? Solution Step 1 Assessed Value x Equalizer = Equalized Assessed Value Calculation = $68,000 x 1.3 = $88,400 Solution 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 Answer: tax rate $1.25 per $100 of tax value 447
6 Chapter 17 Math Problem Solutions 4. 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). Solution Step 1: Market Value x Assessment rate = Assessed Value Calculation  $70,000 x.8 = $56,000 Solution Step 2 Assessed Value x Equalizer = Equalized Assessed Value Calculation  $56,000 x 1.5 = $84,000 Solution Step 3 Equalized Assessed Value divided by 120 mills/$1000 = Annual Tax Bill Calculation $84,000/1000 = x 120 = $10,080 Annual Tax Bill Solution Step 4 Annual Tax Bill/2 = Semiannual Tax Bill Calculation  $10,080/2 = $5, 040 Semiannual Tax Bill Answer: $5,040 semiannual tax bill TRANSFER TAX CALCULATIONS The conveyance in Illinois is taxed as a result of the Illinois Real Estate Transfer Tax Act. The amount subject to taxation is the sales price minus any assumed mortgage or mortgage taken "subject to." State tax  $0.50 per $500 or fraction thereof, County tax  $0.25 per $500 or fraction thereof If the total amount of consideration is less than $100 no tax is required. 1. A property sold for $125,000. The purchaser assumed a mortgage on the property in the amount of $37,450. What is the total amount of transfer tax? Solution Step 1Sales price minus assumed mortgage = taxable amount Calculation  $125,000  $37,450 = $87,550 Solution 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 Solution Step 3 State Tax = Number of Units x $0.50 Calculation 176 x $0.50 = $88.00 Solution Step 4 = County Tax = Number of Units x $0.25 Calculation 176 x $0.25 = $44.00 Solution Step 5 Total Transfer Tax = State Tax plus County Tax. Calculation = $ = $ Answer: $132 total amount of transfer tax PRORATIONS AT CLOSING Proration Rules day Standard Month day standard Year 3. Seller is in possession of the property on the day of closing 448
7 Chapter 17 Math Problem Solutions 1. In preparing a statement for a closing to be held August 14, a real estate broker determines that the annual real 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? Solution Step 1 Determine the monthly Tax Amount Calculation  $360/12 = $30 per month Solution Step 2 Determine the Daily Tax Amount Calculation  $30/30 = $1 per day Solution Step 3 = Determine the Total Monthly Taxes Owed Calculation  $30 X 7 (through July) = $210 Solution Step 4 Determine the Total Monthly Taxes for the month of closing Calculation  $1 x 14 = $14 Solution Step 5 Add the total Tax Amount Calculation  $210 + $14 = $224 Answer: $224 buyer credit (this is the seller's share of the real property taxes to cover the 7 months and 14 days of the tax year during which he owned the property). FINANCIAL CALCULATIONS Simple Interest Interest calculations use the formula: loan balance X rate of interest = annual interest 1. A loan of $15,000 is repaid in full, one year after the loan is made. If the interest rate on the loan is 12.5%, what amount of interest is owed? Solution Step 1 Principle x interest rate = interest dollars Calculation  $ 15,000 x 12.5% = $1,875 Interest Dollars Answer: $1,875 interest Principal and Interest 2. On October 1, a mortgagor makes a $300 payment on 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? Solution Step 1 Monthly Interest x 12 = Annual Interest Calculation  $200 x 12 = $2,400 Solution Step 2 Annual Interest Dollars divided by Interest Rate = Principal Calculation  $2,400/10% (.10) = $24,000  Principal Answer: $24,000 mortgage balance on date of payment 3. If an outstanding mortgage balance is $16, on the payment date and the amount of the payment applied to interest is $150, what is the rate of interest charged on the loan? Solution Step 1 Monthly Interest x 12 = Annual Interest Calculation  $150 X 12 mo = $1,800 annual interest Solution Step 2  Principal x Rate = Interest Dollars Rate = Interest Dollars/Principal Calculation  $1,800/16, = 11% Interest Rate 449
8 Chapter 17 Math Problem Solutions Debt Service 1. A mortgage loan of $50,000 at 11% interest requires monthly payments of principal and interest of $ to fully amortize the loan for a term of 20 years. If the loan is paid over the 20year term, how much interest does the borrower pay? Solution Step 1 Monthly Principal & Interest pmts x 12 = Annual Princ & Int Pmts Calculation  $ x 12 = $6, Solution Step 2 Annual P&I x 20 = Total 20 year principal & interest pmts Calculation  $6, x 20 = $123,864 Solution Step 3 Total P&I Pmts less Original Loan = Interest Dollars Calculation  $123,864  $50,000 = $73,864 Answer: $73,864 interest paid Fees and Points The formula for calculating the dollar amount owed in points on a loan is: loan X number of points (percentage) = dollars in points 1. A house sells for $60,000. The buyer obtains an 80% loan. If the bank charges 3 points at closing, how much in points must the buyer pay? Solution Step 1 Determine the loan Amount Selling Price x LTV Calculation  $60,000 x80% = $48,000 Loan Solution Step 2 Multiply points times Loan = Point Payment Calculation  $48,000 x 3% (.03) = $1,440 Points Payment Answer: $1,440 points payment 2. Mr. and Mrs. Schmidt borrow $64,000. If they pay $4,480 for points at closing, how many points are charged? Solution Step 1 Divide the Point Dollars by the Loan Dollars = Percent of Loan Calculation  $4,480/$64,000 = 7% Solution Step 2 Each Percentage of the loan equals 1 point Calculation 7% = 7 Points Answer: 7 points 3. Mr. and Mrs. Ortega borrow $55,000 at 11% interest for 30 years. The bank requires 2 months interest to be placed in escrow and a 1% loan origination fee to be paid at closing. What is the amount of interest to be escrowed? What is the amount charged for the loan origination fee? Solution Step 1 Annual interest = Principal x Interest Rate Calculation  $55,000 x 11% = $6,050 Annual Interest Solution Step 2 Annual interest divided by 12 = monthly interest Calculation  $6,050/12 = $ Monthly Interest Solution Step 3 2 x monthly interest = Two Months Interest Escrow Calculation 2 x $ = $1, Interest Escrow Answer 1: $1, interest escrow Solution Step 1 Loan times Origination Fee Percentage = Origination Fee Dollars Calculation $ 55,000 x 0.01 = $ Loan origination fee Answer: $550 loan origination fee 450
9 Chapter 17 Math Problem Solutions LoantoValue Ratios 1. In problem 8 above, the appraised value of the home purchased is $68,750. What is the loantovalue ratio? Solution Step 1 Loan divided by Selling Price = Loan to Value Ratio Calculation  $55,000/68,750 = 80% Loan to Value Ratio Answer: 80% loantovalue ratio Yields The percentage of profit is called the yield of the loan. Yields on loans are increased by points paid at closing. Each point charged has the effect of raising the interest rate 1/8 percent. 1. The First Bank lends $100,000 to the borrower and charges 3 points at closing. The interest rate on the loan is 12% for 25 years. What is the bank's effective yield on the loan? Solution Step 1 Each point raises Yield by 1/8%  Multiply 3 points by 118% Calculation 3 x 1/8 = 3/8% Solution Step 2 Convert 3/8 fraction to decimals Divide 3 by 8 Calculation 3/8 = 0.375% Solution Step 3 Add original Interest and Point Equivalent interest to get total interest Yield Calculation 12% +.375% = % Yield Answer: % Yield Qualifying for a Loan The typical housing debttoincome ratio for conventional loans is 2528%. The typical total debttoincome ratio for conventional loans is 3336%. The 2528% means that for the borrower to qualify, PITI (principal, interest, taxes, insurance) must not be more than 2528% of the borrower's monthly gross income. The 3336% means that for the borrower to qualify, the total monthly expenses (including housing expense) must not be more than 3336% of the borrower's monthly gross income. 1. Mr. and Mrs. Jones have a combined total monthly income of $2,500. If the lender requires a debttoincome ratio of 25:33 for housing and total expenses, what is the maximum house payment the Joneses will qualify for? What is the maximum total monthly expenses besides PM that will be allowed? Solution Step 1 Calculate 25% of the Gross monthly Income for PITI Calculation  $2,500 x 25% (.25 ) = $625 PITI Solution Step 2 Calculate 33% of the Gross Monthly Income for Total Debt Calculation  $2,500 x 33% (.33) = $825 Total Debt Solution Step 3 Subtract the PITI Dollars from the Total Debt Dollars = Other Debt Calculation  $825  $625 = $200 for other debt Answer: $200 for other debt 451
10 Chapter 17 Math Problem Solutions Appraisal Calculations Capitalization, income approach, Cap Rate Approach Under the income approach, the estimate of value is arrived at by capitalizing the annual net income. The solution to these problems is based on the following formula: Value X Capitalization rate = Net Operating Income 1. An apartment building produces a net income of $4,320 per annum. The investor paid $36,000 for the apartment building. What is the owner's rate of return (cap rate) on the investment? Solution Step 1 Value X Cap Rate = Net Operating Income so Net Operating Income/Value = Cap Rate Calculation  $4,320/$36,000 = 12% Cap Rate Answer: 12% annual rate of return on investment cap rate 2. An investor is considering the purchase of an office building for $125,000. The investor insists upon a 14% return on investment. What must be the amount of the annual net income from this investment to return a profit to the owner at a rate of 14%? Solution Step 1  Value X Cap Rate = Net Operating Income Calculation  $125,000 x 14% (.14) = $17,500 Net Operating Income Answer: $17,500 net operating income needed 3, In appraising a shopping center, the appraiser establishes that the center produces an annual net income of $97,500. The appraiser determines the capitalization rate to be 13%. What should be the appraiser's estimate of market value for this shopping center? Solution Step 1  Value X Cap Rate = Net Operating Income so Value = Net Operating Income/Cap Rate Calculation $97,500/13%(.13) = $750,000 Answer: $750,000 market value Basis 1. Mr. and Mrs. Swift purchased their home 15 years ago for $32,500. During their ownership, they made capital improvements totaling $19,400. They sold the home for $72,900. What amount of gain did they make on the sale? Solution step 1 Purchase Price Plus Improvements = Basis Calculation  $32, ,400 = $51,900 Basis Solution Step 2 Selling Price less Basis = Gain/Profit Calculation  $72,900 less $51,900 = $21,000 Gain/Profit Answer: $21,000 gain/profit 452
11 Chapter 17 Math Problems & Answers CHAPTER 17  MATH QUESTIONS 1. The value of your house, not including the lot, is $91,000 today. What was the original cost if it has depreciated 5 percent per year for the past seven years? A. $67, B. $95, C. $122, D. $140, What did the owners originally pay for their home if they sold it for $98,672, which gave them 12 percent profit over their original cost? A. $86,830 B. $88,100 C. $89,700 D. $110, What would you pay for a building producing $11,250 annual net income and showing a minimum rate of return of 9 percent? A. $125,000 B. $123,626 C. $101,250 D. $122, An owner agrees to list his property on the condition that he will receive at least $47,300 after paying 5 percent broker's commission and paying $1,150 in closing costs. At what price must it sell? A. $48,450 B. $50,815 C. $50,875 D. $51, A gift shop pays rent of $600 per month plus 2.5 percent of gross annual sales in excess of $50,000. What was the average monthly rent last year if gross annual sales were $75,000? A. $1, B. $ C. $ D. $
12 Chapter 17 Math Problems & Answers 6. If your monthly rent is $1,050, what percent would this be of an annual income of $42,000? A. 25 percent B. 30 percent C. 33 percent D. 40 percent 7. Two managing brokers split the 6 percent commission on a $73,000 home. The selling licensee was paid 70 percent of his broker's share. The listing licensee was paid 30 percent of her broker's share. How much did the listing licensee receive? A. $657 B. $4,380 C. $1,533 D. $1, The buyer has agreed to pay $175,000 in sales price, 2.5 loan discount points, and a 1 percent origination fee. If the buyer receives a 90 percent loantovalue ratio, how much will the buyer owe at closing for points and the origination fee? A. $1, B. $3, C. $5, D. $6, Calculate eight months of interest on a $5,000 interestonly loan at 9.5 percent. A. $ B. $ C. $ D. $ A 100acre farm is divided into lots for homes. The streets require one  eighth of the whole farm, and there are 140 lots. How many square feet are in each lot? A. 43,560 B. 35,004 C. 31,114 D. 27, What is the monthly net income on an investment of $115,000 if the rate of return is 12.5 percent? A. $1, B. $1, C. $7, D. $14, A licensee sells a property for $58,500. The contract he has with his managing broker is 40 percent of the full commission earned. The commission due the managing broker is 6 percent. What is the licensee's share of the commission? A. $2,106 B. $1,404 C. $3,510 D. $2,
13 Chapter 17 Math Problems & Answers 13. What is the interest rate on a $10,000 loan with semiannual interest of $450? A. 7 percent B. 9 percent C. 11 percent D percent 14. A warehouse is 80 feet wide and 120 feet long with ceilings 14 feet high. If 1,200 square feet of floor surface has been partitioned off from floor to ceiling for an office, how many cubic feet of space will be left in the warehouse? A. 151,200 B. 134,400 C. 133,200 D. 117, The lot you purchased five years ago for $30,000 has appreciated 3.5 percent per year. What is it worth today? A. $30,375 B. $33,525 C. $34,500 D. $35, A lease calls for $1,000 per month minimum plus 2 percent of annual sales in excess of $100,000. What is the annual rent if the annual sales were $150,000? A. $12,000 B. $13,000 C. $14,000 D. $15, There is a tract of land that is 1.25 acres. The lot is 150 feet deep. How much will the lot sell for at $65 per front foot? A. $9,750 B. $8,125 C. $23,595 D. $8, A woman earns $20,000 per year and can qualify for a monthly PITI payment equal to 25 percent of her monthly salary. If the annual tax and insurance is $678.24, what is the loan amount she will qualify for if the monthly PI payment factor is $10.29 per $1,000 of loan amount? A. $66,000 B. $43,000 C. $40,500 D. $35, You pay $65.53 monthly interest on a loan bearing 9.25 percent annual interest. What is the loan amount rounded to the nearest hundred dollars? A. $1,400 B. $2,800 C. $6,300 D. $8,
14 Chapter 17 Math Problems & Answers 20. What percentage of profit would you make if you paid $10,500 for a lot, built a home on the lot that cost $93,000, and then sold the lot and house together for $134,550? A. 13 percent B. 23 percent C. 30 percent D. 45 percent 21. An incomeproducing property has $62,500 annual gross income and monthly expenses of $1,530. What is the appraised value if the appraiser uses a 10 percent capitalization rate? A. $441,400 B. $625,000 C. $183,600 D. $609, A man pays $2,500 each for four parcels of land. He subdivides them into six parcels and sells each of the six parcels for $1,950. What was his percentage of profit? A percent B. 17 percent C. 52 percent D. 78 percent 23. A property sells for $96,000. If it has appreciated 4 percent per year straight line for the past five years, what did the owner pay for the property five years ago? A. $76,800 B. $80,000 C. $92,300 D. $115, If you purchase a lot that is 125 feet by 150 feet for $6,468.75, what price did you pay per front foot? A. $23.52 B. $43.13 C. $51.75 D. $ Calculate the amount of commission earned by a broker on a property selling for $61,000 if 6 percent is paid on the first $50,000 and 3 percent is paid on the remaining balance. A. $3,330 B. $3,830 C. $3,600 D. $3,
15 Chapter 17 Math Problems & Answers CHAPTER 17  MATH QUESTIONS ANSWER KEY 1.  D 2.  B 3.  A 4.  D 5.  D 6.  B 7.  A 8.  C 9.  B D B B B D D B C D D C A B B C A 457
16 Chapter 17 Math Problems & Answers Notes: 458
17 0" Chapter 17 Math Problems & Answers CHAPTER 17  MATH PROBLEM SOLUTIONS 1. $140,000 Original Cost 5% Depreciation per year x 7 years 35% Total Depreciation $140,000 Original Cost x 65% = $91,000 Today's Value 2. $88,100 Original Cost = 12% Profit = 112% is the Sales Price $98,672 Sales Price/112% = $88,100 Original Cost 3. $11,250 Net Operating Income divided by cap rate = Selling Price $11,250/.09 = $125,000 Selling Price 4. $47,300 Net to Seller and $1,150 Closing Costs $47,300 + $1,150 = $48,450 Before Commission Commission = 5% therefore Dollars before Commission = 95% $48,450/.95 = $51,000 Selling Price 5. $ Average Monthly Rent $75,000 Gross Annual Sales $50,000 Excluded from Percentage Calculation 2.5 % of Net Gross Annual Sales $75,000  $50,000 = $25,000 Gross Annual Sales used for Rent Calculation $25,000 x 2.5% = $625 Annual Percentage Rent $625/12 = $52.08 = Monthly Percentage Rent Base Rent = Monthly Percentage Rent = Average Monthly Rent $ $52.08 = $ $1,050 Monthly Rent x 12 = $12,600 Annual Rent $42,000 Annual Income Annual Rent/Annual Income = A Rent compared to Annual Income $12,600/$42,000 = 30% 7. $73,000 Selling Price and 6% commission $73,000 x 6% = $4,380 Full Commission Managing Brokers shared commission $4,380/2 = $2,190 = Managing Broker Share Listing Agent = 30% of Managing Broker's Share $2,190 x 30% = $ Listing Agent's Commission 459
18 Chapter 17  Math Problems & Answers 8. $175,000 Purchase Price  90% Loan to Value Ratio $175,000 x.9 = $157,500 loan $157,000 Loan, 2.5 Discount Points and 1 Point Loan Origination Fee 3.5 points total for this loan 1 point = 1% of the Loan 3.5 points = $157,000 x 3.5% = $5, for Total Points 9. $5,000 Loan and 9.5% Annual Interest $5,000 x 9.5% = $475 = Annual Interest Annual Interest divided by 12 = Monthly Interest $475/12 = $39.58 per month Eight months of interest = monthly interest x 12 $38.58 x 8 = $ ($38.58 not rounded off, but extra decimal places included) Acre Plot, 1/8 for streets 100 Acres x 87.5% = 87.5 Acres for Lots 87.5 x 43,560 sq. ft. per Acre = 3,811, 500 sq. ft. for lots 140 lots 3,811,500/140 = 27,225 sq. ft. per lot 11. Net Operating Income = Purchase Price x Cap Rate $115,000 x 12.5% = $14,375 Net Operating Income (Annual) Monthly NOI = Annual NOI/12 $14,375/12 = $1, = Monthly Net Operating income 12. Selling Price = $58,500 and Commission is 6%, with Licensee getting 40% $58,500 x 6% = $3,510 = Sponsoring Broker Commission $3,510 x 40% = $1,404 = Licensee's share of the Commission 13. $10,000 loan, $450 semiannual interest payment $450 x 2 = $900 = Annual Interest Payment $900/$10,000 = 9% Annual Interest 14. Warehouse = 80 x 120 feet in area and 14 feet high Total Cubic Feet = 80 x 120 x 14 = 134,400 Cubic Feet Office Space is 1200 sf x 14 ft. = 16,800 cubic feet Net Warehouse Cubic Space is Total Warehouse Space less Office Cubic Space 134,400 cubic feet  16,800 cubic feet = 117,600 net cubic feet for the warehouse 15. $30,000 original cost, 3.5% appreciation for 5 years 3.5% x 5 = 17.5% Appreciation Original 100% plus 17.5% = 117.5% = Current Value $30,000 x 117.5% = $35,250 = Today's Value 460
19 Chapter 17  Math Problems & Answers 16. $1,000 per month base rent, $150,000 Gross Annual Sales, $100,000 excluded from percentage Percentage of Gross Annual Sales = 2% Gross Sales for Percentage Calculation = $150,000 less $100,000 = $50,000 $50,000 x 2% = $1,000 Annual Percentage Rent $1,000 per month base rent x 12 = $12,000 Annual Base Rent Annual Base Rent and Percentage Rent = $12,000 + $1,000 = $13, acres and a selling price of $65 per front foot One side of the lot is 150 feet Area of lot = 1.25 x 43,560 = 54,450 sq. ft. Divide area by one side to obtain the length of the other side 54,450/150 = 363 feet 363 front feet x $65 per front foot = $23,595 selling price 18. Earns $20,000 per year, 25% PITT per month Annual Income/12 = Monthly income $20,000/12 = $1, per month 25% of Gross Monthly Income = $1,666.6 x 25% = $ for Monthly PITI TI (Taxes & Insurance) = $ per year $678.24/12 = $56.52 = Monthly TI $ $56.52 = $ available for PI (Principle & Interest Payment) $10.29 per $1,000 is the factor $360.15/$10.29 x $1,000 = $35,000 Loan 19. $65.53 per month interest and interest rate of 9.25% $65.53 x 12 = $ = Annual Interest Interest divided by rate = Loan $786.36/.0925 = $8,500 Loan 20. Paid $10,500 for lot and $93,000 for home Total Cost = $10,500 + $93,000 = 103,500 Selling Price = $134,550 Net Profit = Selling Price less Cost $134,500  $103,500 = $31,050 Percent Profit = Profit divided by Cost $31,050/$103,500 =.3 = 30% Profit 21. $1,530 monthly expenses, $62,500 Annual Gross Income,10% cap rate $1,530 x 12 = $18,360 = Annual Expenses Annual Net Operating Income = Annual Gross Income Less Annual Expenses $62,500  $18,360 = $44,140 Net Operating Income Net Operating Income Divided by Cap Rate = Purchase Price $44,140/.1 = $441,400 = Purchase Price 461
20 Chapter 17 Math Problems & Answers 22. $2,500 per parcel, 4 parcels = Cost $1,950 per parcel, 6 parcels = Sales $2,500 x 4 = $10,000 $1,950 x 6 = $11,700 Sales less Cost = Profit $11,700  $10,000 = $1,700 Profit Dollars divided by Cost Dollars = % Profit $1,700/$10,000 = 17% Profit 23. Property worth $96,000, 4% appreciation for 5 years 4% x 5 = 20% Current Value = 120% of original cost $96,000 = 120% of Original Cost Current Value divided by 120% = Original Value $96,000/1.2 = $80, $6, Price for lot on frontage foot basis, lot is 125 x 150 feet 125 is considered the front portion of the lot $6,468.75/125 = $51.75 = Price per front foot. 25. Selling Price of $61,000, 6% on first $50,000 and 3% on remaining $50,000 x 6% = $3,000 $61,000  $50,000 = $11,000 $11,000 x 3% = $330 $3, = $3,330 = Total Commission Notes: 462
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