Model compound change and inverse relationships
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Plan A starts with $2100, adds 5% interest each year, then deducts a $9 fee at the end of each year. Plan B adds 4% each year with no fees. With no other transactions, how much more is in A after two years? Round only the final difference to cents. Give your answer to 2 decimal places.
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Answer: $25.44
- Write the fee after each interest step, so the first fee also reduces the second interest base.
- A = (2100 × 1.05 − 9) × 1.05 − 9.
- B = 2100 × 1.04²; compare A − B.
- 2100 × 21/20 = 2205.
- 2205 − 9 = 2196.
- 2196 × 21/20 = 11529/5.
- 11529/5 − 9 = 11484/5.
- (26/25)^2 = 676/625.
- 2100 × 676/625 = 56784/25.
- 11484/5 − 56784/25 = 636/25.
- The result is $25.44.
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Curriculum reference
Victorian Curriculum F–10 Version 2.0
Pi Leo practice scope
Build growth, decay and inverse-proportion models and evaluate their assumptions and predictions.
Read the official VCAA curriculum description (VC2M10A15)
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Activities to practise beyond the quiz
- Supported by the guided activity; selecting an MCQ does not demonstrate this action.
- Supported by the guided activity; selecting an MCQ does not demonstrate this action.
- VC2M10A15-C01Derive repeated percentage growth from successive simple-interest steps.
- VC2M10A15-C02Formulate, derive, evaluate and report a compound-growth financial model.
- VC2M10A15-C03Distinguish linear, quadratic, exponential and inverse relationships in context.
- VC2M10A15-C04Choose, evaluate, modify and communicate inverse, linear, quadratic or exponential models.
- VC2M10A15-C05Apply and explain model compound change and inverse relationships using calculate and explain each step.
- VC2M10A15-C06Apply and explain model compound change and inverse relationships using build and check a model.
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Subskills
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Descriptor-derived subskills
- D01The balance becomes the next principalDerive repeated percentage growth from successive simple-interest steps.
- D02Choose the relationshipDistinguish linear, quadratic, exponential and inverse relationships in context.
- D03Calculate and explain each stepApply and explain model compound change and inverse relationships using calculate and explain each step.
- D04Build and check a modelApply and explain model compound change and inverse relationships using build and check a model.