Depreciation Wjec-Eduqas Foundation

课 Progress

0% Complete

Exam code:C300

Depreciation

What does depreciation mean?

Depreciation is where an item loses value over time
- E.g. cars, mobile phones, 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 depreciation?

A similar method to compound interest can be used
Change the multiplier to one which represents a percentage decrease
- e.g. a decrease of 15% would be a multiplier of 0.85
If a car worth £ 16 000 depreciates by 15% each year for 6 years
- Its value will be 16 000 × 0.85⁶, which is £ 6034.39
If you are asked to find the amount the value has depreciated by:
- Find the difference between the starting value and the new value

Depreciation formula

An alternate method is to use the following formula to calculate the final balance
- Final balance = $P open parentheses 1 minus r over 100 close parentheses to the power of n space end exponent$ where
  - P is the original amount,
  - r is the % increase
  - and n is the number of years
- Note that all of $1 minus r over 100$ is the multiplier
  - e.g. 0.75 for a 25% depreciation
This formula is not given in the exam

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 = 1 – 0.15 = 0.85

Raise to the power of number of years

0.85³

Multiply by the starting value

£20 000 × 0.85³

£12 282.50

Alternative method
Use the formula for the final amount <img alt=”P open parentheses 1 minus r over 100 close parentheses to the power of n space end exponent” data-mathml='<math ><semantics><mrow><mi >P</mi><msup><mfenced ><mrow><mn>1</mn><mo>-</mo><mfrac><mi>r</mi><mn>100</mn></mfrac></mrow></mfenced><mrow ><mi>n</mi><mo> </mo></mrow></msup></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true}</annotation></semantics></math>’ data-type=”commentary” height=”47″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2247%22%20width%3D%2298%22%20wrs%3Abaseline%3D%2230%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%20mathcolor%3D%22%23000000%22%3EP%3C%2Fmi%3E%3Cmsup%3E%3Cmfenced%20mathcolor%3D%22%23000000%22%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmfrac%3E%3Cmi%3Er%3C%2Fmi%3E%3Cmn%3E100%3C%2Fmn%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3Cmrow%20mathcolor%3D%22%23000000%22%3E%3Cmi%3En%3C%2Fmi%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmath%3E–%3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%3E%40font-face%7Bfont-family%3A’math1da40657c9fece7e48d30af42d3’%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMi7iBBMAAADMAAAATmNtYXDEvmKUAAABHAAAADRjdnQgDVUNBwAAAVAAAAA6Z2x5ZoPi2VsAAAGMAAAAcmhlYWQQC2qxAAACAAAAADZoaGVhCGsXSAAAAjgAAAAkaG10eE2rRkcAAAJcAAAACGxvY2EAHTwYAAACZAAAAAxtYXhwBT0FPgAAAnAAAAAgbmFtZaBxlY4AAAKQAAABn3Bvc3QB9wD6AAAEMAAAACBwcmVwa1uragAABFAAAAAUAAADSwGQAAUAAAQABAAAAAAABAAEAAAAAAAAAQEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAgICAAAAAg1UADev96AAAD6ACWAAAAAAACAAEAAQAAABQAAwABAAAAFAAEACAAAAAEAAQAAQAAIhL%2F%2FwAAIhL%2F%2F93vAAEAAAAAAAABVAMsAIABAABWACoCWAIeAQ4BLAIsAFoBgAKAAKAA1ACAAAAAAAAAACsAVQCAAKsA1QEAASsABwAAAAIAVQAAAwADqwADAAcAADMRIRElIREhVQKr%2FasCAP4AA6v8VVUDAAABAIABVQLVAasAAwAwGAGwBBCxAAP2sAM8sQIH9bABPLEFA%2BYAsQAAExCxAAblsQABExCwATyxAwX1sAI8EyEVIYACVf2rAatWAAAAAQAAAAEAANV4zkFfDzz1AAMEAP%2F%2F%2F%2F%2FWOhNz%2F%2F%2F%2F%2F9Y6E3MAAP8gBIADqwAAAAoAAgABAAAAAAABAAAD6P9qAAAXcAAA%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%2BgAAAAAAAAAAAAAAAAAAAAAAAAAAuQcRAACNhRgAsgAAABUUE7EAAT8%3D)format(‘truetype’)%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%40font-face%7Bfont-family%3A’brack_sm2882ad605b1e27be87c7468’%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMi7PH4UAAADMAAAATmNtYXA3kjw6AAABHAAAADxjdnQgAQYDiAAAAVgAAAASZ2x5ZkyYQ7YAAAFsAAAAkWhlYWQLyR8fAAACAAAAADZoaGVhAq0XCAAAAjgAAAAkaG10eDEjA%2FUAAAJcAAAADGxvY2EAAEKZAAACaAAAABBtYXhwBJsEcQAAAngAAAAgbmFtZW7QvZAAAAKYAAAB5XBvc3QArQBVAAAEgAAAACBwcmVwu5WEAAAABKAAAAAHAAACDAGQAAUAAAQABAAAAAAABAAEAAAAAAAAAQEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAgICAAAAAg9AMD%2FP%2F8AAABVAABAAAAAAACAAEAAQAAABQAAwABAAAAFAAEACgAAAAGAAQAAQACI5wjn%2F%2F%2FAAAjnCOf%2F%2F%2FcZdxjAAEAAAAAAAAAAAFUAFQBAAArAIwAgACoAAcAAAACAAAAAADVAQEAAwAHAAAxMxEjFyM1M9XVq4CAAQHWqwABAAAAAABVAVgAAwAfGAGwAy%2BwADyxAgL1sAE8ALEDAD%2BwAjx8sQAG9bABPBEzESNVVQFY%2FqgAAQDXAAABLAFUAAMAIBgBsAUvsAE8sAI8sQAC9bADPACwAy%2BwAjyxAAH1sAE8EzMRI9dVVQFU%2FqwAAAAAAQAAAAEAAIsesexfDzz1AAMEAP%2F%2F%2F%2F%2FVre5k%2F%2F%2F%2F%2F9Wt7mT%2FgP%2F%2FAdYBWAAAAAoAAgABAAAAAAABAAABVP%2F%2FAAAXcP%2BA%2F4AB1gABAAAAAAAAAAAAAAAAAAAAAwDVAAABLAAAASwA1wAAAAAAAAAhAAAAWAAAAJEAAQAAAAMACgACAAAAAAACAIAEAAAAAAAEAABlAAAAAAAAABUBAgAAAAAAAAABACYAAAAAAAAAAAACAA4AJgAAAAAAAAADAEQANAAAAAAAAAAEACYAeAAAAAAAAAAFABYAngAAAAAAAAAGABMAtAAAAAAAAAAIABwAxwABAAAAAAABACYAAAABAAAAAAACAA4AJgABAAAAAAADAEQANAABAAAAAAAEACYAeAABAAAAAAAFABYAngABAAAAAAAGABMAtAABAAAAAAAIABwAxwADAAEECQABACYAAAADAAEECQACAA4AJgADAAEECQADAEQANAADAAEECQAEACYAeAADAAEECQAFABYAngADAAEECQAGABMAtAADAAEECQAIABwAxwBCAHIAYQBjAGsAZQB0AHMAIABzAG0AYQBsAGwAIABzAGkAegBlAFIAZQBnAHUAbABhAHIATQBhAHQAaABzACAARgBvAHIAIABNAG8AcgBlACAAQgByAGEAYwBrAGUAdABzACAAcwBtAGEAbABsACAAcwBpAHoAZQBCAHIAYQBjAGsAZQB0AHMAIABzAG0AYQBsAGwAIABzAGkAegBlAFYAZQByAHMAaQBvAG4AIAAyAC4AMEJyYWNrZXRzX3NtYWxsX3NpemUATQBhAHQAaABzACAARgBvAHIAIABNAG8AcgBlAAAAAAMAAAAAAAAAqgBVAAAAAAAAAAAAAAAAAAAAAAAAAAC5B%2F8AAo2FAA%3D%3D)format(‘truetype’)%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%40font-face%7Bfont-family%3A’bracketse552f5417ff4680c6b50499’%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMi7RIisAAADMAAAATmNtYXBi7uzYAAABHAAAAExjdnQgBAkDLgAAAWgAAAASZ2x5Zo64f%2BkAAAF8AAABSWhlYWQLniGcAAACyAAAADZoaGVhBK4XLAAAAwAAAAAkaG10eCWq%2F90AAAMkAAAAFGxvY2EAABknAAADOAAAABhtYXhwBJIESAAAA1AAAAAgbmFtZRAA8I4AAANwAAAB3nBvc3QBwwDgAAAFUAAAACBwcmVwupWEAAAABXAAAAAHAAACggGQAAUAAAQABAAAAAAABAAEAAAAAAAAAQEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAgICAAAAAg9AMEAAAAAAADgAAAAAAAAAACAAEAAQAAABQAAwABAAAAFAAEADgAAAAKAAgAAgACI5sjnSOeI6D%2F%2FwAAI5sjnSOeI6D%2F%2F9xm3GXcZdxkAAEAAAAAAAAAAAAAAAABVABWAQAALACoA4AAMgAHAAAAAgAAACoA1QNVAAMABwAANTMRIxMjETPV1auAgCoDK%2F0AAtUAAQAAAAABgAOAAAUAJBgBsAAvsAPFsQEC%2FbADELEEBP0AsQAAP7ABPLEEBj%2BwAzwwMTEzEAEjAFUBKyv%2BqwH8AYT%2BqgABAAAAAAGAA4AABQAmGAGwAC6wA8WxBQL9sAMQsQIE%2FQB8sQAGPxiwBTyxAwb2sAI8MDEREgEzABMBAVQr%2FtMCA4D91v6qAYQB%2FAAB%2F6wAAAEsA4AABQAnGAGwAC%2BwBzywA8WxAQL9sAMQsQQE%2FQCxAAA%2FsAE8sQQGP7ADPDAxISMSATMAASxVAf7UKwFVAfwBhP6rAAH%2FrAAAASwDgAAFACkYAbABL7AHPLAExbEAAv2wBBCxAwT9AHyxAQY%2FsAA8GLEEAD%2BwAzwwMRMzEAEjANdV%2FqsrASsDgP3V%2FqsBhgAAAAABAAAAAQAAeuTcpl8PPPUAAwQA%2F%2F%2F%2F%2F9Wt7o7%2F%2F%2F%2F%2F1a3ujv%2BsAAABgAOAAAAACgACAAEAAAAAAAEAAAOAAAAAABdw%2F6z%2FrAGAAAEAAAAAAAAAAAAAAAAAAAAFANUAAAEsAAABLAAAASz%2FrAEs%2F6wAAAAAAAAAJAAAAGgAAACzAAAA%2FQAAAUkAAQAAAAUACAACAAAAAAACAIAEAAAAAAAEAAA%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%2FAAGNhQA%3D)format(‘truetype’)%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7Dtext%7Bfill%3A%23000000%3B%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20fill%3D%22%23000000%22%20font-family%3D%22Times%20New%20Roman%22%20font-size%3D%2218%22%20font-style%3D%22italic%22%20text-anchor%3D%22middle%22%20x%3D%225.5%22%20y%3D%2230%22%3EP%3C%2Ftext%3E%3Ctext%20fill%3D%22%23000000%22%20font-family%3D%22bracketse552f5417ff4680c6b50499%22%20font-size%3D%2218%22%20text-anchor%3D%22start%22%20x%3D%2212.5%22%20y%3D%2217%22%3E%26%23x239B%3B%3C%2Ftext%3E%3Ctext%20fill%3D%22%23000000%22%20font-family%3D%22brack_sm2882ad605b1e27be87c7468%22%20font-size%3D%2218%22%20text-anchor%3D%22start%22%20x%3D%2212.5%22%20y%3D%2223%22%3E%26%23x239C%3B%3C%2Ftext%3E

Maths Gcse Wjec-Eduqas Foundation