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AQA GCSE Maths

Revision Notes

Home / GCSE / Maths / AQA / Revision Notes / 1. Number / 1.5 Compound Interest / 1.5.2 Depreciation


1.5.2 Depreciation


Depreciation

What is meant by depreciation?

  • Depreciation is where an item loses value over time
    • For example: cars, game consoles, etc
  • Depreciation is usually calculated as a percentage decrease at the end of each year
    • This works the same as compound interest but with a percentage decrease

How do I calculate with depreciation?

  • You would calculate the new value after depreciation using the same method as compound interest
    • Identify the multiplier (100 - % as a decimal)
      • 10% depreciation would have a multiplier of 0.9
      • 1% depreciation would have a multiplier of 0.99
    • Raise the multiply to the power of the number of years (or months etc)
      • m to the power of n
    • Multiply by the starting value
  • New value is A cross times m to the power of n
    • A is the starting value
    • m is the multiplier for the depreciation 
    • n is the number of years
  • If you are asked to find the amount the value has depreciated by:
    • Find the difference between the starting value and the new value

Worked Example

Mercy buys a car for £20 000. Each year its value depreciates by 15%.

Find the value of the car after 3 full years.

Identify the multiplier

100% - 15% = 85%

m = 0.85

Raise to the power of number of years

0.853

Multiply by the starting value

£20 000 × 0.853

= £12 282.50



  • 1. Number
    • 1.1 Arithmetic
      • 1.1.1 Multiplication (non-Calc)
        • 1.1.2 Division (non-Calc)
          • 1.1.3 Mathematical Symbols
            • 1.1.4 Negative Numbers
              • 1.1.5 Order By Size
                • 1.1.6 Time
                • 1.2 Fractions
                  • 1.2.1 Mixed Numbers & Top Heavy Fractions
                    • 1.2.2 Adding & Subtracting Fractions
                      • 1.2.3 Multiplying & Dividing Fractions
                      • 1.3 Basic Percentages
                        • 1.3.1 Basic Percentages
                          • 1.3.2 Percentage Increases & Decreases
                          • 1.4 Reverse Percentages
                            • 1.4.1 Reverse Percentages
                            • 1.5 Compound Interest
                              • 1.5.1 Compound Interest
                                • 1.5.2 Depreciation
                                • 1.6 LCM / HCF / Prime Factors
                                  • 1.6.1 Prime Factors
                                    • 1.6.2 HCFs & LCMs
                                    • 1.7 Roots & Indices
                                      • 1.7.1 Roots & Indices - Basics
                                        • 1.7.2 Roots & Indices - Harder
                                        • 1.8 Rounding & Estimation
                                          • 1.8.1 Rounding & Estimation
                                          • 1.9 Standard Form
                                            • 1.9.1 Standard Form - Basics
                                              • 1.9.2 Standard Form - Harder
                                              • 1.10 Bounds & Error Intervals
                                                • 1.10.1 Bounds & Error Intervals - Basics
                                                  • 1.10.2 Calculations using Bounds
                                                  • 1.11 Recurring Decimals
                                                    • 1.11.1 Recurring Decimals
                                                    • 1.12 Surds
                                                      • 1.12.1 Surds - Basics
                                                        • 1.12.2 Surds - Rationalising Denominators
                                                        • 1.13 Using a Calculator
                                                          • 1.13.1 Using a Calculator
                                                          • 1.14 Counting
                                                            • 1.14.1 Counting
                                                            • 1.15 Best Buy
                                                              • 1.15.1 Best Buy
                                                              • 1.16 Exchange Rates
                                                                • 1.16.1 Exchange Rates
                                                              • 2. Algebra Basics
                                                                • 2.1 Expanding One Bracket
                                                                  • 2.1.1 Expanding One Bracket
                                                                  • 2.2 Simple Factorisation
                                                                    • 2.2.1 Simple Factorisation
                                                                    • 2.3 Expanding Quadratics
                                                                      • 2.3.1 Expanding Two Brackets - Basics
                                                                        • 2.3.2 Expanding Two Brackets - Harder
                                                                          • 2.3.3 Expanding Three Brackets
                                                                          • 2.4 Factorising Quadratics
                                                                            • 2.4.1 Factorising Quadratics - Basics
                                                                              • 2.4.2 Factorising Quadratics - Harder
                                                                                • 2.4.3 Difference of Two Squares
                                                                                  • 2.4.4 Factorising Quadratics - General
                                                                                  • 2.5 Rearranging Formulae
                                                                                    • 2.5.1 Rearranging Formulae - Basics
                                                                                      • 2.5.2 Rearranging Formulae - Harder
                                                                                      • 2.6 Solving Linear Equations
                                                                                        • 2.6.1 Collecting Like Terms
                                                                                          • 2.6.2 Solving Linear Equations
                                                                                            • 2.6.3 Forming Expressions & Equations
                                                                                            • 2.7 Substitution
                                                                                              • 2.7.1 Substitution
                                                                                              • 2.8 Proof/Reasoning
                                                                                                • 2.8.1 Proof/Reasoning - Algebraic
                                                                                                • 2.9 Functions
                                                                                                  • 2.9.1 Functions - Basics
                                                                                                    • 2.9.2 Compound Functions
                                                                                                      • 2.9.3 Inverse Functions
                                                                                                      • 2.10 Algebraic Fractions
                                                                                                        • 2.10.1 Algebraic Fractions - Adding & Subtracting
                                                                                                          • 2.10.2 Algebraic Fractions - Simplifying Fractions
                                                                                                            • 2.10.3 Algebraic Fractions - Multiplying & Dividing
                                                                                                          • 3. Solving Equations & Inequalities
                                                                                                            • 3.1 Quadratic Formula
                                                                                                              • 3.1.1 Quadratic Formula
                                                                                                              • 3.2 Completing the Square
                                                                                                                • 3.2.1 Completing the Square
                                                                                                                • 3.3 Linear Simultaneous Equations
                                                                                                                  • 3.3.1 Linear Simultaneous Equations
                                                                                                                  • 3.4 Quadratic Simultaneous Equations
                                                                                                                    • 3.4.1 Quadratic Simultaneous Equations
                                                                                                                    • 3.5 Inequalities
                                                                                                                      • 3.5.1 Solving Inequalities - Linear
                                                                                                                        • 3.5.2 Solving Inequalities - Quadratic
                                                                                                                        • 3.6 Inequalities on a Graph
                                                                                                                          • 3.6.1 Inequalities on Graphs - Drawing
                                                                                                                            • 3.6.2 Inequalities on Graphs - Interpreting
                                                                                                                            • 3.7 Iteration
                                                                                                                              • 3.7.1 Iteration - Using a Calculator
                                                                                                                                • 3.7.2 Iteration - Applications
                                                                                                                                • 3.8 Equations & Problem Solving
                                                                                                                                  • 3.8.1 Equations & Problem Solving
                                                                                                                                • 4. Sequences
                                                                                                                                  • 4.1 Sequences - Linear
                                                                                                                                    • 4.1.1 Sequences - Linear
                                                                                                                                    • 4.2 Sequences - Quadratic
                                                                                                                                      • 4.2.1 Sequences - Quadratic
                                                                                                                                      • 4.3 Fibonacci & Geometric
                                                                                                                                        • 4.3.1 Sequences - Basics
                                                                                                                                          • 4.3.2 Sequences - Identifying
                                                                                                                                            • 4.3.3 Sequences - Others
                                                                                                                                          • 5. Graphs
                                                                                                                                            • 5.1 Coordinates
                                                                                                                                              • 5.1.1 Coordinates
                                                                                                                                              • 5.2 Drawing Graphs
                                                                                                                                                • 5.2.1 Drawing Graphs - Shapes
                                                                                                                                                  • 5.2.2 Drawing Graphs - Using a Table
                                                                                                                                                    • 5.2.3 Drawing Graphs - Trig Graphs
                                                                                                                                                    • 5.3 Equations of a Line / y = mx + c
                                                                                                                                                      • 5.3.1 Straight Lines - Finding Equations
                                                                                                                                                        • 5.3.2 Straight Lines - Drawing Graphs
                                                                                                                                                        • 5.4 Perpendicular Lines
                                                                                                                                                          • 5.4.1 Perpendicular Lines
                                                                                                                                                          • 5.5 Transformations of Graphs
                                                                                                                                                            • 5.5.1 Transformations of Graphs
                                                                                                                                                            • 5.6 D-T / V-T Graphs
                                                                                                                                                              • 5.6.1 Distance-Time Graphs
                                                                                                                                                                • 5.6.2 Speed-Time Graphs
                                                                                                                                                                • 5.7 Solving Equations using Graphs
                                                                                                                                                                  • 5.7.1 Solving Equations using Graphs
                                                                                                                                                                  • 5.8 Equation of a Circle
                                                                                                                                                                    • 5.8.1 Circles - Equation & Graphs
                                                                                                                                                                      • 5.8.2 Circles - Finding Tangents
                                                                                                                                                                      • 5.9 Estimating Areas & Gradients of Graphs
                                                                                                                                                                        • 5.9.1 Estimating Areas & Gradients of Graphs
                                                                                                                                                                      • 6. Ratios, Proportion & Rate of Change
                                                                                                                                                                        • 6.1 Ratios
                                                                                                                                                                          • 6.1.1 Ratios
                                                                                                                                                                          • 6.2 Direct & Inverse Proportion
                                                                                                                                                                            • 6.2.1 Direct & Inverse Proportion
                                                                                                                                                                            • 6.3 Speed, Density & Pressure
                                                                                                                                                                              • 6.3.1 Speed, Density & Pressure
                                                                                                                                                                                • 6.3.2 Speed, Density & Pressure - Harder
                                                                                                                                                                              • 7. Geometry & Measures
                                                                                                                                                                                • 7.1 Angles in Parallel Lines
                                                                                                                                                                                  • 7.1.1 Angles in Parallel Lines
                                                                                                                                                                                  • 7.2 Angles in Polygons
                                                                                                                                                                                    • 7.2.1 Angles in Polygons
                                                                                                                                                                                    • 7.3 Similarity - Lengths
                                                                                                                                                                                      • 7.3.1 Similarity - Lengths
                                                                                                                                                                                      • 7.4 Similarity - Areas & Volumes
                                                                                                                                                                                        • 7.4.1 Similarity - Areas & Volumes
                                                                                                                                                                                        • 7.5 Congruent Triangles
                                                                                                                                                                                          • 7.5.1 Congruent Triangles
                                                                                                                                                                                          • 7.6 Transformations
                                                                                                                                                                                            • 7.6.1 Transformations - Rotation
                                                                                                                                                                                              • 7.6.2 Transformations - Reflection
                                                                                                                                                                                                • 7.6.3 Transformations - Translation
                                                                                                                                                                                                  • 7.6.4 Transformations - Enlargement
                                                                                                                                                                                                    • 7.6.5 Combined Transformations
                                                                                                                                                                                                    • 7.7 Transformations - Enlargement (Negative Scale Factor)
                                                                                                                                                                                                      • 7.7.1 Transformations - Enlargement (Negative Scale Factor)
                                                                                                                                                                                                      • 7.8 Area - Triangles & Quadrilaterals
                                                                                                                                                                                                        • 7.8.1 Area - Formulae
                                                                                                                                                                                                          • 7.8.2 Area - Adding & Subtracting
                                                                                                                                                                                                          • 7.9 Circles - Area & Circumference
                                                                                                                                                                                                            • 7.9.1 Circles - Area & Circumference
                                                                                                                                                                                                            • 7.10 Circles - Sector & Arcs
                                                                                                                                                                                                              • 7.10.1 Circles - Sector Areas & Arc Lengths
                                                                                                                                                                                                              • 7.11 Problem Solving with Areas
                                                                                                                                                                                                                • 7.11.1 Problem Solving with Areas
                                                                                                                                                                                                                  • 7.11.2 Converting Lengths & Areas
                                                                                                                                                                                                                  • 7.12 3D Shapes
                                                                                                                                                                                                                    • 7.12.1 3D Shapes - Surface Area
                                                                                                                                                                                                                      • 7.12.2 3D Shapes - Volume
                                                                                                                                                                                                                      • 7.13 Pythagoras
                                                                                                                                                                                                                        • 7.13.1 Pythagoras Theorem
                                                                                                                                                                                                                        • 7.14 SOHCAHTOA
                                                                                                                                                                                                                          • 7.14.1 SOHCAHTOA
                                                                                                                                                                                                                            • 7.14.2 3D Pythagoras & SOHCAHTOA
                                                                                                                                                                                                                            • 7.15 Sine/Cos Rules & Area of a Triangle
                                                                                                                                                                                                                              • 7.15.1 Sine & Cosine Rules, Area of Triangle - Basics
                                                                                                                                                                                                                                • 7.15.2 Sine & Cosine Rules, Area of Triangle - Harder
                                                                                                                                                                                                                                • 7.16 Circle Theorems
                                                                                                                                                                                                                                  • 7.16.1 Circle Theorems - Angles at Centre & Circumference
                                                                                                                                                                                                                                    • 7.16.2 Circle Theorems - Tangents
                                                                                                                                                                                                                                      • 7.16.3 Circle Theorems - Cyclic Quadrilaterals
                                                                                                                                                                                                                                        • 7.16.4 Circle Theorems - Alternative Segment
                                                                                                                                                                                                                                        • 7.17 Loci & Construction
                                                                                                                                                                                                                                          • 7.17.1 Loci & Construction
                                                                                                                                                                                                                                          • 7.18 Bearings & Scale
                                                                                                                                                                                                                                            • 7.18.1 Bearings & Scale
                                                                                                                                                                                                                                            • 7.19 Vectors
                                                                                                                                                                                                                                              • 7.19.1 Vectors - Basics
                                                                                                                                                                                                                                                • 7.19.2 Vectors - Finding Paths
                                                                                                                                                                                                                                                  • 7.19.3 Vectors - Proving Things
                                                                                                                                                                                                                                                  • 7.20 Drawing Plans & Elevations
                                                                                                                                                                                                                                                    • 7.20.1 Drawing Plans & Elevations
                                                                                                                                                                                                                                                    • 7.21 Trigonometry - Exact Values
                                                                                                                                                                                                                                                      • 7.21.1 Trigonometry - Exact Values
                                                                                                                                                                                                                                                    • 8. Probability
                                                                                                                                                                                                                                                      • 8.1 Basic Probability
                                                                                                                                                                                                                                                        • 8.1.1 Basic Probability
                                                                                                                                                                                                                                                        • 8.2 Venn Diagrams & Two Way Tables
                                                                                                                                                                                                                                                          • 8.2.1 Probability - Venn Diagrams
                                                                                                                                                                                                                                                            • 8.2.2 Probability - Two Way Tables
                                                                                                                                                                                                                                                              • 8.2.3 Set Notation & Venn Diagrams
                                                                                                                                                                                                                                                              • 8.3 Combined Probability
                                                                                                                                                                                                                                                                • 8.3.1 Combined Probability - Basics
                                                                                                                                                                                                                                                                  • 8.3.2 Combined Probability - Harder
                                                                                                                                                                                                                                                                • 9. Statistics
                                                                                                                                                                                                                                                                  • 9.1 Mean, Median & Mode
                                                                                                                                                                                                                                                                    • 9.1.1 Mean, Median & Mode
                                                                                                                                                                                                                                                                      • 9.1.2 Averages from Tables & Charts
                                                                                                                                                                                                                                                                        • 9.1.3 Averages from Grouped Data
                                                                                                                                                                                                                                                                          • 9.1.4 Calculations with the Mean
                                                                                                                                                                                                                                                                            • 9.1.5 IQR & Range
                                                                                                                                                                                                                                                                            • 9.2 Box Plots
                                                                                                                                                                                                                                                                              • 9.2.1 Box Plots
                                                                                                                                                                                                                                                                              • 9.3 Stem & Leaf Diagrams
                                                                                                                                                                                                                                                                                • 9.3.1 Stem & Leaf Diagrams
                                                                                                                                                                                                                                                                                • 9.4 Frequency Polygons
                                                                                                                                                                                                                                                                                  • 9.4.1 Frequency Polygons
                                                                                                                                                                                                                                                                                  • 9.5 Scatter Graphs (inc. Time Series)
                                                                                                                                                                                                                                                                                    • 9.5.1 Scatter Graphs
                                                                                                                                                                                                                                                                                      • 9.5.2 Time Series Graphs
                                                                                                                                                                                                                                                                                      • 9.6 Histograms
                                                                                                                                                                                                                                                                                        • 9.6.1 Histograms
                                                                                                                                                                                                                                                                                        • 9.7 Cumulative Frequency Graphs
                                                                                                                                                                                                                                                                                          • 9.7.1 Cumulative Frequency
                                                                                                                                                                                                                                                                                          • 9.8 Bar Charts
                                                                                                                                                                                                                                                                                            • 9.8.1 Bar Charts
                                                                                                                                                                                                                                                                                            • 9.9 Population & Samples
                                                                                                                                                                                                                                                                                              • 9.9.1 Comparing Distributions
                                                                                                                                                                                                                                                                                                • 9.9.2 Capture - Recapture


                                                                                                                                                                                                                                                                                                DOWNLOAD PDF

                                                                                                                                                                                                                                                                                              Author: Daniel

                                                                                                                                                                                                                                                                                              Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.


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