Applications of financial mathematics

1. Applications of financial mathematics Module 4 – Chapter 21

2. Percentage changes and charges Tax – refers to revenue collected by the government. The amount of tax paid is calculated as a percentage of the transaction involved. Note: Financial matters are associated with the financial year, which is the inclusive period from July 1 of one year to June 30 of the following year. There are various types of tax that apply. Some of these include: • income tax • capital gains tax • goods and services tax • stamp duty

3. Income tax • Income tax is money deducted by your employer and sent to the government to pay for facilities such as hospitals, schools and roads. • Income tax is calculated using classifications of income levels where different tax rates are applied. • These are known as tax divisions or tax brackets. • The tax rates for each of these subdivisions are known as marginal rates (the % of the tax payable). • A table is commonly provided to show these.

4. The amount you are paid before the income tax is deducted is called your gross salary. • The amount after the income tax is deducted is known as the net salary.

5. Calculating income taxexample John’s gross salary is $45 730 per year. • How much does he pay in income tax? (use tax table on page 556) Solution: Tax on first $6000 = 0 Tax on $6001 - $21600 = 15 600 x 17/100 = $2652 Tax on $21601 - $45730 = 24130 x 30/100 = $7239 Total tax = 0 + 2652 + 7239 = $9891 (b) If he is given a pay raise of $5000 per year, how much will he actually receive? Solution: Tax on raise: 5000 x 30/100 = $1500 Amount received = 5000 – 1500 = $3500

6. Capital gains tax (CGT) • Capital gains tax is the tax payable on any profit made from an investment (ie. property, shares, investment funds, etc.) • The profit is added to your income tax and the tax is calculated according to the same margins.

7. Calculating capital gains taxexample Daisy buys shares for $35 000 in October and sells them for $63 000 in March of the next year. If her salary for the financial year is $82 390, how much capital gains tax will she pay on the profit she makes on the shares? Solution: Profit = selling price – purchase price = 63 000 – 35 000 = $28 000 Capital Gains Tax = 28 000 x 42/100 = $ 11760

8. Goods and services tax (gst) • The Goods and Services Tax (GST) is applicable on most items. • It is charged by the Government at a fixed rate of 10%.

9. Calculating gstexample • If the cost price of electricity per quarter is $288.50, how much GST will be added to the bill? Solution: GST = 288.50 x 10/100 = $28.85 (b) If the selling price of a washing machine is $990, how much of this is GST? Solution: Price without GST = 990 x 100/110 = $900 GST = 990 – 900 = $90

10. Stamp duty • Stamp duty is the duty or tax charged by the government on various commercial transactions. • This includes the purchase of land, houses, motor vehicles, life insurance and livestock. • Stamp duty on property is payable according to the table on page 558.

11. Calculating stamp duty on propertyexample Brett bought a house for $480 000. • What is the value of the stamp duty payable on this purchase? • What is the total price of the purchase? Solution: (a) Stamp duty = 2560 plus 6% of ( 480 000 – 115 000 ) = 2560 + ( 6/100 x 365 000 ) = $24 460 • Total price = $480 000 + $24 460 = $504 460