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Financial Maths, STD1 F1 2021 HSC 19 v1

Maya purchased a motorbike for $12 000. The value of the motorbike decreases according to a linear model. The graph shows the value of the motorbike, $\(V\), against the time, \(t\) months, since it was purchased.
 

  1. By how much does the value of the motorbike decrease every 10 months?   (1 mark)

  2. Find the value of the motorbike after 4 years.   (1 mark)

  3. Identify ONE problem with using this model to determine the value of Maya's motorbike over time.   (1 mark)

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a.     \(\$1000\)

b.     \(\$7200\)

c.     \(\text{Motorbike will have a negative value after 120 months.}\)

Show Worked Solution

a.    \(\text{Total decrease over 100 months}= 12\,000-2000= \$10\,000\)

\(\text{Decrease per 10 months}= \dfrac{10\,000}{10}= \$1000\)
 

b.    \(\text{4 years} = 4 \times 12 = 48\ \text{months}\)

\(\text{Depreciation rate}= \$100\ \text{per month}\)

\(V = 12\,000-(100 \times 48)=\$7200\)
 

c.    \(\text{Model limitations:}\)

\(\text{The linear model will eventually predict a value of \$0 (at 120 months) and negative}\)

\(\text{values beyond that, which is unrealistic.}\)

Financial Maths, STD1 F1 2023 HSC 6 MC v1

A courier van was valued at $48 000 when new. The value of the van depreciates at a rate of 18 cents per kilometre travelled.

What is the value of the van after it has travelled a total distance of 95 400 km?

  1. $17 172
  2. $30 828
  3. $37 440
  4. $65 172
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\(B\)

Show Worked Solution

\(\text{Depreciation} = 95\,400\times\dfrac{18}{100}=\$17\,172\)

\(\text{Value} = 48\,000-17\,172=\$30\,828\)

\(\Rightarrow B\)