2. Percentages

Australian Curriculum 11 Essential Mathematics - 2020 Edition

2.08 Financial calculations

Lesson

The level of debt among teenagers is rising at an alarming rate. One of the ways to help ensure you're always cashed up is to create a budget. A budget is a spending plan for a particular time period, whether it be a weekly budget or a monthly budget, that helps you keep track of your money and create realistic savings goals. People often use tables or spreadsheets to present their budgets in an easily readable format.

Once you subtract your expenses from your income, you know how much money you have left over. This is called your disposable income and it can be used as extra savings, spent on things you like or for something big you're saving for like a new laptop, an awesome pair of shoes or a new phone.

**Income:** Money that is earned.

**Expenses:** Money that is spent

**Fixed expenses:** costs that have to be paid where the amount does not increase or decrease. For example, if Serena pays $\$280$$280 per week rent, she will pay $\$280$$280 every week. This amount is fixed.

**Variable expenses:** costs that are incurred where the amount to be paid may change. For example, Liam may pay $\$125$$125 a week for groceries one week and $\$98$$98 another depending on what he buys. The amount can change.

**Per quarter:** means per quarter of one year or every three months. Bills such as electricity, gas and water are often issued quarterly.

A weekly budget is shown in the table below:

Income | Expenses | ||
---|---|---|---|

Earnings | $\$505$$505 | Mortgage | $\$147$$147 |

Electricity | $\$23$$23 | ||

Food | $\$64$$64 | ||

Council Rates | $\$22$$22 | ||

Insurance | $\$20$$20 | ||

Water | $\$64$$64 | ||

Clothing | $\$46$$46 | ||

Entertainment | $\$56$$56 |

**(a) **Calculate the weekly expenses.

**Think:** What would the total cost of the expenses be?

**Do:** $147+23+64+22+20+64+46+56=\$442$147+23+64+22+20+64+46+56=$442

**(b)** Calculate weekly savings.

**Think:** The savings would be whatever is remaining after you subtract the expenses from the income.

**Do:** $505-442=\$63$505−442=$63

**(c)** Calculate the percentage of income saved correct to $2$2 decimal places. Don't forget to include the percentage sign.

**Think:** We want to express the savings as a percentage of the income.

**Do:**

$\frac{63}{505}\times100%$63505×100% | $=$= | $12.475$12.475 |

$=$= | $12.48%$12.48% (2 d.p.) |

**(d)** Calculate the percentage of income spent on mortgage payments correct to $2$2 decimal places. Don't forget to include the percentage sign.

**Think:** We want to express the mortgage as a percentage of the income.

**Do:**

$\frac{147}{505}\times100%$147505×100% | $=$= | $29.108$29.108 ... |

$=$= | $29.11%$29.11% |

**(e)** Calculate the amount paid on the mortgage in one year.

**Think:** How many weeks are there in a year ($52$52)?

**Do:** $147\times52=\$7644$147×52=$7644

Amerie pays rent of $\$239$$239 per week, and must budget for electricity and water costs of $\$533$$533 per quarter. How much should she put aside each week to cover these expenses?

**Time-and-a-half:** payment to an employee at $1.5$1.5 times their usual hourly rate.

**Double time:** payment to an employee at $2$2 times their usual hourly rate.

A holiday leave loading is a payment **some** employees receive when they take paid annual leave. In Australia, the award rate is $17.5%$17.5% in addition to the regular rate of pay. Some examples of industries whose awards include leave loading include: building and construction, trades, manufacturing, hospitality, hair and beauty and real estate.o basically you're getting paid to take holidays- sounds awesome right?!

There are a couple of reasons why holiday leave loading was introduced

- Since you generally spend more money when you are on holidays than when you are at work, holiday loadings help people with lower incomes afford to take holidays (especially since they are unable to earn overtime when they aren't working).
- It encourages employees to take holidays. Theoretically, a person could "save up" all their annual leave and then take a year off which wouldn't be very helpful to a business who would have to pay the person who is away as well as someone to fill their role.

Just like you may receive a weekly allowance from your parents, *allowances* in terms of employment are additional amounts of money employers pay their employees for various work-related expenses. This may include a car or travel allowance, a tool allowance or a uniform allowance depending on your job.

A *bonus* is an additional amount of money that is not guaranteed but may be paid to employees for various reasons, such as reaching a sales target or for a great job performance!

If the normal rate is $\$13.40$$13.40 per hour:

**(a)** What is the time-and-a-half rate? Give your answer correct to two decimal places.

**Think:** We need to work out what $1.5$1.5 times the normal rate is.

**Do:**

$13.40\times1.5$13.40×1.5 | $=$= | $20.1$20.1 |

$=$= | $\$20.10$$20.10 (to $2$2 d.p.) |

**(b)** What is the double rate? Give your answer correct to two decimal places.

**Think:** We need to work out what two times the normal rate is.

**Do:**

$13.40\times2$13.40×2 | $=$= | $26.8$26.8 |

$=$= | $\$26.80$$26.80 (to $2$2 d.p.) |

Dave, a delivery driver, is paid $\$10$$10 per hour, plus a uniform allowance of $\$15$$15 per week, $\$92$$92 per week for depreciation on his car and a travel allowance of $37$37 cents per kilometre. Calculate his weekly income, to the nearest cent, if he worked $28$28 hours and travelled $1284$1284km.

**Think:** His weekly income will include his wage, uniform allowance and his car depreciation.

**Do:**

Wage: $28\times10=\$280$28×10=$280

Uniform: $\$15$$15

Car depreciation: $\$92$$92

Travel allowance: $0.37\times1284=\$475.08$0.37×1284=$475.08

Total: $280+15+92+475.08=\$862.08$280+15+92+475.08=$862.08

Dave's weekly income is $\$862.08$$862.08.

A job advertisement states that the hourly wage based on a $35$35-hour working week is $\$38$$38 and that there is a $17%$17% holiday loading on 4 weeks wages.

How much holiday loading would the employee receive? Give your answer correct to two decimal places.

Most people don't get to keep all of the money they earn. They have to pay tax, which is a percentage of their income paid to the government based on their taxable income. Taxes are used to fund public projects like schools, hospitals and roads. Depending on where you work, each year you or your employer will have to lodge a tax return, so knowing how to calculate your taxable income is important.

You'll need to know the difference between your *gross* income and your *net* income. Your gross income is all the money you earn. Your *net* income is the amount you actually get paid *after* tax is taken out. Think of this fishing analogy to help you remember: if you lifted your net out of the gross ocean, all the tax and deductions would drain away and all that would be left in the net is the big, juicy amount of money you get paid.

Terminology

**Gross income:** the amount of income you receive before tax and deductions.

**Net income:** the amount of income you receive after tax and deductions.

**Taxable income:** the income you are required to pay tax on.

**Tax rates:** The different tax amounts people are required to pay. This varies depending on your taxable income.

**Deductions:** expenses that are directly related to earning your income which you are allowed to subtract from your gross income. These include uniform expenses, vehicle and travel expenses, self-education expenses, as well as charitable donations.

**Medicare levy:** a tax of $1.5%$1.5% of one's taxable income paid by most Australian taxpayers that is used to provide Australian residents with access to public health care.

Each pay period (whether it's weekly, fortnightly or monthly), your employer will take out a percentage of your income as tax, which is based on your gross income. This is known as PAYG or 'pay as you go'. However, you may have deductions that you can subtract from your gross income, which in turn will reduce your taxable income. If this is the case, and you have paid more tax than you needed to, you may be eligible for a tax return at the end of the financial year.

However, prior to lodging tax returns, it's also helpful to be able to calculate your net income, so you know how much money you will *actually* receive each pay period. To do this, you need to subtract the amount of tax you are required to pay from your gross income. Then you can divide this net amount to find your weekly net wage, monthly net wage etc.

Worked example

Calculate the net **weekly** wage of a carpenter who must pay $16%$16% tax on an annual salary of $\$38080$$38080. Give your answer correct to two decimal places.

**Think:** What would his annual net salary be? Remember that there are $52$52 weeks in a year.

**Do: **His annual net salary would be $100-16$100−16, or $84%$84% of his gross income:

$0.84\times38080=\$31987.20$0.84×38080=$31987.20

Then, to calculate his net weekly income:

$31987.20\div52=\$615.14$31987.20÷52=$615.14

Consider Pauline's taxable income of $\$158$$158$810$810.

Taxable income | Tax on this income |
---|---|

$0-\$18200$0−$18200 | Nil |

$\$18201-\$37000$$18201−$37000 | $19c$19c for each $\$1$$1 over $\$18200$$18200 |

$\$37001-\$90000$$37001−$90000 | $\$3572$$3572 plus $32.5c$32.5c for each $\$1$$1 over $\$37000$$37000 |

$\$90001-\$180000$$90001−$180000 | $\$20797$$20797 plus $37c$37c for each $\$1$$1 over $\$90000$$90000 |

$\$180001$$180001 and over | $\$54097$$54097 plus $45c$45c for each $\$1$$1 over $\$180000$$180000 |

By filling in the gaps, state the range of taxable incomes (income bracket) that Pauline's taxable income falls into.

Range of taxable incomes$=$=$\$$$$\editable{}$$-$−$\$$$$\editable{}$

Fill in the gaps to complete the calculation for the income tax payable.

Income tax payable on $\$158810$$158810 is $\editable{}+\left(158810-\editable{}\right)\times\editable{}$+(158810−)× dollars

Sharon is a project manager with a taxable income of $\$97$$97$192$192.

Throughout the year, her employer has deducted $\$553$$553 per week in tax instalments.

The income tax rates for individuals are provided in the table.

Taxable income | Tax on this income |
---|---|

$0-\$18200$0−$18200 | Nil |

$\$18201-\$37000$$18201−$37000 | $19c$19c for each $\$1$$1 over $\$18200$$18200 |

$\$37001-\$90000$$37001−$90000 | $\$3572$$3572 plus $32.5c$32.5c for each $\$1$$1 over $\$37000$$37000 |

$\$90001-\$180000$$90001−$180000 | $\$20797$$20797 plus $37c$37c for each $\$1$$1 over $\$90000$$90000 |

$\$180001$$180001 and over | $\$54097$$54097 plus $45c$45c for each $\$1$$1 over $\$180000$$180000 |

Calculate the tax payable to the nearest cent.

Calculate the Medicare Levy, which is $2%$2% of taxable income.

Since Sharon's employer has deducted more than is needed from her income, Sharon is entitled to a refund for the year.

Find the amount of this refund correct to the nearest cent.

solve practical problems requiring basic number operations

apply arithmetic operations according to their correct order

evaluate decimal fractions to the required number of decimal places