SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

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)

Show Answers Only

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
Show Answers Only

\(B\)

Show Worked Solution

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

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

\(\Rightarrow B\)

Financial Maths, STD2 F1 2010 HSC 5 MC v2

Noah saw the following advertisement at his local bank in Newcastle:

Noah invests $6000 for a term of 9 months.

How much interest will Noah earn at the end of the term?

  1. $216
  2. $259
  3. $288
  4. $298
Show Answers Only

\(A\)

Show Worked Solution

\(P=\$6000,\ r=4.8\%=0.048,\ n=\dfrac{9}{12}\ \text{years}\)

\(I=Prn=6000 \times 0.048 \times \dfrac{9}{12}=\$216\)

\(\Rightarrow A\)

Financial Maths, STD2 F1 2010 HSC 5 MC v1

Hayden invests $3000 for 1 year and 8 months. Simple interest is paid on the investment at a rate of 5% per annum.

What is the total value of the investment at the end of this period?

  1. $3150
  2. $3250
  3. $3270
  4. $3500
Show Answers Only

\(B\)

Show Worked Solution

\(\text{1 year and 8 months = 20 months}\)

\(I=Prn=3000 \times 0.05 \times \dfrac{20}{12}=\$250\)

\(\therefore\ \text{Value of Investment} =3000+250=\$3250\)

\(\Rightarrow B\)

Financial Maths, STD1 F1 2023 HSC 2 MC v1

Mia deposits $4000 into a savings account at the Commonwealth Bank that pays simple interest at a rate of 4% per annum.

How much interest will she earn in the first three years?

  1. $120
  2. $160
  3. $480
  4. $4480
Show Answers Only

\(C\)

Show Worked Solution

\(P=\$4000,\ r=4\%=0.04,\ n=3\ \text{years}\)

\(I=Prn=4000 \times 0.04 \times 3=\$480\)

\(\Rightarrow C\)