2.08 Financial calculations with percentages

Budgeting and personal finance

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.

 

Terminology

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. 

 

Worked example

Example 1

A weekly budget is shown in the table below:

(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

 

Practice question

Question 1

 

Overtime and extra income

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. 

 

Holiday leave loading

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

1. 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).
2. 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.

 

Allowances and bonuses

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!

 

Worked examples

Example 2

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.)

 

Example 3

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.

 

Practice question

Question 2