Year 9 Maths Chapter 1 - Computation and financial mathematics

Decimal places and significant figures

sig figs!

To round for decimal places:

• Locate digit
• Round down (leave as is) if critical digit (next digit) is less than or equal to 4
• Round up (increase by 1) if critical digit is greater than or equal to 5

Example

1.543 = 1.54 (2dp)
482.3656 = 482.37 (2dp) as 5 is the third digit and requires us to round up the 2nd digit.

To round for significant figures:

• Locate first non-zero digit (from left to right)
• Count number of significant figures including first non-zero digit
• Round last significant digit and use the same rounding rules as mentioned above

Example

1.34341 = 1.343 (3 sig figs)
0.008023 = 0.00802 (3 sig figs)

Profits and Discounts

Profit is money made on a sale. If it is negative, then it is a loss.

profit = selling price - cost prices (expenses)

Mark-up is amount added to a cost price to produce a selling price.

selling price = cost price + mark-up

Percentage profit or loss can be calculated by using the below formula

profit/loss
% profit/loss = ––––––––––– x 100%
cost price

Discount is the amount by which an item is marked down.

new price = original price - discount
discount = % discount x original price

Income

• Wage: fixed rate per hour
• Overtime: hours outside normal working time. Paid at higher rate that can be: - Time and a half = 1.5x the usual hourly rate - Double time = 2x the usual hourly rate
• Salary: fixed amount per annum (per year). Often paid monthly/fortnightly.1

• Leave loading: normal pay + bonus (usually 17.5%) for when wage and salary earners go on holiday
• Piecework: paid according to number of items produced
• Commission: proportion of overall sales amount
• Salespersons usually receive commission and a set weekly or monthly fee called a retainer
• commission = % commission x total sales
• Gross income: total income earned
• Taxable income: total income earned after tax deductions (e.g business expenses)
• Tax deductions: deduction that lowers someone’s tax liability
• Net income: income left after deductions (e.g tax, union fees) net income = gross income - deductions
• Taxation: a compulsory contribution to the government once a person’s taxable income passes a set income.

PAYG System

Tax table

The tax table for FY2019-2020 looks like this. In a test, you will be provided with a tax table.

The tax table is used to calculate taxes.

Taxable income Tax on this income
0 – \$18,200 Nil
\$18,201 – \$37,000 19c for each \$1 over \$18,200
\$37,001 – \$90,000 \$3,572 plus 32.5c for each \$1 over \$37,000
\$90,001 – \$180,000 \$20,797 plus 37c for each \$1 over \$90,000
\$180,001 and over \$54,097 plus 45c for each \$1 over \$180,000

For example, if you earned \$40000, then you would pay \$3572 + each dollar over \$37000.

This also means, that if you maxed out the value of the first threshold, it will equate to the next threshold’s minimum.

\$90000 income fits into the third threshold
Therefore:
3572 + (0.325 x (90000 - 37000))
= \$20797

\$90001 income fits into the foruth threshold
Therefore:
\$20797 (which was the maximum of the third threshold) + 0.37
= \$20797.37

PAYG System

People who are employed usually contribute tax as they receive their money (known as Pay-As-You-Go – PAYG). At the end of the financial year they will have either paid too much tax, paid too little tax or paid the right amount.

Interest

Interest is paid to a lender in return for using their money. If you’re still unsure on the concept of interest see Interest

Simple Interest

To calculate simple interest:

I = PRN

where:

• I is interest
• P is principal (amount invested)
• R is rate as a decimal (so 5% = 0.05)
• N is number of time periods

Ensure that the rate and number of time periods are the same. For example, if the rate is 5% p.a (per annum - yearly) then the number of time periods has to be in terms of years as well.

Compound Interest

To calculate compound interest:

A = P(1 + r)ⁿ

where:

• A is amount generated (interest + principal)
• P is principal (amount invested)
• R is a rate as a decimal (so 5% = 0.05)
• N is number of time periods

Ensure that the rate and number of time periods are the same. They really like to get people out with this one in the exams. And, make sure you answer the question. If it asks for interest you will have to A - P to find interest.

Depreciation

The same as compound interest, but with a minus.

A = P(1 - r)ⁿ
1. IMPORTANT. In tests, the calculation involving years can get confusing. For example, if you wanted to find the fortnightly pay earned from a yearly salary, would you divide by 52, then divide by 2, or 52.14 then 2, or 26? Actually, I’m not sure. If only there was an international specification that we were taught…

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