smc-4335-10-Find S

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)

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`$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-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)

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`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

2020
2021
2022
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.

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

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

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`20text{%}`
`$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?

$952
$1110
$1357
$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)

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`$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)

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`$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?

$8968
$9195
$11 022
$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`

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