1. June 16 Simplification of Real Estate Mathmatics 1

2. June 16 Simplification of Real Estate Mathmatics 2 Mathematical Impact on Test Most state tests have from five to fifteen mathematical problems on any given test. The Brokers’ test will tend to have a greater number of mathematical problems. Regardless, if you can gain three or four points by correctly answering math problems it will be beneficial.

3. June 16 Simplification of Real Estate Mathmatics 3 Your Mathematical Expertise You may be very proficient at math, and that should be helpful to you from a testing standpoint, and in actual practice in the business. Still, real estate is not based on mathematics, but rather on sales, negotiation and recognition of opportunities.

4. June 16 Simplification of Real Estate Mathmatics 4 If you are limited in mathematics, this is not the time to become a mathematician. If you have time try and learn the skill to answer a few basic problems. Don’t delay your test because you lack what you might consider a competent mathematical ability. You could, in fact, miss every math question and still easily pass the sale or brokers test.

5. June 16 Simplification of Real Estate Mathmatics 5 Calculators A.No “musical” calculators unless you can stop the music. B.No printing calculators. C.Programmable calculators are allowed. D.No alphanumeric calculators. E.We recommend that you use a simple, hand-held calculator with large numbers.

6. June 16 Simplification of Real Estate Mathmatics 6 The “Magic Circle” Divide Line Multiplication Line

7. June 16 Simplification of Real Estate Mathmatics 7 The Segments are Labeled A BC  X 

8. June 16 Simplification of Real Estate Mathmatics 8 The Working Segments  X A C Any number in this segment will be divided by numbers in “B” or by numbers in “C”. Giving the answer for the other. Any number in B can be divided into A and give you C or Multiplied by C and give you A B Any number in C can be divided into A and give you B or Multiplied by B and give you A 

9. June 16 Simplification of Real Estate Mathmatics 9 Circle Diagram Rules 1.Percentage always goes in C. 2.Little number in “A”, Big number in “B”, Where “C” is less than 100%. 3.Little number in “B”, Big number in “A”, Where “C” is greater than 100%. 4.“A” always gets divided by the others. 5.Always annualize figures.

10. June 16 Simplification of Real Estate Mathmatics 10 The Rules Visualized A  X CB  LESS than 100% BIG number Little Number %

11. June 16 Simplification of Real Estate Mathmatics 11 The Rules Visualized A  X CB  BIG number MORE than 100% Little Number %

12. June 16 Simplification of Real Estate Mathmatics 12 Capitalization Appraisal Problems A  X CB  Little Number Net Annual Income LESS than 100% CAP Rate BIG Number Property Value

13. June 16 Simplification of Real Estate Mathmatics 13 Let’s Try a Typical Problem 1.The net income of an apartment building went down $400 per month when a freeway was built nearby. If investors demand a 12% capitalization rate in this area, how much has the building lost in value? A.$3,333 B.$20,000 C.$36,000 D.$40,000

14. June 16 Simplification of Real Estate Mathmatics 14 Rule 5 – Always Annualize Figures Rule 5 tells us to always annualize figures. The problem gives us a rent loss of $400 per month. The capitalization rate is 12%, as stated it is already annualized. You will have to annualize the monthly loss of $400. $400X12 Months=$4,800 a Year

15. June 16 Simplification of Real Estate Mathmatics 15 Put Your Information In The Circle A  X CB  $4,800 Annual Loss 12% Value Loss %

16. June 16 Simplification of Real Estate Mathmatics 16 The Reasoning We know that the percentage, the 12% capitalization rate is less than 100% so the smaller number will go in “A” – we can presume that $4,800 is the smaller number since it is the lost income, the building value loss will be the greater number.

17. June 16 Simplification of Real Estate Mathmatics 17 The Calculation A  X CB  $4,800 Annual Loss 12% $40,000 %

18. June 16 Simplification of Real Estate Mathmatics 18 The Circle Points Out The circle tells us that we will divide the “C” segment, the 12% capitalization rate into “A” the rent loss of $4,800, and that will come to $40,000. $4,800  12%=$40,000 The $40,000 answer is at D, so the answer is D.

19. June 16 Simplification of Real Estate Mathmatics 19 Mark The Correct Answer 1.The net income of an apartment building went down $400 per month when a freeway was built nearby. If investors demand a 12% capitalization rate in this area, how much has the building lost in value? A.$3,333 B.$20,000 C.$36,000 D.$40,000

20. June 16 Simplification of Real Estate Mathmatics 20 Let’s Try Another Capitalization Problem Frederick, a typical real estate investor, wants to purchase a 40 unit apartment building that has an annual net income of $174,000. If Frederick uses an 8% capitalization rate how much will he be willing to pay? A.$1,400,000 B.$1,650,000 C.$1,985,000 D.$2,175,000

21. June 16 Simplification of Real Estate Mathmatics 21 Everything is Annualized All of the numbers in this problem are annualized, we don’t have to worry about that. The percentage is less than 100%, so the smaller number will go in the “A” segment of the circle.

22. June 16 Simplification of Real Estate Mathmatics 22 Our Circle Looks Like This A  X CB  $174,000 Net Operating Income 8% Frederick’s Estimate of Value %

23. June 16 Simplification of Real Estate Mathmatics 23 The Circle Tells Us 1.We need to find the answer for circle segment “B”. 2.We will divide “C” into “A”. 3.We will divide the 8% capitalization rate into the $174,000 net operating income. 4.Our answer will be $2,175,000.

24. June 16 Simplification of Real Estate Mathmatics 24 The Finished Circle Looks Like This A  X CB  $174,000 8% $2,175,000 %

25. June 16 Simplification of Real Estate Mathmatics 25 The Answer Is You were given several answers as follows; A.$1,400,000 B.$1,650,000 C.$1,985,000 D.$2,175,000

26. June 16 Simplification of Real Estate Mathmatics 26 This is Another Type of Capitalization Question A small income property generates a monthly gross income of $1,000. Over the last five years it has been vacant for three months. The annual expenses are $3,000. If an appraiser applies a 12% capitalization rate to this property, what will the value of the building be? A.$58,000 B.$65,000 C.$70.000 D.$90,000

27. June 16 Simplification of Real Estate Mathmatics 27 Break The Problem Down The problem has been given to you with monthly rent. That will have to be annualized. The second problem is that they have given you a vacancy factor for a 5 year period. The third dilemma is the problem has assigned an annual expense factor of $3,000. Finally, the capitalization rate has been given to you as an annual rate.

28. June 16 Simplification of Real Estate Mathmatics 28 Make It Understandable 1.Annualize the rent. $1,000 a month times 12 months would be $12,000 a year. 2.Figure the 5 year rent. $12,000 a year times 5 years equals $60,000. 3.Subtract the five year vacancy factor. $60,000 less $3,000 equals $57,000. 4.Annualize the five year gross rents. $57,000 divided by 5 years equals $11,400 a year. 5.Subtract the annual $3,000 expense from the average annual rent. $11,400 less $3,000 equals $8,400.

29. June 16 Simplification of Real Estate Mathmatics 29 Place Your Adjusted Information In the Magic Circle A  X CB  $8,400 12% Estimated Value %

30. June 16 Simplification of Real Estate Mathmatics 30 The 12% Capitalization Rate has to go in segment “C”, the small number, the Net Operating Income will have to go into “A”, you will divide “C” into “A” to find the answer for “B”, the estimated value of the building. A  X CB  $8,400 12% $70,000 %

31. June 16 Simplification of Real Estate Mathmatics 31 You Apply Your Answer A small income property generates a monthly gross income of $1,000. Over the last five years it has been vacant for three months. The annual expenses are $3,000. If an appraiser applies a 12% capitalization rate to this property, what will the value of the building be? A.$58,000 B.$65,000 C.$70.000 D.$90,000

32. June 16 Simplification of Real Estate Mathmatics 32 Investment Problems A  X CB  LITTLE Number INCOME/PROFIT/YIELD (Do not include return of original investment) (Less than 100%) RATE of RETURN BIG Number Amount Invested

33. June 16 Simplification of Real Estate Mathmatics 33 Finding Invested Amount How much would an investor need to invest in order to earn $75 per month from an investment which produces a 5% Return? A.$4,000 B.$9,000 C.$12,000 D.$18,000

34. June 16 Simplification of Real Estate Mathmatics 34 Break The Problem Down 1.They have given you a monthly return. Remember everything has to annualized. So, $75 X 12 Months = $900.00 2.The 5% Capitalization Rate is already annualized. We leave that at 5%. 3.We need to find the amount invested.

35. June 16 Simplification of Real Estate Mathmatics 35 A  X CB  $900 5% Amount Invested % Apply The ‘Magic Circle” Rules

36. June 16 Simplification of Real Estate Mathmatics 36 A  X CB  $900 5% $18,000 % Apply The ‘Magic Circle” Rules

37. June 16 Simplification of Real Estate Mathmatics 37 Equity Profit Upon Sale Joyce purchased a home for $125,000. She obtained a loan from the bank for 88% of the purchase price, payable at $1,549 per month, including 12% interest. Joyce sold the home for $139,750 before she even made the payment on the first loan. What was her equity at the time of the sale? A.$12,000 B.$14,750 C.$29,750 D.$18,000

38. June 16 Simplification of Real Estate Mathmatics 38 First Find The Loan 1.Initial Loan Amount equals $125,000 X 88% =$110,000 original loan amount is $110,000. 2.She has made no payments on the loan, so her loan balance has to be the same, $110,000. 3.Find the After Sale Equity. Sales Price less the loan amount equals the after sale equity. $139,750 - $110,000 = $29,750 $29,750 will be Joyce’s Equity

39. June 16 Simplification of Real Estate Mathmatics 39 Find The Loan Amount Using The Circle A  X CB  Find The Loan Amount 88% $125,000 Purchase Price %

40. June 16 Simplification of Real Estate Mathmatics 40 A  X CB  $110,000 88% $125,000 % Fill in The Loan Amount Purchase PriceX Percent loan to value=Amount of Loan $125,000X88%= $110,000

41. June 16 Simplification of Real Estate Mathmatics 41 Finish The Problem 1.$125,000X88%=$110,000 2.$139,500- $110,000=$29,750 The equity at sale is $29,750

42. June 16 Simplification of Real Estate Mathmatics 42 Select The Proper Answer Joyce purchased a home for $125,000. She obtained a loan from the bank for 88% of the purchase price, payable at $1,549 per month, including 12% interest. Joyce sold the home for $139,750 before she even made the payment on the first loan. What was her equity at the time of the sale? A.$12,000 B.$14,750 C.$29,750 D.$18,000

43. June 16 Simplification of Real Estate Mathmatics 43 Returns on Discounted Notes An investor purchased a $5,000 straight note for $4,500. (A straight note is interest only) The note is due in one year. The note bears an interest rate of 6%. What rate of return, as a percentage, will the investor receive at the end of one year? A.6% B.12% C.17.8% D.20%

44. June 16 Simplification of Real Estate Mathmatics 44 The Sequential Logic 1.Find the interest that will be earned in one year. $5,000X6%=$300 2.Find the money earned from the discount at the end of the year. Face -Purchase Price=Profit $5,000-$4,500=$500 3.You have two profit sources. The interest earned and the discount gained when the loan is repaid. This means that the return will be the interest earned plus the discount, or; $300+$500=$800

45. June 16 Simplification of Real Estate Mathmatics 45 A  X CB  Return = Interest Plus Discount Find % Return Total Investment % Fill The Information as Follows

46. June 16 Simplification of Real Estate Mathmatics 46 A  X CB  $300 + $500 = $800 ??% $4,500 % Find the Percent Return

47. June 16 Simplification of Real Estate Mathmatics 47 A  X CB  $800 17.78% $4,500 % Fill in The Loan Amount

48. June 16 Simplification of Real Estate Mathmatics 48 Pick Your Answer An investor purchased a $5,000 straight note for $4,500. (A straight note is interest only) The note is due in one year. The note bears an interest rate of 6%. What rate of return, as a percentage, will the investor receive at the end of one year? A.6% B.12% C.17.8% D.20%

49. June 16 Simplification of Real Estate Mathmatics 49 Finance Problems A  X CB  LITTLE Number INTEREST (Lender’s Profit) (Less Than 100%) INTEREST RATE BIG Number LOAN BALANCE

50. June 16 Simplification of Real Estate Mathmatics 50 Mary borrowed $26,500 using a straight note, for 20 years at an interest rate of 15% per annum. How much interest will Mary pay during the term of the note? A.$26,500 B.$79,500 C.$95,000 D.None of the above.

51. June 16 Simplification of Real Estate Mathmatics 51 The Logic of This Problem 1.The note is a straight note, so only interest is paid, no principal. This means we can figure it easily with a simple calculator. 2.The interest for one year on this note will be the face value of the note, multiplied by 15% or; $26,500 X 15% = $3,975. Mary is paying $3,975 each year. 3.Mary has the loan for 20 years, so she will have 20 Years X $3,975 = $79,500,

52. June 16 Simplification of Real Estate Mathmatics 52 Select The Answer That Matches Mary borrowed $25,650 using a straight note, for 20 years at an interest rate of 15% per annum. How much interest will Mary pay during the term of the note? A.$26,500 B.$79,500 C.$95,000 D.None of the above.

53. June 16 Simplification of Real Estate Mathmatics 53 Mary’s Problem has Circle Solutions – First Find The Interest A  X CB  Annual Interest Interest Rate Loan Amount

54. June 16 Simplification of Real Estate Mathmatics 54 Mary’s Problem has Circle Solutions – First Find The Interest A  X CB  $3,975 15% $26,500

55. June 16 Simplification of Real Estate Mathmatics 55 Second Step of Problem – Find The Total Interest Paid For The Term A  X CB  Total Interest Paid Period of Time Annual Interest

56. June 16 Simplification of Real Estate Mathmatics 56 Second Step of Problem – Find The Total Interest Paid For The Term A  X CB  $79,500 Total Interest Paid 20 Year $3,975 Per Year

57. June 16 Simplification of Real Estate Mathmatics 57 Select The Answer That Matches Mary borrowed $26,500 using a straight note, for 20 years at an interest rate of 15% per annum. How much interest will Mary pay during the term of the note? A.$26,500 B.$79,500 C.$95,000 D.None of the above.

58. June 16 Simplification of Real Estate Mathmatics 58 Second Finance Problem William is the beneficiary on a 10 year note. The annual interest rate is 8.4%. If in five years William has received $5,460 in interest, what is the principle amount of the loan? A.$5,460 B.$11,050 C.$13,000 D.$65,000

59. June 16 Simplification of Real Estate Mathmatics 59 Approaching The Problem 1.We know that the interest for 5 years is $5,460. 2.Rule #5 of the Circle Rules tells us to annualize all figures. To annualize this 5 year interest of $5,460 we will have to divide that by 5 years. 3.$5,460  5 Years = $1,092 a year. 4.The annual interest rate is 8.4%. We can conclude that 8.4% X some number = $1,092. 5. Little number in “A”, Big number in “B”, Where “C” is less than 100%.

60. June 16 Simplification of Real Estate Mathmatics 60 Place Numbers in Circle A  X CB  $1,092 Annual Interest Earned 8.4% Principle Amount of Note

61. June 16 Simplification of Real Estate Mathmatics 61 Divide “C” Into “A” to Get “B” A  X CB  $1,092 Annual Interest Earned 8.4% $13,000

62. June 16 Simplification of Real Estate Mathmatics 62 Apply The Answer William is the beneficiary on a 10 year note. The annual interest rate is 8.4%. If in five years William has received $5,460 in interest, what is the principle amount of the loan? A.$5,460 B.$11,050 C.$13,000 D.$65,000

63. June 16 Simplification of Real Estate Mathmatics 63 Finance Problem #3 John borrowed $20,000 from a bank to purchase a small piece of real estate. He paid 4 points to get the loan. The loan contained a 2% prepayment penalty, based upon the original loan amount. His monthly payment is $163.00 including interest at 8% per year. Five years later John sold the real estate and paid off the loan. If the loan had an average balance of $18,500, during the five years John owned the property, what was the bank’s gross profit on this loan? A.$7,000 B.$7,248 C.$8,600 D.$9,999

64. June 16 Simplification of Real Estate Mathmatics 64 Analyzing The Question What the question is really asking you is how much money has the lender made. This is a flip from most questions that ask how much has the borrower paid. Break the question down. 1.Total Points Paid. = $20,000 X 4% = $800 2.Total Pre-payment penalty 2% = $20,000 X 2% = $400 3.They give you an average balance so that you can estimate the interest paid. $18,500 X 8% = $1,480 X 5 Years = $7,400

65. June 16 Simplification of Real Estate Mathmatics 65 You Would Then Add The Three Areas of Profit Points= $ 800 Prepayment Penalty= $ 400 Total Interest= $7,400 Total Earned $8,600 The total earnings by the bank on this loan, with the information given is $8,600

66. June 16 Simplification of Real Estate Mathmatics 66 Total Bank Earnings Problem #3 John borrowed $20,000 from a bank to purchase a small piece of real estate. He paid 4 points to get the loan. The loan contained a 2% prepayment penalty, based upon the original loan amount. His monthly payment is $163.00 including interest at 8% per year. Five years later John sold the real estate and paid off the loan. If the loan had an average balance of $18,500, during the five years John owned the property, what was the bank’s gross profit on this loan? A.$7,000 B.$7,248 C.$8,600 D.$9,999

67. June 16 Simplification of Real Estate Mathmatics 67 The Magic Circle If we use the “Magic Circle” on this problem it would have to be implemented on all three of the questions. The Points would involve one circle, the Pre-Payment Penalty would involve another circle, and the interest would involve still a third circle. You would then add the three answers up and find the total 5 year earnings.

68. June 16 Simplification of Real Estate Mathmatics 68 Find the Earnings From Points A  X CB  $800 Earnings From Points 4% $20,000

69. June 16 Simplification of Real Estate Mathmatics 69 Calculating The Pre-Payment Penalty A  X CB  $400 Pre-Payment Penalty 2% $20,000

70. June 16 Simplification of Real Estate Mathmatics 70 Estimate the Total Interest Paid A  X CB  $1,480 Annual Interest 8% $18,500

71. June 16 Simplification of Real Estate Mathmatics 71 Add All The Income Sources Finally, the annual interest has to be estimated for the 5 year period. $1,480X5 Years=$7,400 Now you will add the three sources of income or earnings; 1.Points=$ 800 2.Pre-Payment=$ 400 3.Earned Interest=$7,400 Total Earnings=$8,600

72. June 16 Simplification of Real Estate Mathmatics 72 Commission Problems A  X CB  Little Number Commission (Figure the total commission received by broker) (Less Than 100%) Commission Rate Big Number Selling Price

73. June 16 Simplification of Real Estate Mathmatics 73 Commission Question #1 Broker Bob and Broker Bill agreed to divide a 4 ½ % Commission equally on the sale of a home, which sold for $162,500. Mary, the listing salesperson, works for Broker Bob on a 50-50 commission split. Mary would receive approximately how much commission as a result of the sale? A.$1,828 B.$2,828 C.$3,656 D.$7,312

74. June 16 Simplification of Real Estate Mathmatics 74 Logic of This Problem 1.First Broker Bob and Broker Bill split a 4 1/2 % commission. That is a 50-50 split between the brokers. 2.After the split between the brokers Broker Bob and Mary further split the commission that Broker Bob got, 50-50, or ½ each. 3.There are a number of ways to figure a correct answer for this problem.

75. June 16 Simplification of Real Estate Mathmatics 75 Our Solution Today Today we’ll first figure the total commission earned upon the close of escrow. That will be 4½% of $162,500. $162,500X4 ½%=$7,312.50 Each broker is to get ½ of this commission, or 50% each. $7,312.50X50%=$3,656.25

76. June 16 Simplification of Real Estate Mathmatics 76 Each Broker Now Has Their Half At this point both brokers are getting $3,656.25. Mary and Broker Bob are sharing this $3,656.25 ½ Each, or 50% each. Mary will get 50% of $3,656.25 $3,656.25X50%=$1,828.125 Mary’s share is $1,828.125

77. June 16 Simplification of Real Estate Mathmatics 77 The Closes Answer Would Be Broker Bob and Broker Bill agreed to divide a 4 ½% Commission equally on the sale of a home, which sold for $162,500. Mary, the listing salesperson, works for Broker Bob on a 50-50 commission split. Mary would receive approximately how much commission as a result of the sale? A.$1,828 B.$2,828 C.$3,656 D.$7,312

78. June 16 Simplification of Real Estate Mathmatics 78 Applying the Problem to the Circle A  X CB  $7,312.50 4 ½% $162,500

79. June 16 Simplification of Real Estate Mathmatics 79 Second Part Is Figure What Each Broker Gets A  X CB  $3,656.25 to Each Broker 50% $7,312.50

80. June 16 Simplification of Real Estate Mathmatics 80 Third Part Is What Do Mary & Broker Bill Get? A  X CB  $1,828.125 For Mary & Broker Bill 50% $3,656.25

81. June 16 Simplification of Real Estate Mathmatics 81 The Closes Answer Would Be Broker Bob and Broker Bill agreed to divide a 4 ½% Commission equally on the sale of a home, which sold for $162,500. Mary, the listing salesperson, works for Broker Bob on a 50-50 commission split. Mary would receive approximately how much commission as a result of the sale? A.$1,828 B.$2,828 C.$3,656 D.$7,312

82. June 16 Simplification of Real Estate Mathmatics 82 Commission Problem #2 2.Sam, a salesperson working for Broker Martha, received a 45% share of a 6% commission. Sam’s share came to $8,100. What was the selling price of the property? A.$100,000 B.$150,000 C.$250,000 D.$300,000

83. June 16 Simplification of Real Estate Mathmatics 83 The First Part is to Find the Total Commission A  X CB  $8,100 45% Total Commission

84. June 16 Simplification of Real Estate Mathmatics 84 First Part is to Find the Total Commission A  X CB  $8,100 45% $18,000

85. June 16 Simplification of Real Estate Mathmatics 85 2nd Part Divide the Total Commission Commission By 6% to Find the Sales Price. A  X CB  $18,000 6% Selling Price

86. June 16 Simplification of Real Estate Mathmatics 86 2nd Part Divide the Total Commission Commission By 6% to Find the Sales Price. A  X CB  $18,000 6% $300,000

87. June 16 Simplification of Real Estate Mathmatics 87 Selling Price Problems A  X CB  (Little Number) Net Amount (Less than 100%) 100% Minus the Commission, cost of sale, or discount (Big Number) Selling Price

88. June 16 Simplification of Real Estate Mathmatics 88 Selling Price Problem One Mark sold his home and carried back a $37,400 second trust deed. He immediately sold the loan at a discount to an investor and received a$24,310. What was the rate of discount? A.25% B.30% C.35% D.None of the above

89. June 16 Simplification of Real Estate Mathmatics 89 Estimating the Discount You can approach this problem using this logic; 1.$24,310  $37,400=.65=65% 2.100% - 65%=35% The Discount The discount is 35%, or answer C

90. June 16 Simplification of Real Estate Mathmatics 90 Using The “Magic Circle” A  X CB  $24,310 Selling Price Unknown = The Discount $37,400 Face Value

91. June 16 Simplification of Real Estate Mathmatics 91 Using The “Magic Circle” A  X CB  $24,310 Selling Price Mark Got 65% of the Face Value $37,400 Face Value

92. June 16 Simplification of Real Estate Mathmatics 92 Selling Price Problem One Mark sold his home and carried back a $37,400 second trust deed. He immediately sold the loan at a discount to an investor and received a$24,310. What was the rate of discount? A.25% B.30% C.35% D.None of the above

93. June 16 Simplification of Real Estate Mathmatics 93 Selling Price Problem #2 A bank charged a borrower 4 points for making a loan. The bank then sold the loan immediately to an investor at a discount of 3½ points, or a 3 1/2 % discount, the bank received $34,790. What was the original amount of the note? A.$35,750 B.$36,052 C.$36,350 D.$37,987

94. June 16 Simplification of Real Estate Mathmatics 94 One Logical Approach 100% equals the full value of the loan. 100% less the 3 ½% discount equals the original value of the note. 100%-3.5%=96.5% 96.5% of something equals the discounted note value. Then $34,790 = 96.5% of something. The rules of the circle with selling price problems is that A is the net amount, so A is $34,790, the percentage goes in C so we have enough to construct a circle and solve the problem.

95. June 16 Simplification of Real Estate Mathmatics 95 Solve Number 2 Problem A  X CB  $34,790 Selling Price of Note Value of the discounted note is 96.5% Note Value

96. June 16 Simplification of Real Estate Mathmatics 96 Divide A by C and Find B A  X CB  $34,790 Selling Price of Note Value of the discounted note is 96.5% $36,051.8135 Note Value

97. June 16 Simplification of Real Estate Mathmatics 97 Pick the Closest Answer A bank charged a borrower 4 points for making a loan. The bank then sold the loan immediately to an investor at a discount of 3½ points, or a 31/2 % discount, the bank received $34,790. What was the original amount of the note? A.$35,750 B.$36,052 C.$36,350 D.$37,987

98. June 16 Simplification of Real Estate Mathmatics 98 Selling Price Problem #3 Ron sold his home which had no loans against it. He received a settlement check from escrow in the amount of $91,740 after paying escrow fees of $1,291.80 plus a 6% real estate broker’s commission. What was the selling price? A.$92,000 B.$96,857 C.$97,995 D.$98,970

99. June 16 Simplification of Real Estate Mathmatics 99 Approaching a logic Since Ron got $91,740 at the close of escrow, and paid $1,291.80 we can add those two together and come up with his net before expenses. $91,740 + $1,291.80 = $93,031.80 from the total sales price Ron paid 6% and then got $93,031.80. 100% - 6% = 94%. So, $93,031.80 = 94% of the sales price. 94% is less than 100% so the smaller number, the $93,031.80 will go in A, the 94% will go into C, and we will solve for B.

100. June 16 Simplification of Real Estate Mathmatics 100 Divide A by C and Find B A  X CB  Net Before Commission $93,031.80 Value of Net is 94% Selling Price of Home

101. June 16 Simplification of Real Estate Mathmatics 101 Divide A by C and Find B A  X CB  Net Before Commission $93,031.80 Value of Net is 94% $98,970

102. June 16 Simplification of Real Estate Mathmatics 102 Find the Answer A  X CB  Net Before Commission $93,031.80 Value of Net is 94% $98,970.00

103. June 16 Simplification of Real Estate Mathmatics 103 Pick the Closest Answer Ron sold his home which had no loans against it. He received a settlement check from escrow in the amount of $91,740 after paying escrow fees of $1,291.80 plus a 6% real estate broker’s commission. What was the selling price? A.$92,000 B.$96,857 C.$97,995 D.$98,970

104. June 16 Simplification of Real Estate Mathmatics 104 Cost Problems A  X CB  (Big Number) Selling Price (More than 100%) 100% Plus Profit (Little Number) Original Cost

105. June 16 Simplification of Real Estate Mathmatics 105 Cost Problem #1 Brenda Sold a home for $600,000. She made a 20% profit. What did the home cost? A.$500,000 B.$720,000 C.$750,000 D.$700,000

106. June 16 Simplification of Real Estate Mathmatics 106 Solution Cost Problem #1 A  X CB  (Big Number) $600,000 (More than 100%) 100% + 20% = 120% (Little Number) $500,000

107. June 16 Simplification of Real Estate Mathmatics 107 Cost Problem #1 Solved Brenda Sold a home for $600,000. She made a 20% profit. What did the home cost? A.$500,000 B.$720,000 C.$750,000 D.$700,000

108. June 16 Simplification of Real Estate Mathmatics 108 Cost Problem #2 Mr. Goldstein sold an apartment building for $2,450,000. This was 15% more than he had paid for it. Mr. Goldstein’s original cost was approximately how much? A.$2,050,000 B.$2,000,000 C.$2,825,000 D.$2,130,500

109. June 16 Simplification of Real Estate Mathmatics 109 Solution Cost Problem #1 A  X CB  (Big Number) $2,450,000 (More than 100%) 100% + 15% = 115% (Little Number) $2,130,435

110. June 16 Simplification of Real Estate Mathmatics 110 Cost Problem #2 Solution Mr. Goldstein sold an apartment building for $2,450,000. This was 15% more than he had paid for it. Mr. Goldstein’s original cost was approximately how much? A.$2,050,000 B.$2,000,000 C.$2,825,000 D.$2,130,500

111. June 16 Simplification of Real Estate Mathmatics 111 Cost Problem #3 3.Mr. Sankey sold a vacant piece of land for $825,000. He broke even after paying the expenses of sale. The expenses of sale represented 10% of the original cost of the land. What was his original cost of the land? A.$907,500 B.$742,500 C.$750,000 D.$790,000

112. June 16 Simplification of Real Estate Mathmatics 112 Solution Cost Problem #2 A  X CB  (Big Number) $825,000 (More than 100%) 100% + 10% = 110% (Little Number) $750,000

113. June 16 Simplification of Real Estate Mathmatics 113 Area Problems A  X CB  (Big Number) Area Width Length

114. June 16 Simplification of Real Estate Mathmatics 114 Area Problem #1 1.A rectangular lot 50 feet wide contains 555 Square Yards. What is the approximate depth of this lot? A.100 ft. B.111 ft. C.150 ft. D. 50 ft.

115. June 16 Simplification of Real Estate Mathmatics 115 First Steps The first thing you need to do is figure out how many square feet in the lot. A square yard is 3 feet X 3 feet or 9 square feet. So 555 Square yards would contain 555 X 9 = 4,950 square feet.

116. June 16 Simplification of Real Estate Mathmatics 116 Square Feet of Lot A  X CB  (Big Number) Area In Feet Square Feet in 1 Square Yard Square Yards

117. June 16 Simplification of Real Estate Mathmatics 117 Plug In The Proper Numbers A  X CB  (Big Number) 4,995 Square Feet 9 Square Feet in 1 Square Yard 555 Sq. Yards

118. June 16 Simplification of Real Estate Mathmatics 118 Now Find The Depth A  X CB  (Big Number) 4,995 Square Feet 50 Feet Wide 99.90 Feet Deep

119. June 16 Simplification of Real Estate Mathmatics 119 The Closest Answer 1.A rectangular lot 50 feet wide contains 555 Square Yards. What is the approximate depth of this lot? A.100 ft. B.111 ft. C.150 ft. D. 50 ft.

120. June 16 Simplification of Real Estate Mathmatics 120

121. June 16 Simplification of Real Estate Mathmatics 121