Year 9 Maths Chapter 1  Computation and financial mathematics
no, we’re not doing addition, i don’t care that it is in the Y9 textbook, WE’RE NOT!
Table of Contents
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 nonzero digit (from left to right)
 Count number of significant figures including first nonzero 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)
Markup is amount added to a cost price to produce a selling price.
selling price = cost price + markup
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 FY20192020 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 PayAsYouGo – 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

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… ↩