Depreciation

Question 1 of 4

A television set with an original price of

$$1750$ depreciates in value by

$9%$ per year over

$8$ years. Solve for the following values:

Round your answer to two decimal places

$\text(New price (A)):$$ (822.94)

$\text(Depreciation Amount (Dep)):$$ (927.06)

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Depreciation Formula

$\mathsf{\color{#00880A}{A}}=\mathsf{\color{#9a00c7}{P}(1-\color{#e85e00}{R})^{\color{#007DDC}{n}}}$

Depreciation Amount

$\mathsf{Dep=\color{#9a00c7}{P}-\color{#00880A}{A}}$

First, summarise the data and draw a diagram for easier understanding of the problem

$\text(Original amount (P))=$1750$

$\text(Depreciation rate (R))=9% (0.09)$

$\text(Depreciation time (n))=8 \text(years)$

$\text(New amount (A))=?$

Substitute the known values into the depreciation formula to solve for the new amount.

Use the decimal value of the percentage.

$\mathsf{\color{#00880A}{A}}$	$=$	$\mathsf{\color{#9a00c7}{P}(1-\color{#e85e00}{R})^{\color{#007DDC}{n}}}$
$\mathsf{\color{#00880A}{A}}$	$=$	$\color{#9a00c7}{1750}(1-\color{#e85e00}{0.09})^{\color{#007DDC}{8}}$	Substitute known values
	$=$	$1750times0.4702525$
	$=$	$$822.94$	Rounded to two decimal places

Finally, subtract the new amount from the original amount to get the depreciation amount.

$\mathsf{Dep}$	$=$	$\mathsf{\color{#9a00c7}{P}-\color{#00880A}{A}}$
$\mathsf{Dep}$	$=$	$\color{#9a00c7}{1750}-\color{#00880A}{822.94}$
	$=$	$$927.06$

$A=$822.94$

$\text(Dep)=$927.06$

Question 2 of 4

A truck with an original price of $$190{,}000$ depreciates in value by

$15%$ per year over

$5$ years. Solve for the following values:

Round the new amount to two decimal places

Round the depreciation amount to a whole number

$\text(New price (A)):$$ (84304.01)

$\text(Depreciation Amount (Dep)):$$ (105696)

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Depreciation Formula

$\mathsf{\color{#00880A}{A}}=\mathsf{\color{#9a00c7}{P}(1-\color{#e85e00}{R})^{\color{#007DDC}{n}}}$

Depreciation Amount

$\mathsf{Dep=\color{#9a00c7}{P}-\color{#00880A}{A}}$

First, summarise the data and draw a diagram for easier understanding of the problem

$\text{Original amount (P)}=$190{,}000$

$\text(Depreciation rate (R))=15% (0.15)$

$\text(Depreciation time (n))=5 \text(years)$

$\text(New amount (A))=?$

Substitute the known values into the depreciation formula to solve for the new amount.

Use the decimal value of the percentage.

$\mathsf{\color{#00880A}{A}}$	$=$	$\mathsf{\color{#9a00c7}{P}(1-\color{#e85e00}{R})^{\color{#007DDC}{n}}}$
$\mathsf{\color{#00880A}{A}}$	$=$	$\color{#9a00c7}{190{,}000}(1-\color{#e85e00}{0.15})^{\color{#007DDC}{5}}$	Substitute known values
	$=$	$190{,}000\times(0.85)^{5}$
	$=$	$190{,}000\times0.4437053$
	$=$	$$84{,}304.01$	Rounded to two decimal places

Finally, subtract the new amount from the original amount to get the depreciation amount.

$\mathsf{Dep}$	$=$	$\mathsf{\color{#9a00c7}{P}-\color{#00880A}{A}}$
$\mathsf{Dep}$	$=$	$\color{#9a00c7}{190{,}000}-\color{#00880A}{84{,}304.01}$
	$=$	$$105{,}696$	Rounded to a whole number

$A=$84{,}304.01$

$\text{Dep}=$105{,}696$

Question 3 of 4

An off-road vehicle depreciates in value by

$14%$ per year. After

$3$ years, its new price is now $$27{,}300$ . What was its original price?

Round your answer to a whole number

$\text(Original price )=$ (42921)

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Depreciation Formula

$\mathsf{\color{#00880A}{A}}=\mathsf{\color{#9a00c7}{P}(1-\color{#e85e00}{R})^{\color{#007DDC}{n}}}$

Depreciation Amount

$\mathsf{Dep=\color{#9a00c7}{P}-\color{#00880A}{A}}$

First, summarise the data and draw a diagram for easier understanding of the problem

$\text{New amount (A)}=$27{,}300$

$\text(Depreciation rate (R))=14% (0.14)$

$\text(Depreciation time (n))=3 \text(years)$

$\text(Original price (P))=?$

Substitute the known values into the depreciation formula to solve for the new amount.

Use the decimal value of the percentage.

$\mathsf{\color{#00880A}{A}}$	$=$	$\mathsf{\color{#9a00c7}{P}(1-\color{#e85e00}{R})^{\color{#007DDC}{n}}}$
$\color{#00880A}{27{,}300}$	$=$	$\color{#9a00c7}{P}(1-\color{#e85e00}{0.14})^{\color{#007DDC}{3}}$	Substitute known values
$27{,}300$	$=$	$P\times(0.86)^{3}$
$27{,}300\color{#CC0000}{\div(0.86)^{3}}$	$=$	$Ptimes(0.86)^3$ $divide(0.86)^3$	Divide both sides by $(0.86)^3$
$\frac{27{,}300}{0.636056}$	$=$	$P$
$42{,}920.75$	$=$	$P$
$P$	$=$	$$42{,}921$	Rounded to a whole number

$\text(Original price)=$42,921$

Question 4 of 4

If a computer with a value of

$$1550$ depreciates at

$8%$ per year, how many years will it take for its price to drop to

$$865?$

(7) $\text(years)$

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Depreciation Formula

$\mathsf{\color{#00880A}{A}}=\mathsf{\color{#9a00c7}{P}(1-\color{#e85e00}{R})^{\color{#007DDC}{n}}}$

Depreciation Amount

$\mathsf{Dep=\color{#9a00c7}{P}-\color{#00880A}{A}}$

First, summarise the data and draw a diagram for easier understanding of the problem

$\text(Original amount (P))=$1550$

$\text(Depreciation rate (R))=8% (0.08)$

$\text(New amount (A))=$865$

$\text(Depreciation time (n))=?$

Substitute the known values into the depreciation formula to solve for the depreciation time.

Use the decimal value of the percentage.

$\mathsf{\color{#00880A}{A}}$	$=$	$\mathsf{\color{#9a00c7}{P}(1-\color{#e85e00}{R})^{\color{#007DDC}{n}}}$
$\color{#00880A}{865}$	$=$	$\color{#9a00c7}{1550}(1-\color{#e85e00}{0.08})^{\color{#007DDC}{n}}$	Substitute known values
$865$	$=$	$1550times(0.92)^n$
$865$ $divide1550$	$=$	$1550times(0.92)^n$ $divide1550$	Divide both sides by $1550$
$\frac{865}{1550}$	$=$	$(0.92)^n$
$0.558$	$=$	$(0.92)^n$	Rounded to three decimal places

Finally, use trial and error by substituting values to

$n$ to which will make the left and right sides equal.

Start by substituting

$n=6$ and

$n=7$ .

$n=6$

$0.558$	$=$	$(0.92)^n$
$0.558$	$=$	$(0.92)^6$	Substitute $n=6$
$0.558$	$=$	$0.606355001344$
$0.558$	$=$	$0.606$	Rounded to three decimal places

$n=7$

$0.558$	$=$	$(0.92)^n$
$0.558$	$=$	$(0.92)^7$	Substitute $n=7$
$0.558$	$=$	$0.55784660123648$
$0.558$	$=$	$0.558$	Rounded to three decimal places

Substituting $n=7$ makes the left and right sides of the equation equal.

Therefore, it will take $7$ years for the computer’s price to drop to

$$865$

$7 \text(years)$

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Depreciation Formula

Depreciation Amount

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