smc-602-10-Flat rate

Recursion and Finance, GEN2 2024 VCAA 5

Emi operates a mobile dog-grooming business.

The value of her grooming equipment will depreciate.

Based on average usage, a rule for the value, in dollars, of the equipment, $V_n$, after $n$ weeks is

$V_n=15000-60 n$

Assume that there are exactly 52 weeks in a year.

By what amount, in dollars, does the value of the grooming equipment depreciate each week? (1 mark)

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Emi plans to replace the grooming equipment after four years.
What will be its value, in dollars, at this time? (1 mark)

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$V_n$ is the value of the grooming equipment, in dollars, after $n$ weeks.
Write a recurrence relation in terms of $V_0, V_{n+1}$ and $V_n$ that can model this value from one week to the next. (1 mark)

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The value of the grooming equipment decreases from one year to the next by the same percentage of the original $\$ 15000$ value.
What is this annual flat rate percentage? (1 mark)

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Show Answers Only

a. $$60$

b. $$2520$

c. $V_0=15\,000 , \ \ V_{n+1}=V_n-60$

d. $20.8\%$

Show Worked Solution

a. $$60$

b. $n=4\times 52=208$

$V_{208}$	$=15\,000-60\times208$
	$=$2520$

c. $V_0=15\,000 , \ \ V_{n+1}=V_n-60$

d. $\text{Flat rate}\ =\dfrac{60}{15\,000}\times 52\times 100\%=20.8\%$

Recursion and Finance, GEN1 2023 VCAA 20-21 MC

For taxation purposes, Audrey depreciates the value of her $3000 computer over a four-year period. At the end of the four years, the value of the computer is $600.

Question 20

If Audrey uses flat rate depreciation, the depreciation rate, per annum is

Question 21

If Audrey uses reducing balance depreciation, the depreciation rate, per annum is closest to

Show Answers Only

$\text{Question 20:}\ C$

$\text{Question 21:}\ E$

Show Worked Solution

$\text{Question 20}$

$\text{Depreciation value}\ = 3000-600=$2400 $

$\text{Depreciation value (per year)}\ = \dfrac{2400}{4} =$600 $

$\text{Depreciation rate}\ = \dfrac{600}{3000} \times 100 =20\% $

$\Rightarrow C$

$\text{Question 21}$

$A = $600, \ P= $3000,\ n=4$

$A$	$=PR^n$
$600$	$=3000 \times R^4$
$R^4$	$=\dfrac{600}{3000} $
$R$	$=\sqrt[4]{0.2} $
	$=0.668…$

$\text{Depreciation rate}\ =1-0.668… = 0.331… \approx 33\% $

$\Rightarrow E$

CORE, FUR1-NHT 2019 VCAA 20 MC

Marty has been depreciating the value of his car each year using flat rate depreciation.

After three years of ownership, the value of the car was halved due to an accident.

Marty continued to depreciate the value of his car by the same amount each year after the accident.

Which one of the following graphs could show the value of Marty’s car after `n` years, `C_n`?

A.		B.
C.		D.
E.

Show Answers Only

`C`

Show Worked Solution

`text(Flat rate depression)`

`=>\ text{graph decreases in a straight line.}`

`text(Value of the car halves between)\ C_3\ text(and)\ C_4\ \ text(and then)`

`text(continues with the same gradient.)`

`=>\ C`

CORE*, FUR2 2008 VCAA 4

Michelle intends to keep a car purchased for $17 000 for 15 years. At the end of this time its value will be $3500.

By what amount, in dollars, would the car’s value depreciate annually if Michelle used the flat rate method of depreciation? (1 mark)
Determine the annual flat rate of depreciation correct to one decimal place. (1 mark)

Show Answers Only

`$900`
`5.3text{% (1 d.p.)}`

Show Worked Solution

a.	`text(Depreciation)`	`= (17\ 000 – 3500)/15`
		`= $13\ 500`

`:.\ text(Annual depreciation)`

`= (13\ 500)/15`

`= $900`

b. `:.\ text(Flat rate of depreciation )`

`= 900/(17\ 000) xx 100text(%)`

`= 5.29…`

`= 5.3text{% (1 d.p.)}`

CORE*, FUR1 2010 VCAA 8 MC

Rae paid $40 000 for new office equipment at the start of the 2007 financial year.

At the start of each following financial year, she used flat rate depreciation to revalue her equipment.

At the start of the 2010 financial year she revalued her equipment at $22 000.

The annual flat rate of depreciation she used, as a percentage of the purchase price, was

A. 11.25%

B. 15%

C. 17.5%

D. 35%

E. 45%

Show Answers Only

`B`

Show Worked Solution

`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(%)`

`=> B`

CORE*, FUR1 2014 VCAA 7 MC

New furniture was purchased for an office at a cost of $18 000.

Using flat rate depreciation, the furniture will be valued at $5000 after four years.

The expression that can be used to determine the value of the furniture, in dollars, after one year is

A. `18\ 000 - (4 xx 5000)`

B. `18\ 000 - ({18\ 000 - 5000}/4)`

C. `18\ 000 - 5000/4`

D. `(18\ 000)/4 - 5000`

E. `18\ 000 xx 0.726`

Show Answers Only

`B`

Show Worked Solution

`text(Annual Depreciation)`

`= (18\ 000 – 5000) -: 4`

`:.\ text(After 1 year,)`

`text(Value) = 18\ 000 – ({18\ 000 – 5000}/4)`

`=> B`

\(A\)	\(=PR^n\)
\(600\)	\(=3000 \times R^4\)
\(R^4\)	\(=\dfrac{600}{3000} \)
\(R\)	\(=\sqrt[4]{0.2} \)
	\(=0.668…\)

\(V_{208}\)	\(=15\,000-60\times208\)
	\(=$2520\)