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v1 Financial Maths, STD2 F4 2019 HSC 37

A machine is purchased for $32 800. Each year the value of the machine is depreciated by the same percentage.

The table shows the value of the machine, based on the declining-balance method of depreciation, for the first three years.

\[ \begin{array} {|c|c|} \hline \textit{End of year} & \textit{Value} \\ \hline 1 & \$27\,056.00 \\ \hline 2 & \$22\,888.16 \\ \hline 3 & \$19\,377.82 \\ \hline \end{array} \]

What is the value of the machine at the end of 10 years?  (3 marks)

Show Answers Only

`$4783.78`

Show Worked Solution

`text(Find the depreciation rate:)`

`S` `= V_0(1-r)^n`
`27\ 056` `= 32\ 800(1-r)^1`
`1-r` `= \frac{27\ 056}{32\ 800} = 0.82488`
`r` `= 0.17512`

 

`:.\ \text(Value after 10 years)`

`= 32\ 800(1-0.17512)^{10}`

`= 32\ 800(0.82488)^{10}`

`= 32\ 800 × 0.1458`

`= $4783.78`

v1 Financial Maths, STD2 F4 2018 HSC 26h

A piece of machinery is purchased for $18,500.

The value of the machine depreciates by 14% each year using the declining-balance method.

What is the value of the machine after three years?  (2 marks)

Show Answers Only

`$11\ 767\ \ (text(nearest dollar))`

Show Worked Solution
`S` `= V_0(1 – r)^n`
  `= 18\ 500(1 – 0.14)^3`
  `= 18\ 500(0.86)^3`
  `= 18\ 500 × 0.636056`
  `= 11\ 767.04`
  `= $11\ 767\ \ (text(nearest dollar))`

v1 Financial Maths, STD2 F4 2014 HSC 9 MC

A laptop is purchased for $2500. It depreciates at a rate of 25% per annum using the declining balance method.

What will be the salvage value of the laptop after 2 years, to the nearest dollar?

  1. $1406
  2. $1250
  3. $1681
  4. $1875
Show Answers Only

`A`

Show Worked Solution
`S` `= V_0 (1-r)^n`
  `= 2500 (1-25/100)^2`
  `= 2500 (0.75)^2`
  `= 2500 × 0.5625`
  `= $1406.25`

 

`Rightarrow \ text(To the nearest dollar, the salvage value is **$1406**)`

`Rightarrow A`

v1 Financial Maths, STD2 F4 2021 HSC 4 MC

A machine was purchased for $3200 four years ago. It depreciates at a rate of 12% per year using the declining-balance method.

What is the machine’s current value, to the nearest dollar?

  1. $1850
  2. $1919
  3. $1945
  4. $2010
Show Answers Only

`B`

Show Worked Solution
`S` `= V_0 (1-r)^n`
  `= 3200 (1-0.12)^4`
  `= 3200 (0.88)^4`
  `= 3200 × 0.5997`
  `= 1919`

⇒ `B`

Depreciation, SMB-004

A new electric vehicle costs $46 000 and is depreciated using the reducing balance method by 15% of its value each year.

Find its value after four years, giving your answer to the nearest dollar.   (2 marks)

Show Answers Only

`$24\ 012`

Show Worked Solution

`V_o = 46\ 000,\ \ \ r = 15% = 0.15,\ \ \ n = 4`

`S` `= V_0 (1-r)^n`
  `= 46\ 000 (1-0.15)^4`
  `=46\ 000 xx 0.85^4`
  `= $24\ 012\ \ \text{(nearest dollar)}`

 

Depreciation, SMB-003 MC

A new car costs $30 000 and is depreciated using the reducing balance method by 20% of its value each year.

After three years its value is

  1. `$6000`
  2. `$12\ 000`
  3. `$15\ 360`
  4. `$24\ 000`
Show Answers Only

`C`

Show Worked Solution

`V_0= 30\ 000,\ \ \ r = 20% = 0.2,\ \ \ n = 3`

`S` `= V_0 (1-r)^n`
  `= 30\ 000 (1-0.2)^3`
  `=30\ 000 xx 0.8^3`
  `= $15\ 360`

 
`=>  C`

Depreciation, SMB-002

Peter installed his new pool fence on 1 January 2013 at a cost of $12 000.

On 1 January of each year after 2013 its value is depreciated by 15% using the reducing balance method.

The value of the pool fence will be below $4000 for the first time on 1 January of what year? Show all working.   (3 marks)

Show Answers Only

`text{Test the values of different years using:}\ \ S=V_0(1-r)^n`

`S \text{(Jan17)} = 12\ 000(1-0.15)^4= 5000 xx 0.85^4= $2560`

`S \text{(Jan19)} = 12\ 000 xx 0.85^6= $4525.79`

`S \text{(Jan20)} = 12\ 000 xx 0.85^7= $3846.93`

`\text{2020 is the 1st year its value is below $4000 on 1 January.}`

Show Worked Solution

`r=15% = 0.15`

`text{Test the values of different years using:}\ \ S=V_0(1-r)^n`

`S \text{(Jan17)} = 12\ 000(1-0.15)^4= 5000 xx 0.85^4= $2560`

`S \text{(Jan19)} = 12\ 000 xx 0.85^6= $4525.79`

`S \text{(Jan20)} = 12\ 000 xx 0.85^7= $3846.93`

`\text{2020 is the 1st year its value is below $4000 on 1 January.}`

Depreciation, SMB-001 MC

A new air-conditioning unit was purchased for $5000 on 1 January 2017.

On 1 January of each year after 2017 its value is depreciated by 20% using the reducing balance method.

The value of the air conditioner will be below $1500 for the first time on 1 January

  1. 2020
  2. 2021
  3. 2022
  4. 2023
Show Answers Only

`D`

Show Worked Solution

`r=20% = 0.2`

`text{Test the values of given options using:}\ \ S=V_0(1-r)^n`

`S \text{(Jan20)} = 5000(1-0.2)^3= 5000 xx 0.8^3= $2560`

`S \text{(Jan22)} = 5000 xx 0.8^5= $1638.40`

`S \text{(Jan23)} = 5000 xx 0.8^6= $1310.72`

 `=>  D`

Financial Maths, SMB-020

A company purchases a machine for $50 000. The two methods of depreciation being considered are the declining-balance method and the straight-line method.

For the declining-balance method, the salvage value of the machine after `n` years is given by the formula

    `S=V_(0)xx(0.80)^(n),`

where `S` is the salvage value and `V_(0)` is the initial value of the asset.

  1. What is the annual rate of depreciation used in this formula?  (1 mark)

  2. Calculate the salvage value of the machine after 3 years, based on the given formula.  (2 marks)

Show Answers Only
  1.  `20text{%}`
  2. `$25\ 600`
Show Worked Solution

a.  `text{Depreciation rate}\ = 1-0.8=0.2=20text{%}`
 

b.  `text{Find}\ \ S\ \ text{when}\ \ n=3:`

`S` `=V_0 xx (0.80)^n`  
  `=50\ 000 xx (0.80)^3`  
  `=$25\ 600`  

♦♦ Mean mark (a) 24%.
COMMENT: A poor State result in part (a) that warrants attention.

Financial Maths, SMB-019

Alan bought a light aircraft for $76 500. It will depreciate at 14% per annum. 

Using the declining balance method, what will be the salvage value of the light aircraft after 6 years, to the nearest dollar? 

Show Answers Only

`$30\ 949`

Show Worked Solution
`S` `= V_0 (1-r)^n`
  `= 76\ 500 (1-14/100)^6`
  `= 76\ 500 (0.86)^6`
  `= $30\ 949.39`
  `=$30\ 949\ \ text{(nearest dollar)}`

Financial Maths, SMB-018

Marnus bought a cricket bowling machine two years ago that cost $3400. Its value has depreciated by 10% each year, based on the declining-balance method.

What is the salvage value today, to the nearest dollar?  (2 marks)

Show Answers Only

`$2754`

Show Worked Solution
`S` `= V_0 (1-r)^n`
  `= 3400 (1-0.10)^2`
  `= 3400 (0.90)^2`
  `= $2754`

Financial Maths, STD2 F4 2021 HSC 4 MC

Three years ago an appliance was valued at $2467. Its value has depreciated by 15% each year, based on the declining-balance method.

What is the salvage value today, to the nearest dollar?

  1. $952
  2. $1110
  3. $1357
  4. $1515
Show Answers Only

`D`

Show Worked Solution
`S` `= V_0 (1-r)^n`
  `= 2467 (1-0.15)^3`
  `= 2467 (0.85)^3`
  `= $1515`

 
`=>  D`

Financial Maths, STD2 F4 2019 HSC 37

A new car is bought for $24 950. Each year the value of the car is depreciated by the same percentage.

The table shows the value of the car, based on the declining-balance method of depreciation, for the first three years.

\begin{array} {|c|c|}
\hline
\rule{0pt}{2.5ex}\textit{End of year}\rule[-1ex]{0pt}{0pt} & \textit{Value}\\
\hline
\rule{0pt}{2.5ex}1\rule[-1ex]{0pt}{0pt} & \$21\ 457.00 \\
\hline
\rule{0pt}{2.5ex}2\rule[-1ex]{0pt}{0pt} & \$18\ 453.02 \\
\hline
\rule{0pt}{2.5ex}3\rule[-1ex]{0pt}{0pt} & \$15\ 869.60 \\
\hline
\end{array}

What is the value of the car at the end of 10 years?  (3 marks)

Show Answers Only

`$5521.47`

Show Worked Solution

`text(Find the depreciation rate:)`

`S` `= V_0(1-r)^n`
`21\ 457` `= 24\ 950(1-r)^1`
`1-r` `= (21\ 457)/(24\ 950)`
`1-r` `= 0.86`
`r` `= 0.14`

 
`:.\ text(Value after 10 years)`

`= 24\ 950(1-0.14)^10`

`= 5521.474…`

`= $5521.47\ \ (text(nearest cent))`

Financial Maths, STD2 F4 2018 HSC 26h

A car is purchased for $23 900.

The value of the car is depreciated by 11.5% each year using the declining-balance method.

What is the value of the car after three years?  (2 marks)

Show Answers Only

`$16\ 566\ \ (text(nearest dollar))`

Show Worked Solution
`S` `= V_0(1-r)^n`
  `= 23\ 900(1-0.115)^3`
  `= 23\ 900(0.885)^3`
  `= 16\ 566.383…`
  `= $16\ 566\ \ (text(nearest dollar))`

Financial Maths, STD2 F4 2014 HSC 9 MC

A car is bought for  $19 990. It will depreciate at 18% per annum. 

Using the declining balance method, what will be the salvage value of the car after 3 years, to the nearest dollar? 

  1. $8968
  2. $9195
  3. $11 022
  4. $16 392
Show Answers Only

`C`

Show Worked Solution
`S` `= V_0 (1-r)^n`
  `= 19\ 990 (1-18/100)^3`
  `= 19\ 990 (0.82)^3`
  `= $11\ 021.85`

 
`=>  C`