Financial Maths, STD2 EQ-Bank 34

Baron is 19 years old, single with no children, and lives away from his parents' home to study. He receives the maximum Youth Allowance payment of $663.30 per fortnight.

Baron supplements his payments by working part-time and earns $15.50 per hour in a retail position. His Youth Allowance is reduced by 50 cents for each dollar earned over $236 per fortnight.

Baron works 22 hours per fortnight. Calculate his total fortnightly income including his reduced Youth Allowance payment and earnings. (2 marks)
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What is the maximum number of hours Baron can work per fortnight before his Youth Allowance payment is reduced to zero? Give your answer to the nearest whole hour. (2 marks)
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Show Answers Only

a. $\text{\$951.80 per fortnight}$

b. $\text{101 hours per fortnight}$

Show Worked Solution

a. $\text{Baron’s earnings} = 15.50\times 22=$341$

$\text{Income over free area} = 341-236 = $105$

$\text{Reduction in payment} = 0.50\times 105= $52.50$

$\text{Reduced Youth Allowance} = 663.30-52.50=$610.80$

$\text{Total fortnightly income} = 610.80+341=$951.80$

b. $\text{For payment to reduce to zero, reduction needed} = $663.30$

$\text{Income over free area} = \dfrac{663.30}{0.50}=$1326.60$

$\text{Total earnings needed} = 1326.60+236=$1562.60$

$\text{Hours needed}=\dfrac{1562.60}{15.50}=100.8$

$\therefore\ \text{Baron can work a maximum of 101 hours per fortnight}$