Học Thi Real Estate License ở California: Practice Real Estate Mathematics Dat Hoang March 26, 2020 No Comments 1. What percentage of a section is 1/90 of a township? 45 percent 40 percent 38 percent 10 percent Hint36 / 90 2. On a 25-year lease at $15,000 a year, a broker gets a commission of seven percent for the first year, five percent for the next four years, three percent for the next 10 years, and one percent for the remainder of the lease. How much commission has the broker earned by the end of the nineteenth year? $9,150 $7,350 $12,750 $7,950 3. A borrower was required to give the lender a deposit equal to three months' taxes and insurance cost. If the property was 0,024 per dollar of assessment and the yearly insurance cost was $462, what deposit was required? $3,883.50 $2,794.86 $4,033.33 $3,944.33 4. A board foot of lumber cannot be obtained from a board: 5" x 12" x 12" 1" x 6" x 20" 6" x 6" x 6" 1" x 2" x 5" Hint1" x 6" x 20" = 120 cubic inches. 5. Claude wishes to pour a concrete patio 40' x 10' and four inches thick. How many cubic yards of concrete are needed? 5 45 12 3 Hint40 x 10 = 400 square feet. 400/(3 * 27) 6. A 10-arce rectangular parcel is divided into six equal lots, each having a depth of 250'. The width of each lot is approximately how many feet? 348.48' 290.4' 1,742.4' 217.4' 7. A man purchased three lots for $17,000. Lot 2 sells for $1,500 more than Lot 1, and Lot 3 sells for $2,000 more than Lot 2. What is the full price of Lot 2? $4,000 none of these $5,500 $7,500 8. The interest paid last month on a six percent loan was $4,900. The balance on the loan was: $490,000 $720,000 $245,000 $980,000 9. Lot E has a building setback of 30 feet from each side. The maximum square footage of a two-story building on Lot E would be: 20,000 square feet 3,200 square feet 1,600 square feet 120,000 square feet Hint40'x40'x2. 10. A property was purchased for $87,500. The buyer now wishes to sell it. If selling costs will equal 11 percent of any sales price, how much must the property appreciate in value for the seller to break even? $9,625 $10,815 $9,738 $11,315 11. A road runs along the south boundary of a section. It contains three acres. Its width is: 18.1 feet 43 feet 50 feet 24.7 feet HintDivide the area in square feet by 5,280. (Known Dimension) 12. A sales manager received $3,500 per month plus 0.1 percent of office sales. For March, she received $7,400. This was based on monthly sales of: $3,900,000 $39,000,000 $390,000 $418,000 13. A man owned a rectangular property with an area of 3/4 of an acre and a depth of 110 feet. He purchased the adjoining property, which was 2/3 the size of his own with the same depth, for $1,400. Putting them together into rectangular lots of 82.5' x 110' each, he sold the lots for $750 each, which was 50 percent over his cost. How much did he pay for his original property? $2,800 $1,600 $850 $3,100 14. The easiest way to compute one month's interest at 7.2 percent would be to multiply the principal by: 0.072, and divide by 12 .06 7.2 0.006 Hint0.0006 = 1/12 of 7.2% 15. On a 90' x 90' lot, the building setbacks are 30' from the front, and 10' from the sides, and 20' from rear line. The net building area is: 1,750 square feet none of these 2,800 square feet 2,650 square feet Hint40' x 70' 16. A rectangular piece of property has 200 feet on one side and an apartment building that is worth $193,600, which is the equivalent of $4.40 per square foot for the lot. What is the front footgage? 440 feet 880 feet 220 feet 110 feet 17. How many acres are there in 580,800 square yards? 120 197.5 133.3 1,200 18. Nate has 10 apartments fully rented at $100 per month. He raises his rent 10 percent and experiences a 10 percent vacancy factor. his monthly income decreases his yearly income remains the same his monthly income increases this is an example of maximization of the net HintTotal rent decreased to $990. 19. A property owner had an assessed value of $10,000 on his home, with taxes at $8 per $100 assessed valuation, making his taxes $800. The next year, the tax rate went up to $9 per $100, making his taxes $900. The assessed value: increased 12.5 percent increased 11.1 percent remained the same increased 10 percent HintOnly the rate changed. 20. In a cubic yard there are: all of these 3 linear feet 9 square feet 27 cubic feet Hint3' x 3' x 3' 21. An owner divides a one-acre parcel into four equal rectangular lots, each 200 feet deep. What is the approximate width of each lot? 118.3 feet 87.12 feet 54.45 feet 217.8 feet Hint43,560/200 = 217.8. So 217.8/4 22. Which of the following possible transaction will result in the greatest net to a seller? Sale Price Commission Closing Costsa. $640,000 5% $13,800b. $638,000 6 1/2% $10,200c. $637,500 6 .4% $3,100c. $628,000 4.5% $2,450 c b d a 23. Frank buys a $1,200 trust deed at a 25 percent discount. The trust deed requires payments of $104 per month, including interest for one year. Frank's percentage of return for the year on his investment is: 9.6 percent 29.8 percent 38 percent 4.8 percent HintDivide investmet $900 into net $348. Net is gross ($104 x $12) minus cost ($900). 24. A property was listed to give the owner $41,000 after the six percent commission was paid. It was listed at: $43,437 $38,640 $43,617 $43,918 25. To find the square footage of a square 40 arce parcel: neither a nor b multifly 40 x 43,560 feet either a or b multifly 1,320 x 1,320 26. Nine cubic yards of concrete is equal to: 72 cubic feet 27 cubic feet 243 cubic feet 81 cubic feet Hint9 x 27 27. An investor purchased two lots at $6,000 each and divided them into three lots, which he sold for $4,800 each. His percentage of profit based on cost was: 24 percent 12 percent 20 percent 6 percent 28. A 5 foot fence will be built around the perimeter of a 50' x 120' rectangular lot. If the fence will cost $1.80 per linear foot for labor and $.40 per square foot for material, what will be the cost of the fence? $1,824 $1,292 $1,936 $1,700 29. A lender agrees to make a 90 percent loan on a home selling for $220,000 providing the borrower pays loan costs of 1 1/2 percent. What are the loan costs? $3,300 $2,970 $1,436 $1,980 30. A rectangular parcel 422 feet wide contains 8.3 acres. Its depth is: 856.75 feet 801.11 feet 1,187.2 feet 435.6 feet HintDivide the area in square feet by the known dimension. 31. Lucy owes $8,100 on a note. Her next monthly interest payment will be $58.32 Annual interest on the note is: 1/2 percent 8.64 percent 4.5 percent 5 percent Hint$58.32 = 1/12 of interest. Rate = Part/Whole. 32. If the lots in the figure sell for $10 per front foot on Main Street, Lot D would sell for: $10,000 $20,000 $1,000 none of these Hint100x10. 33. You wish to earn $50 per month on a six percent investment. How much would you have to invest? $10,000 $20,000 $5,000 $6,000 34. Mr. Jones had sales of $25,000. His markup was 50 percent of his cost. The merchandise cost him: $16,666.66 $17,500 $12,500 $18,200 HintHis markup was 1/3 of selling price. 35. Elena sells her home for $40,000, making a 30 percent profit on what she paid for it: $12,000 $9,231 $30,769 $9,000 Hint$40,000 = 130% of cost. 36. If the lots in the figure sell for $100 per front foot on Main Street, Lot A would sell for: $1,000 none of these $10,000 $20,000 Hint100x$100. 37. A three-strand wire fence around a square 40-acre parcel would require how much wire? 4.5 miles none of these 3 miles 6 miles Hint1/4 mile each side, so 1 mile around. 38. Lance sells a new note at a four percent discount. He receives $5,200. The face amount of the note is: $5,408.00 $5,611.27 $5,416.66 $4,992.00 Hint$5,200 = 0.96 x the face amount. Rate = Part/Whole 39. If thw buyer's down payment is $12,000 and the property has a net income of $8,300, the buyer's percentage of return on the down payment is: 71 percent 69 percent 14.5 percent 70 percent HintDivide down payment into net. 40. A speculator purchased a home at 25 percent less than list price and later sold it for the original list price. The percentage of profit was: 33 1/2 percent 50 percent 20 percent 25 percent HintHe made 25 percent of list price on investment of 75 percent of list price. 41. A man paid off an eight percent term loan for $800. His total interest cost was $42.66. He paid off the loan in: nine months seven months eight months six months 42. A $10,000 loan requires payments of $100 per month plus interest. As to the monthly payments, the amount of money applying to: neither a nor b interest will decrease both a and b principal will increase HintThe amount paid on the principal is the same "plus interest." 43. To find the depth of a rectangular parcel when the width and the total area are known: multiply the width by the area divide the width by the area none of these divide the area by the width 44. In the preceding question, the percentage of profit based on selling price is: 200 percent 40 percent 60 percent 150 percent HintNet/Selling Price = 600/400 45. An 80 -acre parcel purchased for $400 per acre is resold in four 20-acre parcels at $1000 per acre. The percentage of profit based on cost is: 60 percent 150 percent 40 percent 200 percent HintNet / cost = 600 / 400. 46. A lot is assessed at 25 percent of its $7,500 market value. The tax rate is .02392 per dollar of valuation. Taxes would be: none of the above $284.03 $44.85 $11.13 Hint$1,875 assessed value x tax rate. 47. A road runs along the south boundary of the SW 1/4 of the SW 1/4 of a section. If the road contains two acres in area, the width of the road would be: 33 feet 47 feet 66 feet 16 feet 48. A woman borrowed $5,000 for one year with six percent prepaid interest. She received: $4,700 $5,300 none of these $5,000 49. Seller A offers the S 1/2 of the NW 1/4 of the NE 1/4 of Section 21 for sale through Broker B at a list price of $350 per acre. Broker B presents Buyer C's offer of $6,100 to Seller A. Seller A accepts Buyer C's offer provided that the buyer pays the broker 10 percent commission on the offered price. If the buyer accepts this provision, how much less than the original list price did the buyer actually pay? $280 $270 $290 $330 50. Given the amount of interest paid, the rate of interest, and the time, which formula would you use to find the amount of the principal? P = R/I P = I/R P = I/(R x T) P = R x T x I 51. Oliver sells his house for $14,900. This is 18 percent more than he paid for it. Oliver paid: $12,218 $13,100 $17,582 $12,627 Hint$14,900 = 118% of its original cost. Whole = Part/rate. 52. Two houses sold together for $49,911. If one was valued $3,176 more than the other, what did the more expensive home sell for? $28,081 $28,730 $29,813 $26,543.50 53. A property was purchased for $10,000 and has a gross income of $2,000. The only expense is the owner's interest payment of nine percent on an $8,000 trust deed. The owner's percentage of return on his equity is: 80 percent 280 percent 11 percent 64 percent HintDivide equity ($2,000) into net ($1,280). Net is gross less interest payment. 54. If barberd wire weighs one pound per rod, how many pounds of barbed wire will it take to put a single-strand fence around a section? 1,280 lbs 687 lbs 211 lbs 420 lbs 55. The maximum number of 50' x 75' lots that can be made from one acre would be: 11 12 10 13 Hint43,560/(50x75) 56. A 10-acre rectangular lot on High Street sold for $60,000. Assuming a depth of 300', the price paid per front foot is: $34.14 $344.14 $83.11 $713.23 57. The last month's interest on a six percent loan was $739.12. What was the loan balance? $147,824 $136,826 $198,413 $152,316 HintWhole = Part/Rate = 739.12 / (6%*12) 58. A woman purchased a property for $15,000 with $2,000 down and no payments or interest for one year. At the end of the year, she sold the property at double the purchase price. Each dollar of the original investment is now worth: $11.00 $7.50 $8.50 $6.50 Hint$7.50 profit per dollar invested "plus" the dollar. 59. A 2'' x 8'' board 9 feet long would contain ___ board feet, 12 8.3 1 9 Hint2" x 8" x 108" = 1,728 / 144 60. If the tax rate is $2.392 per $100 of assessed valuation and a property is assessed at 25 percent of its real value of $47,500, what are the taxes? $1,136.20 $11,875.00 $284.05 $4,750.00 Hint25%x47,500/100 = 118.75 x 2.392 = 284.05 61. An investment that would pay $100 per month interest at six percent would require an investment of: $12,000.00 $20,000.00 $1,666.66 $10,000.00 HintPrincipal. = Yearly interest = Part/Rate. 62. The cost-of-living index increased from 100 to 120. What effect does this have the purchasing power of the dollar? lowers it 25 percent lowers it 16 2/3 percent lowers it 20 percent none of these HintIt now takes $6 to buy what $5 purchased. Each dollar is worth 1/6 less. 63. Jay sells a lot for 20 percent more than he paid for it and invests the entire proceeds in an investment yielding nine percent per year. His monthly return on his investment is $320. What did Jay originally pay for the lot? $3,840 $35,555 $28,730 $42,667 HintWhole = Part / Rate. 64. A mil is expressed as: .001 .1 .01 .0001 Hint1/10 of a cent. 65. If Lot C sells for $1 per square foot, it would sell for: $15,000 $1,000 $10,000 $20,000 HintIt contains 15,000 square feet. 66. In the figure, how many square feet are contained in the living area of the dwelling only? 2,236 2,272 2,476 cannot be computed HintSee drawing.