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Interest Calculation and Geometric Transformations

Interest Calculation and Geometric Transformations
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2019-04-11 03:30
FunctionCoordinate GeometryCalculus
This example demonstrates the integration of interest calculation with geometric transformations, dynamically showing area changes in isosceles triangles. Core math concepts include interest calculation, functions, coordinate geometry, geometric transformations, isosceles triangles, and area computation. GeoGebra commands like Polygon, Integral, Segment, and Point are used to construct the model. Suitable for high school mathematics education to understand the connection between functions and geometry, and dynamic transformations.

GeoGebra Commands & Parameters

  1. NumToMoney(E2) → G2
  2. NumToMoney(C3) → F3
  3. Polygon({(left, top), (left, bottom), (right, bottom), (right, top)}) → viewbox
  4. LaTeX((((("\text{\textbf{Question: }" * MainInstruc) * "\\\textbf{Instructions: } ") * SpecInstruc) * "}")) → allInstruc
  5. TableText({{"\text{\(1.5%\)}", "\text{\(3%\)}", "\text{\(4.5%\)}", "\text{\(6%\)}"}}) → txtIntRate
  6. Segment((0, 0), (25, 0)) → mySlider
  7. Point(mySlider) → sliderPt
  8. Integral(f, 0, x(sliderPt)) → compoundArea
  9. Integral(g, 0, x(sliderPt)) → simpleArea
  10. Polygon({(0, 0), (0, principal), (x(sliderPt), principal), (x(sliderPt), 0)}) → principalArea
  11. VerticalText("\text{Accumulated value in \$}") → yLabel
  12. Polygon({coverAnchor1, coverAnchor2, coverAnchor3, coverAnchor4}) → cover
  13. TableText({{"\cellcolor{#1565c0}{\phantom{hi}}", "\text{Compound Interest}"}, {"\cellcolor{#9c27b0}{\phantom{hi}}", "Simple Interest"}, {"\cellcolor{#1b5e20}{\phantom{hi}}", "No Interest"}}) → legend
  14. NumToMoney(C2) → F2
  15. NumToMoney(C4) → F4
  16. NumToMoney(C5) → F5
  17. NumToMoney(C6) → F6
  18. NumToMoney(C7) → F7
  19. NumToMoney(C8) → F8
  20. NumToMoney(C9) → F9
  21. NumToMoney(C10) → F10
  22. NumToMoney(C11) → F11
  23. NumToMoney(C12) → F12
  24. NumToMoney(C13) → F13
  25. NumToMoney(C14) → F14
  26. NumToMoney(C15) → F15
  27. NumToMoney(C16) → F16
  28. NumToMoney(C17) → F17
  29. NumToMoney(C18) → F18
  30. NumToMoney(C19) → F19
  31. NumToMoney(C20) → F20
  32. NumToMoney(C21) → F21
  33. NumToMoney(C22) → F22
  34. NumToMoney(C23) → F23
  35. NumToMoney(C24) → F24
  36. NumToMoney(C25) → F25
  37. NumToMoney(C26) → F26
  38. NumToMoney(C27) → F27
  39. NumToMoney(E3) → G3
  40. NumToMoney(E4) → G4
  41. NumToMoney(E5) → G5
  42. NumToMoney(E6) → G6
  43. NumToMoney(E7) → G7
  44. NumToMoney(E8) → G8
  45. NumToMoney(E9) → G9
  46. NumToMoney(E10) → G10
  47. NumToMoney(E11) → G11
  48. NumToMoney(E12) → G12
  49. NumToMoney(E13) → G13
  50. NumToMoney(E14) → G14
  51. NumToMoney(E15) → G15
  52. NumToMoney(E16) → G16
  53. NumToMoney(E17) → G17
  54. NumToMoney(E18) → G18
  55. NumToMoney(E19) → G19
  56. NumToMoney(E20) → G20
  57. NumToMoney(E21) → G21
  58. NumToMoney(E22) → G22
  59. NumToMoney(E23) → G23
  60. NumToMoney(E24) → G24
  61. NumToMoney(E25) → G25
  62. NumToMoney(E26) → G26
  63. NumToMoney(E27) → G27
  64. TableText({col1, col2}, "v|_10011111") → tblAccumulated
  65. NumToMoney(principal + ((A3 * principal) * currRate)) → I3
  66. NumToMoney(principal + ((A4 * principal) * currRate)) → I4
  67. NumToMoney(principal + ((A5 * principal) * currRate)) → I5
  68. NumToMoney(principal + ((A6 * principal) * currRate)) → I6
  69. NumToMoney(principal + ((A7 * principal) * currRate)) → I7
  70. NumToMoney(principal + ((A8 * principal) * currRate)) → I8
  71. NumToMoney(principal + ((A9 * principal) * currRate)) → I9
  72. NumToMoney(principal + ((A10 * principal) * currRate)) → I10
  73. NumToMoney(principal + ((A11 * principal) * currRate)) → I11
  74. NumToMoney(principal + ((A12 * principal) * currRate)) → I12
  75. NumToMoney(principal + ((A13 * principal) * currRate)) → I13
  76. NumToMoney(principal + ((A14 * principal) * currRate)) → I14
  77. NumToMoney(principal + ((A15 * principal) * currRate)) → I15
  78. NumToMoney(principal + ((A16 * principal) * currRate)) → I16
  79. NumToMoney(principal + ((A17 * principal) * currRate)) → I17
  80. NumToMoney(principal + ((A18 * principal) * currRate)) → I18
  81. NumToMoney(principal + ((A19 * principal) * currRate)) → I19
  82. NumToMoney(principal + ((A20 * principal) * currRate)) → I20
  83. NumToMoney(principal + ((A21 * principal) * currRate)) → I21
  84. NumToMoney(principal + ((A22 * principal) * currRate)) → I22
  85. NumToMoney(principal + ((A23 * principal) * currRate)) → I23
  86. NumToMoney(principal + ((A24 * principal) * currRate)) → I24
  87. NumToMoney(principal + ((A25 * principal) * currRate)) → I25
  88. NumToMoney(principal + ((A26 * principal) * currRate)) → I26
  89. NumToMoney(principal + ((A27 * principal) * currRate)) → I27
  90. Sequence(D3, i, 1, If[pageNum ≟ 1, 12, 13]) → simpleInterestCalc
  91. TableText({A1:A14, D1:D14, Join[{{E1}, G2:G14}], Join[{{H2, ""}, simpleInterestCalc}], Join[{{E1, G2}, I3:I14}]}, "vc|_") → dataPg1
  92. TableText({Join[{{A1}, A15:A27}], Join[{{D1}, D15:D27}], Join[{{E1}, G15:G27}], Join[{{H2}, simpleInterestCalc}], Join[{{E1}, I15:I29}]}, "vc|_") → dataPg2

AI Drawing Prompt Reference

Create a visual demonstrating interest calculation and geometric transformations, featuring an isosceles triangle with dynamically changing area, showing compound and simple interest calculations in different colors, with amounts and rates labeled. Start with a slider for the base length, calculate and display area changes under varying interest rates, forming a complete model with multiple shapes and text elements.
The prompt above was compiled from the original drawing commands and is for reference only.