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Financial, STD2 EQ-Bank 02

  1. Kylie is a financial broker who earns a salary of \(\$93\,600\) per annum.
  2. She has 35% of her salary deducted for tax.
  3. Show that her net weekly pay is $1170.   (1 marks)
  5. Ben, Kylie's partner, works as a carpenter.
  6. He works 36 hours per week at a normal rate of $40 per hour and averages 6 hours overtime at time-and-a-half.
  7. Show that his average weekly pay before tax is $1800.  (2 marks)
  9. Kylie and Ben drew up the weekly budget below.
  10. They need to save $400 per week for an overseas holiday and also want to continue to save for a home.
  11. Ben has 25% of his gross wage deducted for taxation.

    1.   
  12. Comment on the budget as it appears in the table, indicating where they may have made an error, and suggest some practical ways to make the budget work for them.   (3 marks)
Show Answers Only
a.     \(\text{Kylie’s net salary}\) \(=\dfrac{$93\,600\times 0.65}{52}\)
    \(=$1170\)

 

b.     \(\text{Ben’s gross pay}\) \(=$40\times (36+1.5\times 6)\)
    \(=$1800\)
c.     \(\text{Ben’s net pay}\) \(=1800\times 0.75\)
    \(=$1350\)
  \(\text{Total net income}\) \(=1170+1350=$2520\)
  \(\text{Total expenses}\) \(=1000+360+210+250+250+400+500\)
    \(=$2720\)

\(\text{They have mistakenly used Ben’s gross salary in their}\)

\(\text{calculations which will leave them short of their savings}\)

\(\text{target of }$500\ \text{per week by } $200. \)

\(\text{Option 1.  Reduce savings by }$200\ \text{per week.}\)

\(\text{Option 2.  Reduce entertainment by by }$100 \)

\(\text{per week and reduce savings by }$100\ \text{per week.}\)

Show Worked Solution
a.     \(\text{Kylie’s net salary}\) \(=\dfrac{93\,600\times 0.65}{52}\)
    \(=$1170\)

 

b.     \(\text{Ben’s gross pay}\) \(=40\times (36+1.5\times 6)\)
    \(=$1800\)

 

c.     \(\text{Ben’s net pay}\) \(=1800\times 0.75\)
    \(=$1350\)
  \(\text{Total net income}\) \(=1170+1350=$2520\)
  \(\text{Total expenses}\) \(=1000+360+210+250+250+400+500\)
    \(=$2720\)

\(\text{They have mistakenly used Ben’s gross salary in their}\)

\(\text{calculations which will leave them short of their savings}\)

\(\text{target of }$500\ \text{per week by } $200. \)

\(\text{Option 1.  Reduce savings by }$200\ \text{per week.}\)

\(\text{Option 2.  Reduce entertainment by by }$100 \)

\(\text{per week and reduce savings by }$100\ \text{per week.}\)

Financial Maths, STD2 F1 2023 HSC 13 MC

An item is discounted by 30% and then a further discount of 20% is applied to the reduced price.

What is the total percentage discount?

  1. 25%
  2. 44%
  3. 50%
  4. 56%
Show Answers Only

`=>B`

Show Worked Solution

`text{Method 1}`

`text{Let original price}\ =x`

`text{1st discount}\ =0.7x`

`text{2nd discount}\ = 0.7x xx 0.8=0.56x`

`text{Total discount}\ = 1-0.56=0.44`
 

♦♦ Mean mark 47%.

`text{Method 2}`

`text{$100 less 30% = $70}`

`text{$70 less 20%} = 70-0.2xx70=$56`

`text{Total discount $100 ↓ $56 = 44%}`

`=>B`

Financial Maths, STD2 F1 2018 HSC 14 MC

To determine the retail price of an item, a shop owner increases its cost price by 30%. In a sale, the retails price is reduced by 30% to give the sale price.

How does the sale price compare to the cost price?

  1. The sale price is less than the cost price.
  2. The sale price is the same as the cost price.
  3. The sale price is more than the cost price.
  4. It is impossible to compare without knowing the cost price.
Show Answers Only

`text(A)`

Show Worked Solution

`text{Take an item that costs $100 (for example):}`

♦ Mean mark 50%.

`=>\ text(Original price) = 100 xx 1.3 = $130`

`=>\ text(Sale Price) = 130 xx 0.7 = $91`

`:.\ text(Sale price < cost price)`

`=>\ text(A)`

Financial Maths, STD2 F1 SM-Bank 7

A dress was on sale with 25% discount.

As a regular customer, Kate received a further 10% on the already discounted price.

What was the overall percentage discount Kate received?  (2 marks)

Show Answers Only

`text(32.5%)`

Show Worked Solution

`text{Solution 1 (efficient method)}`

`text(Overall discount)` `=1-(0.75 xx 0.90)`
  `=1-0.675`
  `=0.325`
  `=32.5text(%)`

 

`text(Solution 2)`

`text(Let the dress cost) = $100`

`text(C) text(ost after 25% discount) = $75`

 

`text(C) text(ost after another 10% discount)`

`= 75 – (10 text{%} xx 75)`

`= $67.50`
 

`:.\ text(Overall discount) = 32.5text(%)`

Financial Maths, STD2 F1 SM-Bank 12

A golf shop is having a Boxing Day sale.

  1. What is the percentage discount on a putter which is reduced from $120.00 to $102.00?  (1 mark)

  2. The same discount applies storewide. What discount amount is applicable to a box of golf balls whose original price was $25.00?  (1 mark)

  3. What is the sale price of a golf bag which originally cost $160.00  (1 mark)

Show Answers Only
  1. `15 text(%)`
  2. `$3.75`
  3. `$136.00`
Show Worked Solution
i.     `text(Percentage Discount)` `=(120-102)/120 xx 100`
    `=18/120 xx 100`
    `=15 text(%)`

 

ii.    `text(Discounted Amount)` `=15 text(%) xx 25`
    `=$3.75`

 

iii.    `text(Sale Price)` `= 160 – 15 text(%) xx 160`
    `=0.85 xx 160`
    `=$136.00`

Financial Maths, STD2 F1 2014 HSC 18 MC

The average NSW annual water consumption from the residential sector is equal to  90 340  litres per person per year. The Building Sustainability Index (BASIX) uses this as the benchmark to set a target for reducing water consumption by up to 40%.

A new building, planned to house 50 people, has been designed to meet a 25% reduction on this water consumption benchmark.

How much water per year, to the nearest kilolitre, is this building designed to save when fully occupied?

  1.    1129
  2.    1807
  3.    2710
  4.    3388
Show Answers Only

`A`

Show Worked Solution

`text(Benchmark) = 90\ 340\ text(L)`

`text(Water saved if usage)\ darr text(25%)`

`= 90\ 340 xx text(25%)`

`= 22\ 585\ text(L per person)`

 
`:.\ text(Water saved for 50 people)`

`= 50 xx 22\ 585`

`= 1\ 129\ 250\ text(L)`

`~~ 1129\ text(kL)`

`=>  A`