Skip to content Skip to navigation

Connexions

You are here: Home » Content » Finansiële wiskunde: saamgestelde depresiasie (Graad 11)

Navigation

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • FETWisk display tagshide tags

    This module is approved and included inLens: Siyavula: Wiskunde (Gr 10 - 12)
    By: Siyavula

    Review Status: Approved

    Click the "FETWisk" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

Saamgestelde depresiasie

Die tweede metode om waardevermindering te bereken is om te veronderstel dat die waarde van die bate afneem teen 'n sekere jaarlikse koers, maar dat die aanvanklike waarde van die bate hierdie jaar, is die boekwaarde van die bate aan die einde van verlede jaar.

Byvoorbeeld, as ons tweedehandse motor 'n beperkte nuttige lewensduur van 5 jaar het en dit het 'n aanvanklike waarde van R60 000 , dan is die rentekoers van waardevermindering 20% (100% / 5 jaar). Na 1 jaar, is die motor werd :

Boekwaarde na eerste jaar = P ( 1 - n × i ) = R 60 000 ( 1 - 1 × 20 % ) = R 60 000 ( 1 - 0 , 2 ) = R 60 000 ( 0 , 8 ) = R 48 000 Boekwaarde na eerste jaar = P ( 1 - n × i ) = R 60 000 ( 1 - 1 × 20 % ) = R 60 000 ( 1 - 0 , 2 ) = R 60 000 ( 0 , 8 ) = R 48 000
(1)

Aan die begin van die tweede jaar is die motor se waarde nou R48 000; dus na twee jaar is die motor se waarde :

Boekwaarde na tweede jaar = P ( 1 - n × i ) = R 48 000 ( 1 - 1 × 20 % ) = R 48 000 ( 1 - 0 , 2 ) = R 48 000 ( 0 , 8 ) = R 38 400 Boekwaarde na tweede jaar = P ( 1 - n × i ) = R 48 000 ( 1 - 1 × 20 % ) = R 48 000 ( 1 - 0 , 2 ) = R 48 000 ( 0 , 8 ) = R 38 400
(2)

Ons kan hierdie waardes tabelleer

Tabel 1
Einde van eerste jaar R60000(1-1×20%)60000(1-1×20%)=R60000(1-1×20%)160000(1-1×20%)1 = R48 000,00
Einde van tweede jaar R48000(1-1×20%)48000(1-1×20%)=R60000(1-1×20%)260000(1-1×20%)2 = R38 400,00
Einde van derde jaar R38 400(1-1×20%)(1-1×20%)=R60000(1-1×20%)360000(1-1×20%)3 = R30 720,00
Einde van vierde jaar R30 720(1-1×20%)(1-1×20%)=R60000(1-1×20%)460000(1-1×20%)4 = R24 576,00
Einde van vyfde jaar R24 576(1-1×20%)(1-1×20%)=R60000(1-1×20%)560000(1-1×20%)5 = R19 608,80

Ons kan nou die algemene formule vir die boekwaarde van 'n bate neerskryf indien die waardevermindering saamgesteld is.

Oorspronklike waarde - Totale waardevermindering na n jaar = P ( 1 - i ) n Oorspronklike waarde - Totale waardevermindering na n jaar = P ( 1 - i ) n
(3)

Byvoorbeeld, die boekwaarde van 'n motor na twee jaar kan eenvoudig soos volg bereken word:

Boekwaarde na 2 jaar = P ( 1 - i ) n = R 60 000 ( 1 - 20 % ) 2 = R 60 000 ( 1 - 0 , 2 ) 2 = R 60 000 ( 0 , 8 ) 2 = R 38 400 Boekwaarde na 2 jaar = P ( 1 - i ) n = R 60 000 ( 1 - 20 % ) 2 = R 60 000 ( 1 - 0 , 2 ) 2 = R 60 000 ( 0 , 8 ) 2 = R 38 400
(4)

soos verwag.

Let daarop dat die verskil tussen die saamgestelde rente berekeninge en saamgestelde waardevermindering berekeninge is dat terwyl die rente waarde voeg by die aanvangsbedrag, die waardeverminderingbedrag die waarde verminder!

Exercise 1: Saamgestelde waardevermindering

Die Flamingo bevolking van die Bergrivier mond verminder teen 'n koers van 12% p.a. As daar nou 3 200 flaminke in die vleilande van die Bergrivier mond is, hoeveel sal daar wees na 5 jaar? Beantwoord tot drie beduidende syfers.

Solution

  1. Stap 1. Bepaal wat gegee is en wat gevra word :
    P = R 3 200 i = 0 , 12 n = 5 A word gevra P = R 3 200 i = 0 , 12 n = 5 A word gevra
    (5)
  2. Stap 2. Bepaal hoe om die probleem te benader:
    A = 3 200 ( 1 - 0 , 12 ) 5 A = 3 200 ( 1 - 0 , 12 ) 5
    (6)
  3. Stap 3. Los die probleem op :
    A = 3 200 ( 0 , 88 ) 5 = 3 200 × 0 , 527731916 = 1688 , 742134 A = 3 200 ( 0 , 88 ) 5 = 3 200 × 0 , 527731916 = 1688 , 742134
    (7)
  4. Stap 4. Skryf finale antwoord neer : Daar sal ongeveer 1690 flaminke na 5 jaar wees

Exercise 2: Saamgestelde waardevermindering

Saamgestelde waardevermindering

Farmer Brown koop 'n trekker vir R250 000 en dit verminder in waarde teen 20% per jaar saamgestelde waardevermindering . Wat is die gedepresieerde waarde van die trekker na 5 jaar?

Solution

Oplossing
  1. Stap 1. Bepaal wat gegee is en wat gevra word :
    P = R 250 000 i = 0 , 2 n = 5 A word gevra P = R 250 000 i = 0 , 2 n = 5 A word gevra
    (8)
  2. Stap 2. Bepaal hoe om probleem te benader :
    A = 250 000 ( 1 - 0 , 2 ) 5 A = 250 000 ( 1 - 0 , 2 ) 5
    (9)
  3. Stap 3. Los probleem op :
    A = 250 000 ( 0 , 8 ) 5 = 250 000 × 0 , 32768 = 81 920 A = 250 000 ( 0 , 8 ) 5 = 250 000 × 0 , 32768 = 81 920
    (10)
  4. Stap 4. Skryf finale antwoord neer :

    Verminderde waarde na 5 jaar is R81 920

Saamgestelde Waardevermindering

  1. Op 1 Januarie 2008 is die waarde van my Kia Sorento R320 000. Elke jaar daarna, sal die motor se waarde verminder teen 20% van die vorige jaar se waarde. Wat is die waarde van die motor op 1 Januarie 2012?
  2. Die bevolking van Bonduel verminder teen 'n koers van 9,5% per jaar soos mense na die stede migreer. Bereken die afname in die bevolking oor 'n tydperk van 5 jaar indien die aanvanklike bevolking 2 178 000 is.
  3. 'n 20 kg waatlemoen bestaan ​​uit 98% water. As dit buite in die son gelaat word, verloor dit 3% van sy water elke dag. Hoeveel sal dit weeg na 'n maand van 31 dae?
  4. 'n Rekenaar verminder in waarde teen x%x% per annum as die verminderde saldo metode gebruik word. Vier jaar gelede was die rekenaar se waarde R10 000 en dit is nou R4 520 werd. Bereken die waarde van xx korrek tot twee desimale plekke.

Content actions

Download module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks