Question

full working out is required. no working out = no marks
13 a secondhand store buys a toy car for $40 and sells it for $120.
a) how much profit did they make in dollars?
b) what is the percentage profit?

14 a watch costs $750. its discounted by 15%. after a week, the sale ends and they increase it 10%.
what is the final price?
(2 marks)

15 a calculate the amount of simple interest earned in a $40,000 investment which pays 7% p.a interest, if it was invested for 8 years?
(3 marks)
b calculate the amount of simple interest earned in a $6.3 million investment which pays 8.12% p.a interest, if it was invested for 8 years and 6 months?

Explanation:

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<reasoning>

Calculate profit in dollars

Using the Percentage Calculations knowledge point
\[
\text{Profit} = \text{Selling Price} - \text{Cost Price}
\]
\[
\text{Profit} = \$120 - \$40 = \$80
\]

Calculate percentage profit

Using the Percentage Change knowledge point
\[
\text{Percentage Profit} = \frac{\text{Profit}}{\text{Cost Price}} \times 100\%
\]
\[
\text{Percentage Profit} = \frac{\$80}{\$40} \times 100\% = 200\%
\]

Calculate final watch price

Using the Percentage Calculations knowledge point
\[
\text{Discounted Price} = \$750 \times (1 - 0.15) = \$750 \times 0.85 = \$637.50
\]
\[
\text{Final Price} = \$637.50 \times (1 + 0.10) = \$637.50 \times 1.10 = \$701.25
\]

Calculate simple interest for first investment

Using the Simple Interest knowledge point
\[
I = P \times r \times t
\]
\[
I = \$40,000 \times 0.07 \times 8 = \$22,400
\]

Calculate simple interest for second investment

Using the Simple Interest knowledge point
\[
t = 8 + \frac{6}{12} = 8.5\text{ years}
\]
\[
I = \$6,300,000 \times 0.0812 \times 8.5 = \$4,348,320
\]
</reasoning>

<answer>

Question 13

a) The profit is <blank>\$80</blank>.

b) The percentage profit is <blank>200%</blank>.

Question 14

The final price of the watch is <blank>\$701.25</blank>.

Question 15

a) The amount of Simple Interest earned is <blank>\$22,400</blank>.

b) The amount of Simple Interest earned is <blank>\$4,348,320 (or \$4.34832\text{ million}</blank>).
</answer>

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"Simple Interest"
]
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Answer:

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<reasoning>

Calculate profit in dollars

Using the Percentage Calculations knowledge point
\[
\text{Profit} = \text{Selling Price} - \text{Cost Price}
\]
\[
\text{Profit} = \$120 - \$40 = \$80
\]

Calculate percentage profit

Using the Percentage Change knowledge point
\[
\text{Percentage Profit} = \frac{\text{Profit}}{\text{Cost Price}} \times 100\%
\]
\[
\text{Percentage Profit} = \frac{\$80}{\$40} \times 100\% = 200\%
\]

Calculate final watch price

Using the Percentage Calculations knowledge point
\[
\text{Discounted Price} = \$750 \times (1 - 0.15) = \$750 \times 0.85 = \$637.50
\]
\[
\text{Final Price} = \$637.50 \times (1 + 0.10) = \$637.50 \times 1.10 = \$701.25
\]

Calculate simple interest for first investment

Using the Simple Interest knowledge point
\[
I = P \times r \times t
\]
\[
I = \$40,000 \times 0.07 \times 8 = \$22,400
\]

Calculate simple interest for second investment

Using the Simple Interest knowledge point
\[
t = 8 + \frac{6}{12} = 8.5\text{ years}
\]
\[
I = \$6,300,000 \times 0.0812 \times 8.5 = \$4,348,320
\]
</reasoning>

<answer>

Question 13

a) The profit is <blank>\$80</blank>.

b) The percentage profit is <blank>200%</blank>.

Question 14

The final price of the watch is <blank>\$701.25</blank>.

Question 15

a) The amount of Simple Interest earned is <blank>\$22,400</blank>.

b) The amount of Simple Interest earned is <blank>\$4,348,320 (or \$4.34832\text{ million}</blank>).
</answer>

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