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v1 Financial Maths, STD2 F1 2021 HSC 19

Sophie bought a set of gym equipment four years ago. It depreciated by $1800 each year using the straight-line method of depreciation. The equipment is now valued at $6200.

Find the initial value of the gym equipment.  (2 marks)

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`$13\ 400`

Show Worked Solution

`text{Find initial value}\ (V_0):`

`S` `=V_0-Dn`  
`6200` `=V_0-1800 xx 4`  
`V_0` `=6200 + 7200`  
  `=$13\ 400`  

Financial Maths, SMB-015

Hugo is a professional bike rider.

The value of his bike will be depreciated over time using the flat rate method of depreciation.

The graph below shows his bike’s initial purchase price and its value at the end of each year for a period of three years.
 

  1. What was the initial purchase price of the bike?  (1 mark)

  2. Use calculations to show that the bike depreciates in value by $1500 each year.  (1 mark)

  3. Assume that the bike's value continues to depreciate by $1500 each year. Determine its value five years after it was purchased.  (1 mark)

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  1. `$8000`
  2. `text(See Worked Solutions)`
  3. `$500`
Show Worked Solution

i.   `$8000`
 

ii.   `text(Value after 1 year) = $6500\ \ \ text{(from graph)}`

`:.\ text(Annual depreciation)` `= 8000-6500`
  `= $1500`

 

iii.  `text(After 5 years:)`

`S` `=V_0-Dn`
  `=8000-5 xx 1500`
  `=$500`

Financial Maths, SMB-014

Rae paid  $40 000  for new office equipment at the start of the 2019 financial year.

At the start of each following financial year, she used straight-line (flat rate) depreciation to revalue her equipment.

At the start of the 2022 financial year she revalued her equipment at  $22 000.

Calculate the annual straight-line rate of depreciation she used, as a percentage of the purchase price.  (2 marks)

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`15text(%)`

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`text(Depreciation over 3 years)`

♦ Mean mark 50%.

`=40\ 000-22\ 000`

`=$18\ 000`
 

`:.\ text(Annual depreciation) = (18\ 000)/3 = $6000`

`:.\ text(Depreciation rate) = 6000/(40\ 000) = 0.15 = 15text(%)`

Financial Maths, STD2 F1 2021 HSC 19

Adam purchased some office furniture five years ago. It depreciated by $2300 each year based on the straight-line method of depreciation. The salvage value of the furniture is now $7500.

Find the initial value of the office furniture.  (2 marks)

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`$19\ 000`

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`text{Find initial value}\ (V_0):`

`S` `=V_0-Dn`  
`7500` `=V_0-2300 xx 5`  
`V_0` `=7500 + 11\ 500`  
  `=$19\ 000`