Year 11 · Financial mathematics
Quick tips — memory joggers
Percentages & GST
Interest & depreciation
Earning money & tax
Cars & budgeting
Level 1 · Fluency
The price of an item is $85, excluding GST. Calculate the price after 10% GST is added.
$93.50
85 × 1.10 = $93.50.
A jacket is priced at $120, excluding GST. Calculate the price after 10% GST is added.
$132.00
120 × 1.10 = $132.00.
A $60 item is discounted by 15%. Calculate the sale price.
$51.00
60 × (1 − 0.15) = 60 × 0.85 = $51.00.
Level 2 · Application
A business buys stock for $2400 (excluding GST) and sells it for $3600 (excluding GST). Calculate the profit as a percentage of the cost price.
50%
Profit = 3600 − 2400 = $1200. Percentage = 1200/2400 × 100 = 50%.
A shop buys a bicycle for $480 and sells it for $600. Calculate the profit as a percentage of the cost price.
25%
Profit = 600 − 480 = $120. Percentage = 120/480 × 100 = 25%.
An item costing $250 is sold for only $210. Calculate the loss as a percentage of the cost price.
16%
Loss = 250 − 210 = $40. Percentage = 40/250 × 100 = 16%.
Level 3 · Further Application
A repair bill has two components: $187 for parts (this amount includes 10% GST) and $85 for labour (excluding GST). The mechanic must add 10% GST to the labour charge.
$17; $25.50
(a) GST in a GST-inclusive price = price ÷ 11 = 187 ÷ 11 = $17.
(b) GST on labour = 10% × 85 = $8.50. Total GST = 17 + 8.50 = $25.50.
A catering bill has two components: $242 for food (this amount includes 10% GST) and $60 for room hire (excluding GST). The caterer must add 10% GST to the room-hire charge.
$22; $28
(a) GST in the inclusive food price = 242 ÷ 11 = $22.
(b) GST on room hire = 10% × 60 = $6. Total GST = 22 + 6 = $28.
An invoice lists $319 for materials (this amount includes 10% GST) and $150 for labour (excluding GST). The tradesperson must add 10% GST to the labour charge.
$29; $44
(a) GST in the inclusive materials price = 319 ÷ 11 = $29.
(b) GST on labour = 10% × 150 = $15. Total GST = 29 + 15 = $44.
Level 1 · Fluency
Calculate the simple interest on $4000 at 5% p.a. for 3 years.
$600
I = Prn = 4000 × 0.05 × 3 = $600.
Calculate the simple interest on $6000 at 4% p.a. for 5 years.
$1200
I = Prn = 6000 × 0.04 × 5 = $1200.
Calculate the simple interest on $2500 at 6% p.a. for 4 years.
$600
I = Prn = 2500 × 0.06 × 4 = $600.
Level 2 · Application
Compare the simple interest on $5000 at 3.5% p.a. for 5 years with $5000 at 5% p.a. for 3 years. State which earns more, and by how much.
$125
First: 5000 × 0.035 × 5 = $875. Second: 5000 × 0.05 × 3 = $750. The first earns $125 more.
Compare the simple interest on $8000 at 4% p.a. for 6 years with $8000 at 6% p.a. for 3 years. State which earns more, and by how much.
$480
First: 8000 × 0.04 × 6 = $1920. Second: 8000 × 0.06 × 3 = $1440. The first earns $480 more.
Compare the simple interest on $12 000 at 3% p.a. for 4 years with $9000 at 5% p.a. for 4 years. State which earns more, and by how much.
$360
First: 12 000 × 0.03 × 4 = $1440. Second: 9000 × 0.05 × 4 = $1800. The second earns $360 more.
Level 3 · Further Application
Layla takes out a loan of $7500. Simple interest is charged, and the loan plus interest is repaid with monthly repayments of $200 over 5 years.
12% p.a.
(a) Total repaid = 200 × 60 = $12 000. Interest = 12 000 − 7500 = $4500.
(b) 4500 = 7500 × r × 5 ⇒ r = 4500 ÷ 37 500 = 0.12 = 12% p.a.
Sam borrows $9000. Simple interest is charged, and the loan plus interest is repaid with monthly repayments of $250 over 4 years.
8% p.a.
(a) Total repaid = 250 × 48 = $12 000. Interest = 12 000 − 9000 = $3000.
(b) 3000 = 9000 × r × 4 ⇒ r = 3000 ÷ 36 000 = 0.0833 ≈ 8% p.a.
Nabil borrows $6000. Simple interest is charged, and the loan plus interest is repaid with monthly repayments of $175 over 4 years.
10% p.a.
(a) Total repaid = 175 × 48 = $8400. Interest = 8400 − 6000 = $2400.
(b) 2400 = 6000 × r × 4 ⇒ r = 2400 ÷ 24 000 = 0.10 = 10% p.a.
Level 1 · Fluency
On a graph of the value of an investment earning simple interest against time, what is the shape of the graph?
straight line
A straight line — equal interest is added each period, so the value increases at a constant rate.
$2000 earns simple interest at 5% p.a. By how much does the value rise each year (the gradient of the graph)?
$100 per year
Gradient = Pr = 2000 × 0.05 = $100 per year.
Two investments earn simple interest at the same rate but have different principals. On a value-against-time graph, how do their two lines differ?
The line for the larger principal starts higher (greater y-intercept) and is steeper, because the gradient Pr grows with the principal. Both are straight lines.
Level 2 · Application
$5000 is invested. Two simple-interest graphs are drawn, one at 3% p.a. and one at 6% p.a. Describe how the two lines differ.
steeper
Both start at $5000. The 6% line is steeper (gradient = Pr = 5000 × 0.06 = $300/year) than the 3% line (gradient = $150/year); the higher rate gives the greater gradient.
$8000 is invested. Two simple-interest graphs are drawn, one at 4% p.a. and one at 7% p.a. Describe how the two lines differ.
steeper
Both start at $8000. The 7% line is steeper (gradient = Pr = 8000 × 0.07 = $560/year) than the 4% line (gradient = 8000 × 0.04 = $320/year).
$10 000 is invested at simple interest at 5% p.a. and graphed against time. Find the gradient of the line and the value of the investment after 8 years.
$500/year; $14 000
Gradient = Pr = 10 000 × 0.05 = $500/year. Value after 8 years = 10 000 + 500 × 8 = $14 000.
Level 3 · Further Application
$5000 is invested at simple interest, drawn for 3% p.a. and 6% p.a. over 10 years.
$1500
(a) Gradients are $150/year (3%) and $300/year (6%); each gradient is the annual interest (Pr).
(b) At 10 years: 6% gives 5000 + 3000 = $8000; 3% gives 5000 + 1500 = $6500. Gap = $1500.
$8000 is invested at simple interest, drawn for 4% p.a. and 7% p.a. over 10 years.
$2400
(a) Gradients are $320/year (4%) and $560/year (7%); each gradient is the annual interest (Pr).
(b) At 10 years: 7% gives 8000 + 5600 = $13 600; 4% gives 8000 + 3200 = $11 200. Gap = $2400.
$6000 is invested at simple interest, drawn for 2.5% p.a. and 5% p.a. over 8 years.
$1200
(a) Gradients are $150/year (2.5%) and $300/year (5%); each gradient is the annual interest (Pr).
(b) At 8 years: 5% gives 6000 + 2400 = $8400; 2.5% gives 6000 + 1200 = $7200. Gap = $1200.
Level 1 · Fluency
A car depreciates by $6000 each year (straight-line). If it is worth $60 000 now, what is its value after 3 years?
$42 000
60 000 − 6000 × 3 = $42 000.
A machine depreciates by $4500 each year (straight-line). If it is worth $50 000 now, what is its value after 4 years?
$32 000
50 000 − 4500 × 4 = 50 000 − 18 000 = $32 000.
A laptop worth $2400 depreciates by $300 each year (straight-line). What is its value after 5 years?
$900
2400 − 300 × 5 = 2400 − 1500 = $900.
Level 2 · Application
A $60 000 car depreciates by 12% of its original value each year (straight-line). Find its value after 5 years, and state after how many years its value reaches zero.
$24 000; 8⅓ years
Annual depreciation = 12% × 60 000 = $7200. Value after 5 years = 60 000 − 7200 × 5 = $24 000. Reaches zero when 7200n = 60 000, i.e. after 8⅓ years.
A $45 000 van depreciates by 10% of its original value each year (straight-line). Find its value after 6 years, and state after how many years its value reaches zero.
$18 000; 10 years
Annual depreciation = 10% × 45 000 = $4500. Value after 6 years = 45 000 − 4500 × 6 = $18 000. Reaches zero when 4500n = 45 000, i.e. after 10 years.
An $80 000 excavator depreciates by 8% of its original value each year (straight-line). Find its value after 7 years, and state after how many years its value reaches zero.
$35 200; 12.5 years
Annual depreciation = 8% × 80 000 = $6400. Value after 7 years = 80 000 − 6400 × 7 = $35 200. Reaches zero when 6400n = 80 000, i.e. after 12.5 years.
Level 3 · Further Application
A delivery van worth $42 000 depreciates by $5200 each year (straight-line).
$10 800; 7 years
(a) 42 000 − 5200 × 6 = $10 800.
(b) 42 000 − 5200n < 10 000 ⇒ 5200n > 32 000 ⇒ n > 6.15, so after 7 years.
A truck worth $56 000 depreciates by $6400 each year (straight-line).
$24 000; 7 years
(a) 56 000 − 6400 × 5 = $24 000.
(b) 56 000 − 6400n < 15 000 ⇒ 6400n > 41 000 ⇒ n > 6.41, so after 7 years.
A tractor worth $38 000 depreciates by $4100 each year (straight-line).
$21 600; 7 years
(a) 38 000 − 4100 × 4 = $21 600.
(b) 38 000 − 4100n < 12 000 ⇒ 4100n > 26 000 ⇒ n > 6.34, so after 7 years.
Level 1 · Fluency
Write the straight-line salvage-value formula and state what each symbol represents.
S = V₀ − Dn, where S = salvage value, V₀ = initial value, D = annual depreciation, n = number of years.
Use S = V₀ − Dn to find the salvage value of an asset with V₀ = $20 000, D = $2500 and n = 4.
$10 000
S = 20 000 − 2500 × 4 = 20 000 − 10 000 = $10 000.
Use S = V₀ − Dn to find the salvage value of an asset with V₀ = $9000, D = $750 and n = 6.
$4500
S = 9000 − 750 × 6 = 9000 − 4500 = $4500.
Level 2 · Application
A business asset worth $15 000 is to be written down to a salvage value of $3000 over 8 years (straight-line). Find the annual depreciation amount D.
$1500 per year
3000 = 15 000 − 8D ⇒ 8D = 12 000 ⇒ D = $1500 per year.
A vehicle worth $28 000 is to be written down to a salvage value of $4000 over 6 years (straight-line). Find the annual depreciation amount D.
$4000 per year
4000 = 28 000 − 6D ⇒ 6D = 24 000 ⇒ D = $4000 per year.
Equipment worth $22 000 is to be written down to a salvage value of $2500 over 5 years (straight-line). Find the annual depreciation amount D.
$3900 per year
2500 = 22 000 − 5D ⇒ 5D = 19 500 ⇒ D = $3900 per year.
Level 3 · Further Application
A printing press bought for $18 500 depreciates by $1850 per year.
$5550
(a) S = 18 500 − 1850 × 7 = $5550.
(b) For large n the formula eventually gives a negative value, which is impossible — an asset cannot be worth less than $0 (or its scrap value).
A commercial oven bought for $24 000 depreciates by $2600 per year.
$3200
(a) S = 24 000 − 2600 × 8 = 24 000 − 20 800 = $3200.
(b) For large n the formula eventually gives a negative value, which is impossible — an asset cannot be worth less than $0 (or its scrap value).
A ute bought for $34 000 depreciates by $3200 per year.
$5200
(a) S = 34 000 − 3200 × 9 = 34 000 − 28 800 = $5200.
(b) For large n the formula eventually gives a negative value, which is impossible — an asset cannot be worth less than $0 (or its scrap value).
Level 1 · Fluency
$1000 earns 10% p.a. compound interest. The interest in the second year is calculated on what amount?
On the balance at the start of the second year, $1100 (the original $1000 plus the first year’s interest).
$2000 earns 8% p.a. compound interest. The interest in the second year is calculated on what amount?
On the end-of-Year-1 balance of $2160 (the original $2000 plus the first year’s $160 interest).
$5000 earns 6% p.a. compound interest. The interest in the second year is calculated on what amount?
On the end-of-Year-1 balance of $5300 (the original $5000 plus the first year’s $300 interest).
Level 2 · Application
$3000 earns 4.5% p.a. compound interest. Using repeated simple interest, calculate the balance at the end of Year 1 and Year 2.
$3276.08
End of Year 1: 3000 × 1.045 = $3135.00. End of Year 2: 3135 × 1.045 = $3276.08.
$4000 earns 6% p.a. compound interest. Using repeated simple interest, calculate the balance at the end of Year 1 and Year 2.
$4494.40
End of Year 1: 4000 × 1.06 = $4240.00. End of Year 2: 4240 × 1.06 = $4494.40.
$2500 earns 8% p.a. compound interest. Using repeated simple interest, calculate the balance at the end of Year 1 and Year 2.
$2916.00
End of Year 1: 2500 × 1.08 = $2700.00. End of Year 2: 2700 × 1.08 = $2916.00.
Level 3 · Further Application
$6000 is invested at 5% p.a., compounded annually, for 4 years.
$93.04
(a) FV = 6000(1.05)⁴ = $7293.04; compound interest = $1293.04.
(b) Simple interest = 6000 × 0.05 × 4 = $1200, so compound earns $93.04 more.
$8000 is invested at 6% p.a., compounded annually, for 3 years.
$88.13
(a) FV = 8000(1.06)³ = $9528.13; compound interest = $1528.13.
(b) Simple interest = 8000 × 0.06 × 3 = $1440, so compound earns $88.13 more.
$5000 is invested at 4% p.a., compounded annually, for 4 years.
$49.29
(a) FV = 5000(1.04)⁴ = $5849.29; compound interest = $849.29.
(b) Simple interest = 5000 × 0.04 × 4 = $800, so compound earns $49.29 more.
Level 1 · Fluency
An employee is paid $24 per hour and works 38 hours. Calculate the pay.
$912
38 × 24 = $912.
A salesperson earns 4% commission on $18 500 of sales. Calculate the commission.
$740
4% × 18 500 = 0.04 × 18 500 = $740.
A worker is paid $6.50 per item made (piecework) and completes 140 items. Calculate the pay.
$910
140 × 6.50 = $910.
Level 2 · Application
An employee earns $24/hour, with time-and-a-half for overtime and double time on Sundays. In one week they work 38 ordinary hours, 4 overtime hours and 5 hours on Sunday. Calculate the total pay.
$1296
38 × 24 + 4 × (1.5 × 24) + 5 × (2 × 24) = 912 + 144 + 240 = $1296.
A worker earns $28/hour, with time-and-a-half for overtime and double time on public holidays. In one week they work 35 ordinary hours, 6 overtime hours and 4 hours on a public holiday. Calculate the total pay.
$1456
35 × 28 + 6 × (1.5 × 28) + 4 × (2 × 28) = 980 + 252 + 224 = $1456.
A car salesperson earns a $600/week retainer plus 2% commission on sales. In one week they sell $85 000 of cars. Calculate the total pay.
$2300
Commission = 2% × 85 000 = $1700. Total = 600 + 1700 = $2300.
Level 3 · Further Application
Tariq works a regular 36-hour week at $42/hour. Overtime is paid at time-and-a-half. In one week he earns $1827 in total.
5 hours
(a) 36 × 42 = $1512.
(b) Overtime pay = 1827 − 1512 = $315. Overtime rate = 1.5 × 42 = $63/hour. Hours = 315 ÷ 63 = 5 hours.
Mia works a regular 38-hour week at $30/hour. Overtime is paid at time-and-a-half. In one week she earns $1275 in total.
3 hours
(a) 38 × 30 = $1140.
(b) Overtime pay = 1275 − 1140 = $135. Overtime rate = 1.5 × 30 = $45/hour. Hours = 135 ÷ 45 = 3 hours.
Jack works a regular 40-hour week at $35/hour. Overtime is paid at time-and-a-half. In one week he earns $1610 in total.
4 hours
(a) 40 × 35 = $1400.
(b) Overtime pay = 1610 − 1400 = $210. Overtime rate = 1.5 × 35 = $52.50/hour. Hours = 210 ÷ 52.50 = 4 hours.
Level 1 · Fluency
Leave loading is 17.5%. Calculate the loading on $2000 of leave pay.
$350
17.5% × 2000 = $350.
Leave loading is 17.5%. Calculate the loading on $3200 of leave pay.
$560
17.5% × 3200 = $560.
Leave loading is 17.5%. Calculate the loading on $1800 of normal leave pay.
$315
17.5% × 1800 = $315.
Level 2 · Application
An employee’s normal weekly pay is $1150. They take 4 weeks of annual leave with 17.5% leave loading. Calculate the total amount paid for the leave.
$5405
Normal leave pay = 4 × 1150 = $4600. Loading = 17.5% × 4600 = $805. Total = $5405.
An employee’s normal weekly pay is $1320. They take 4 weeks of annual leave with 17.5% leave loading. Calculate the total amount paid for the leave.
$6204
Normal leave pay = 4 × 1320 = $5280. Loading = 17.5% × 5280 = $924. Total = $6204.
An employee’s normal weekly pay is $950. They take 2 weeks of annual leave with 17.5% leave loading. Calculate the total amount paid for the leave.
$2232.50
Normal leave pay = 2 × 950 = $1900. Loading = 17.5% × 1900 = $332.50. Total = $2232.50.
Level 3 · Further Application
An employee earning $67 600 p.a. takes 4 weeks of annual leave with 17.5% loading. (Assume 52 weeks per year.)
$6110
(a) Weekly pay = 67 600 ÷ 52 = $1300; 4 weeks = $5200.
(b) Loading = 17.5% × 5200 = $910. Total = $6110.
An employee earning $83 200 p.a. takes 4 weeks of annual leave with 17.5% loading. (Assume 52 weeks per year.)
$7520
(a) Weekly pay = 83 200 ÷ 52 = $1600; 4 weeks = $6400.
(b) Loading = 17.5% × 6400 = $1120. Total = $7520.
An employee earning $54 600 p.a. takes 4 weeks of annual leave with 17.5% loading. (Assume 52 weeks per year.)
$4935
(a) Weekly pay = 54 600 ÷ 52 = $1050; 4 weeks = $4200.
(b) Loading = 17.5% × 4200 = $735. Total = $4935.
Level 1 · Fluency
A pensioner receives a base rate of $1002 per fortnight. Calculate the annual amount (26 fortnights).
$26 052
1002 × 26 = $26 052.
A carer allowance is $144 per fortnight. Calculate the annual amount (26 fortnights).
$3744
144 × 26 = $3744.
A youth allowance is $562 per fortnight. Calculate the annual amount (26 fortnights).
$14 612
562 × 26 = $14 612.
Level 2 · Application
A pensioner receives a fortnightly base rate of $1002 plus a supplement of $81. Calculate the total annual pension income (26 fortnights).
$28 158
Per fortnight = 1002 + 81 = $1083. Annual = 1083 × 26 = $28 158.
A pensioner receives a fortnightly base rate of $1064 plus a supplement of $75. Calculate the total annual pension income (26 fortnights).
$29 614
Per fortnight = 1064 + 75 = $1139. Annual = 1139 × 26 = $29 614.
A pensioner receives a fortnightly base rate of $920 plus an energy supplement of $14 and a pension supplement of $71. Calculate the total annual pension income (26 fortnights).
$26 130
Per fortnight = 920 + 14 + 71 = $1005. Annual = 1005 × 26 = $26 130.
Level 3 · Further Application
A pension has a base rate of $980 per fortnight but reduces by 50c for every $1 of income over $200 per fortnight. A pensioner earns $350 per fortnight in other income.
$905 per fortnight
(a) Excess income = 350 − 200 = $150. Reduction = 0.5 × 150 = $75.
(b) Pension = 980 − 75 = $905 per fortnight.
A pension has a base rate of $1020 per fortnight but reduces by 50c for every $1 of income over $250 per fortnight. A pensioner earns $450 per fortnight in other income.
$920 per fortnight
(a) Excess income = 450 − 250 = $200. Reduction = 0.5 × 200 = $100.
(b) Pension = 1020 − 100 = $920 per fortnight.
A pension has a base rate of $960 per fortnight but reduces by 40c for every $1 of income over $300 per fortnight. A pensioner earns $500 per fortnight in other income.
$880 per fortnight
(a) Excess income = 500 − 300 = $200. Reduction = 0.4 × 200 = $80.
(b) Pension = 960 − 80 = $880 per fortnight.
Level 1 · Fluency
Using the tax table below, state the tax payable on a taxable income of $15 000.
| Taxable income | Tax on this income |
|---|---|
| 0 – $18 200 | Nil |
| $18 201 – $45 000 | 19c for each $1 over $18 200 |
| $45 001 – $120 000 | $5 092 + 32.5c for each $1 over $45 000 |
| $120 001 – $180 000 | $29 467 + 37c for each $1 over $120 000 |
| $180 001 and over | $51 667 + 45c for each $1 over $180 000 |
Nil
$15 000 is in the tax-free threshold (0 – $18 200), so tax payable = Nil.
Tax on the $18 201–$45 000 bracket is “19c for each $1 over $18 200”. Calculate the tax payable on a taxable income of $30 000.
$2242
0.19 × (30 000 − 18 200) = 0.19 × 11 800 = $2242.
Tax on the $18 201–$45 000 bracket is “19c for each $1 over $18 200”. Calculate the tax payable on a taxable income of $40 000.
$4142
0.19 × (40 000 − 18 200) = 0.19 × 21 800 = $4142.
Level 2 · Application
Using the tax table above, calculate the tax payable on a taxable income of $95 000.
$21,342
$95 000 is in the $45 001–$120 000 bracket: 5092 + 0.325 × (95 000 − 45 000) = 5092 + 16 250 = $21,342.
The $45 001–$120 000 bracket is “$5092 + 32.5c for each $1 over $45 000”. Calculate the tax payable on a taxable income of $72 000.
$13,867
5092 + 0.325 × (72 000 − 45 000) = 5092 + 0.325 × 27 000 = 5092 + 8775 = $13,867.
The $45 001–$120 000 bracket is “$5092 + 32.5c for each $1 over $45 000”. Calculate the tax payable on a taxable income of $110 000.
$26,217
5092 + 0.325 × (110 000 − 45 000) = 5092 + 0.325 × 65 000 = 5092 + 21 125 = $26,217.
Level 3 · Further Application
Using the tax table above:
$12,567
(a) 5092 + 0.325 × (68 000 − 45 000) = 5092 + 7475 = $12,567.
(b) 32.5 cents in every dollar (the marginal rate for this bracket).
The $120 001–$180 000 bracket is “$29 467 + 37c for each $1 over $120 000”.
$40,567
(a) 29 467 + 0.37 × (150 000 − 120 000) = 29 467 + 0.37 × 30 000 = 29 467 + 11 100 = $40,567.
(b) 37 cents in every dollar (the marginal rate for this bracket).
The $45 001–$120 000 bracket is “$5092 + 32.5c for each $1 over $45 000”.
$19,067
(a) 5092 + 0.325 × (88 000 − 45 000) = 5092 + 0.325 × 43 000 = 5092 + 13 975 = $19,067.
(b) 32.5 cents in every dollar (the marginal rate for this bracket).
Level 1 · Fluency
Is the cost of a compulsory work uniform generally an allowable tax deduction?
Yes
Yes — it is a work-related expense.
Is the daily cost of travel between home and work generally an allowable tax deduction?
No
No — ordinary home-to-work travel is a private expense, not an allowable deduction.
Are tools and equipment bought specifically for your job generally an allowable tax deduction?
Yes
Yes — they are a work-related expense used to earn income.
Level 2 · Application
A tradesperson with a gross income of $68 000 claims allowable deductions for tools ($850), a work uniform ($220) and work vehicle use ($1400). Calculate their taxable income.
$65 530
Deductions = 850 + 220 + 1400 = $2470. Taxable income = 68 000 − 2470 = $65 530.
A nurse with a gross income of $74 000 claims allowable deductions for uniforms ($260), professional registration ($480) and self-education ($1150). Calculate their taxable income.
$72 110
Deductions = 260 + 480 + 1150 = $1890. Taxable income = 74 000 − 1890 = $72 110.
An electrician with a gross income of $92 000 claims allowable deductions for tools ($1200), a work vehicle ($2600) and union fees ($540). Calculate their taxable income.
$87 660
Deductions = 1200 + 2600 + 540 = $4340. Taxable income = 92 000 − 4340 = $87 660.
Level 3 · Further Application
A courier claims deductions for work petrol, work uniforms, and a weekly gym membership.
not
(a) Work petrol and work uniforms are allowable (directly related to earning income).
(b) The gym membership is a private expense, not required to perform the job, so it is not an allowable deduction.
An office worker claims deductions for a work laptop, professional development courses, and daily coffee bought near the office.
not
(a) The work laptop and professional development courses are allowable (directly related to earning income).
(b) The daily coffee is a private expense, not required to do the job, so it is not an allowable deduction.
A construction worker claims deductions for steel-capped boots, a hard hat, and weekend sports club fees.
not
(a) The steel-capped boots and hard hat are allowable (required protective equipment for the job).
(b) The sports club fees are a private, recreational expense unrelated to earning income, so they are not an allowable deduction.
Level 1 · Fluency
An employee has a gross income of $72 000 and allowable deductions of $3200. Calculate the taxable income.
$68 800
72 000 − 3200 = $68 800.
A worker has a gross income of $58 000 and allowable deductions of $2450. Calculate the taxable income.
$55 550
58 000 − 2450 = $55 550.
A worker has a gross income of $96 000 and allowable deductions of $4100. Calculate the taxable income.
$91 900
96 000 − 4100 = $91 900.
Level 2 · Application
A person earns a gross income of $72 000 with $3200 of deductions. Calculate the taxable income, then the tax payable using the table above.
$12,827
Taxable income = $68 800. Tax = 5092 + 0.325 × (68 800 − 45 000) = $12,827.
A person earns a gross income of $85 000 with $3600 of deductions. Calculate the taxable income, then the tax payable using the bracket “$5092 + 32.5c for each $1 over $45 000”.
$16,922
Taxable income = 85 000 − 3600 = $81 400. Tax = 5092 + 0.325 × (81 400 − 45 000) = 5092 + 11 830 = $16,922.
A person earns a gross income of $63 000 with $2800 of deductions. Calculate the taxable income, then the tax payable using the bracket “$5092 + 32.5c for each $1 over $45 000”.
$10,032
Taxable income = 63 000 − 2800 = $60 200. Tax = 5092 + 0.325 × (60 200 − 45 000) = 5092 + 4940 = $10,032.
Level 3 · Further Application
A person earns $82 000 gross with $3400 in allowable deductions.
$16,012
(a) 82 000 − 3400 = $78 600.
(b) 5092 + 0.325 × (78 600 − 45 000) = 5092 + 10 920 = $16,012.
A person earns $102 000 gross with $4200 in allowable deductions.
$22,252
(a) 102 000 − 4200 = $97 800.
(b) 5092 + 0.325 × (97 800 − 45 000) = 5092 + 17 160 = $22,252.
A person earns $69 000 gross with $2600 in allowable deductions.
$12,047
(a) 69 000 − 2600 = $66 400.
(b) 5092 + 0.325 × (66 400 − 45 000) = 5092 + 6955 = $12,047.
Level 1 · Fluency
The Medicare levy is 2% of taxable income. Calculate the levy on a taxable income of $75 000.
$1500
2% × 75 000 = $1500.
The Medicare levy is 2% of taxable income. Calculate the levy on a taxable income of $62 000.
$1240
2% × 62 000 = $1240.
The Medicare levy is 2% of taxable income. Calculate the levy on a taxable income of $88 500.
$1770
2% × 88 500 = $1770.
Level 2 · Application
Calculate and compare the Medicare levy (2%) paid by someone earning $40 000 with someone earning $90 000.
$40 000 → $800; $90 000 → $1800. The rate is the same (2%) but the higher income pays more dollars because it is a percentage of income.
Calculate and compare the Medicare levy (2%) paid by someone earning $55 000 with someone earning $120 000.
$55 000 → $1100; $120 000 → $2400. The rate is the same (2%) but the higher income pays more dollars because the levy is a percentage of income.
Calculate and compare the Medicare levy (2%) paid by someone earning $48 000 with someone earning $96 000.
$48 000 → $960; $96 000 → $1920. Since $96 000 is double $48 000, the levy also doubles (same 2% rate).
Level 3 · Further Application
A person has a taxable income of $75 000.
$16,342
(a) Tax = 5092 + 0.325 × (75 000 − 45 000) = $14,842; levy = 2% × 75 000 = $1500.
(b) Total = $14,842 + $1500 = $16,342.
A person has a taxable income of $90 000. (Use the bracket “$5092 + 32.5c for each $1 over $45 000”.)
$21,517
(a) Tax = 5092 + 0.325 × (90 000 − 45 000) = 5092 + 14 625 = $19,717; levy = 2% × 90 000 = $1800.
(b) Total = $19,717 + $1800 = $21,517.
A person has a taxable income of $60 000. (Use the bracket “$5092 + 32.5c for each $1 over $45 000”.)
$11,167
(a) Tax = 5092 + 0.325 × (60 000 − 45 000) = 5092 + 4875 = $9967; levy = 2% × 60 000 = $1200.
(b) Total = $9967 + $1200 = $11,167.
Level 1 · Fluency
An employee’s tax payable is $9200, but $9650 was withheld through PAYG. Do they receive a refund or owe money, and how much?
refund of $450
Withheld exceeds tax payable, so a refund of $450 (9650 − 9200).
An employee’s tax payable is $11 400, but only $10 900 was withheld through PAYG. Do they receive a refund or owe money, and how much?
owes $500
Tax payable exceeds the amount withheld, so they owe $500 (11 400 − 10 900).
An employee’s tax payable is $7300 and exactly $7300 was withheld through PAYG. Do they receive a refund or owe money?
neither ($0)
The amounts are equal, so there is neither a refund nor anything owing ($0).
Level 2 · Application
An employee had $14 200 withheld through PAYG, but their actual tax payable is $12 850. Determine whether they receive a refund or owe extra, and how much.
refund of $1350
14 200 − 12 850 = $1350 withheld above the tax owed, so a refund of $1350.
An employee had $9800 withheld through PAYG, but their actual tax payable is $10 550. Determine whether they receive a refund or owe extra, and how much.
owes $750
Tax payable exceeds the amount withheld: 10 550 − 9800 = $750, so they owe $750.
An employee had $16 500 withheld through PAYG, but their actual tax payable is $15 200. Determine whether they receive a refund or owe extra, and how much.
refund of $1300
Withheld exceeds tax payable: 16 500 − 15 200 = $1300, so a refund of $1300.
Level 3 · Further Application
Wally has a taxable income of $122 680 and paid $3000 per month in PAYG tax. (Ignore the Medicare levy; use the table above.)
$5,541.40
(a) $122 680 is in the $120 001–$180 000 bracket: 29 467 + 0.37 × (122 680 − 120 000) = $30,458.60.
(b) PAYG paid = 3000 × 12 = $36 000. Refund = 36 000 − $30,458.60 = $5,541.40.
Nadia has a taxable income of $98 000 and paid $2100 per month in PAYG tax. (Ignore the Medicare levy; use the bracket “$5092 + 32.5c for each $1 over $45 000”.)
refund of $2883
(a) 5092 + 0.325 × (98 000 − 45 000) = 5092 + 17 225 = $22,317.
(b) PAYG paid = 2100 × 12 = $25 200. Refund = 25 200 − 22 317 = $2883.
Ben has a taxable income of $135 000 and paid $3200 per month in PAYG tax. (Ignore the Medicare levy; use the bracket “$29 467 + 37c for each $1 over $120 000”.)
refund of $3383
(a) 29 467 + 0.37 × (135 000 − 120 000) = 29 467 + 5550 = $35,017.
(b) PAYG paid = 3200 × 12 = $38 400. Refund = 38 400 − 35 017 = $3383.
Level 1 · Fluency
An employee’s gross fortnightly pay is $2400, with total deductions of $578. Calculate the net pay.
$1822
2400 − 578 = $1822.
An employee’s gross weekly pay is $1850, with total deductions of $612. Calculate the net pay.
$1238
1850 − 612 = $1238.
An employee’s gross monthly pay is $6400, with total deductions of $1780. Calculate the net pay.
$4620
6400 − 1780 = $4620.
Level 2 · Application
An employee’s gross fortnightly pay is $2400, with $410 PAYG tax, $48 Medicare levy and $120 salary-sacrificed super deducted. Calculate the net pay.
$1822
Deductions = 410 + 48 + 120 = $578. Net pay = 2400 − 578 = $1822.
An employee’s gross fortnightly pay is $3200, with $620 PAYG tax, $64 Medicare levy and $180 salary-sacrificed super deducted. Calculate the net pay.
$2336
Deductions = 620 + 64 + 180 = $864. Net pay = 3200 − 864 = $2336.
An employee’s gross fortnightly pay is $2800, with $505 PAYG tax, $56 Medicare levy and $140 in union and super deductions. Calculate the net pay.
$2099
Deductions = 505 + 56 + 140 = $701. Net pay = 2800 − 701 = $2099.
Level 3 · Further Application
An employee has a gross annual salary of $75 000, with $14 600 tax, $1500 Medicare levy and $3000 salary-sacrificed super.
$55 900; 75%
(a) 75 000 − (14 600 + 1500 + 3000) = 75 000 − 19 100 = $55 900.
(b) 55 900 ÷ 75 000 × 100 ≈ 75%.
An employee has a gross annual salary of $96 000, with $20 100 tax, $1920 Medicare levy and $4800 salary-sacrificed super.
$69 180; 72%
(a) 96 000 − (20 100 + 1920 + 4800) = 96 000 − 26 820 = $69 180.
(b) 69 180 ÷ 96 000 × 100 ≈ 72%.
An employee has a gross annual salary of $60 000, with $9967 tax, $1200 Medicare levy and $2400 salary-sacrificed super.
$46 433; 77%
(a) 60 000 − (9967 + 1200 + 2400) = 60 000 − 13 567 = $46 433.
(b) 46 433 ÷ 60 000 × 100 ≈ 77%.
Level 1 · Fluency
An hourly rate is in cell B2 and hours worked in cell B3. Write a spreadsheet formula for the total wage (no overtime).
=B2*B3.
An annual salary is in cell B2. Write a spreadsheet formula for the fortnightly pay (26 fortnights per year).
=B2/26.
A gross weekly pay is in cell B2 and total deductions in cell B3. Write a formula for the net weekly pay.
=B2−B3.
Level 2 · Application
An hourly rate is in B2 and hours worked in B3, with time-and-a-half for hours over 38. Write a formula for the weekly wage.
=38*B2 + (B3−38)*1.5*B2 (valid when B3 > 38).
An hourly rate is in B2 and total hours in B3, with double time for hours over 40. Write a formula for the weekly wage (valid when B3 > 40).
=40*B2 + (B3−40)*2*B2 (valid when B3 > 40).
A base salary is in B2 and total sales in B3, with a 5% commission on sales. Write a formula for the total pay.
=B2 + B3*0.05.
Level 3 · Further Application
A spreadsheet has gross pay in B2, total tax in B3 and other deductions in B4.
(a) =B2−B3−B4.
(b) =B2*1.03 (or =B2+B2*0.03).
A spreadsheet has gross pay in B2 and total tax in B3.
(a) =B3/B2*100.
(b) =B2−B3−B2*0.02.
A spreadsheet has last year’s salary in cell B2.
(a) =B2*1.04.
(b) =B2*0.04.
Level 1 · Fluency
Water costs $2.20 per kilolitre. Calculate the usage charge for 85 kL.
$187
85 × 2.20 = $187.
Electricity costs 28c per kilowatt-hour. Calculate the usage charge for 640 kWh.
$179.20
640 × 0.28 = $179.20.
Gas costs 4.2c per megajoule. Calculate the usage charge for 5000 MJ.
$210
5000 × 0.042 = $210.
Level 2 · Application
A water bill shows 85 kL used at $2.20/kL plus a $95 service charge. Calculate the total bill, and the average daily water use in litres over a 90-day period.
$282; 944 L/day
Total = 85 × 2.20 + 95 = 187 + 95 = $282. Daily use = 85 000 L ÷ 90 ≈ 944 L/day.
An electricity bill shows 820 kWh used at 27c/kWh plus an $88 supply charge. Calculate the total bill, and the average daily usage in kWh over a 90-day quarter.
$309.40; ≈9.11 kWh/day
Usage = 820 × 0.27 = $221.40. Total = 221.40 + 88 = $309.40. Daily usage = 820 ÷ 90 ≈ 9.11 kWh/day.
A gas bill shows 4800 MJ used at 3.8c/MJ plus a $75 supply charge. Calculate the total bill, and the average daily usage in MJ over a 60-day period.
$257.40; 80 MJ/day
Usage = 4800 × 0.038 = $182.40. Total = 182.40 + 75 = $257.40. Daily usage = 4800 ÷ 60 = 80 MJ/day.
Level 3 · Further Application
An electricity bill shows 1240 kWh used over a 91-day quarter, charged at 26.4c/kWh plus a 98c per day supply charge.
$416.54
(a) Usage = 1240 × 0.264 = $327.36; supply = 91 × 0.98 = $89.18.
(b) Total = 327.36 + 89.18 = $416.54.
A water bill shows 96 kL used over a 90-day quarter, charged at $2.35/kL plus a $1.05 per day service charge.
$320.10
(a) Usage = 96 × 2.35 = $225.60; service = 90 × 1.05 = $94.50.
(b) Total = 225.60 + 94.50 = $320.10.
A gas bill shows 6200 MJ used over a 92-day quarter, charged at 3.6c/MJ plus an 85c per day supply charge.
$301.40
(a) Usage = 6200 × 0.036 = $223.20; supply = 92 × 0.85 = $78.20.
(b) Total = 223.20 + 78.20 = $301.40.
Level 1 · Fluency
A car has a drive-away price of $28 990, plus a $600 inspection. Calculate the total so far.
$29 590
28 990 + 600 = $29 590.
A car has a drive-away price of $23 500, plus $480 in accessories. Calculate the total so far.
$23 980
23 500 + 480 = $23 980.
A car has a drive-away price of $34 900, plus a $750 delivery fee. Calculate the total so far.
$35 650
34 900 + 750 = $35 650.
Level 2 · Application
A car has a drive-away price of $28 990, plus a $600 inspection, $450 in accessories, and a $1200 trade-in shortfall. Calculate the total amount the buyer needs available.
$31 240
28 990 + 600 + 450 + 1200 = $31 240.
A car has a drive-away price of $26 500, plus a $550 inspection, $700 in accessories, and a $900 trade-in shortfall. Calculate the total amount the buyer needs available.
$28 650
26 500 + 550 + 700 + 900 = $28 650.
A car has a drive-away price of $41 200, plus a $620 inspection, $1300 in accessories, and a $2000 trade-in shortfall. Calculate the total amount the buyer needs available.
$45 120
41 200 + 620 + 1300 + 2000 = $45 120.
Level 3 · Further Application
A buyer compares two cars, each with 3% stamp duty, $650 registration and insurance as shown.
| New car | Used car | |
|---|---|---|
| Sale price | $32 000 | $24 000 |
| Insurance | $1400 | $1100 |
$8540
(a) New: 32 000 + 960 + 650 + 1400 = $35 010. Used: 24 000 + 720 + 650 + 1100 = $26 470.
(b) Difference = $8540.
A buyer compares two cars, each with 3% stamp duty, $700 registration and insurance as shown.
| New car | Used car | |
|---|---|---|
| Sale price | $34 000 | $22 000 |
| Insurance | $1500 | $1050 |
$12 810
(a) New: 34 000 + 1020 + 700 + 1500 = $37 220. Used: 22 000 + 660 + 700 + 1050 = $24 410.
(b) Difference = $12 810.
A buyer compares two cars, each with 3% stamp duty, $600 registration and insurance as shown.
| Car P | Car Q | |
|---|---|---|
| Sale price | $28 000 | $19 500 |
| Insurance | $1300 | $980 |
$9075
(a) Car P: 28 000 + 840 + 600 + 1300 = $30 740. Car Q: 19 500 + 585 + 600 + 980 = $21 665.
(b) Difference = $9075.
Level 1 · Fluency
Stamp duty is 3% of the sale price. Calculate the stamp duty on a $32 000 car.
$960
3% × 32 000 = $960.
Stamp duty is 3% of the sale price. Calculate the stamp duty on a $45 000 car.
$1350
3% × 45 000 = $1350.
Stamp duty is 3% of the sale price. Calculate the stamp duty on a $27 500 car.
$825
3% × 27 500 = $825.
Level 2 · Application
A new car has a sale price of $32 000, registration of $850, comprehensive insurance of $1400, and stamp duty of 3% of the sale price. Calculate the total on-road cost.
$35 210
Stamp duty = 960. Total = 32 000 + 850 + 1400 + 960 = $35 210.
A new car has a sale price of $38 000, registration of $920, comprehensive insurance of $1550, and stamp duty of 3% of the sale price. Calculate the total on-road cost.
$41 610
Stamp duty = 3% × 38 000 = $1140. Total = 38 000 + 920 + 1550 + 1140 = $41 610.
A car has a sale price of $26 000, registration of $780, comprehensive insurance of $1150, and stamp duty of 3% of the sale price. Calculate the total on-road cost.
$28 710
Stamp duty = 3% × 26 000 = $780. Total = 26 000 + 780 + 1150 + 780 = $28 710.
Level 3 · Further Application
A $36 000 car has registration $890, comprehensive insurance $1500, and stamp duty 3%.
$39 470
(a) 3% × 36 000 = $1080.
(b) 36 000 + 890 + 1500 + 1080 = $39 470.
A $42 000 car has registration $950, comprehensive insurance $1650, and stamp duty 3%.
$45 860
(a) 3% × 42 000 = $1260.
(b) 42 000 + 950 + 1650 + 1260 = $45 860.
A $30 000 car has registration $820, comprehensive insurance $1300, and stamp duty 3%.
$33 020
(a) 3% × 30 000 = $900.
(b) 30 000 + 820 + 1300 + 900 = $33 020.
Level 1 · Fluency
A car uses 7 L of fuel per 100 km. How much fuel is used over 100 km?
7 litres
A car uses 8 L of fuel per 100 km. How much fuel is used over 250 km?
20 litres
8/100 × 250 = 20 litres.
A car uses 6 L of fuel per 100 km. How much fuel is used over 350 km?
21 litres
6/100 × 350 = 21 litres.
Level 2 · Application
Two cars are driven 20 000 km per year. Car X uses 6.2 L/100 km and Car Y uses 9.8 L/100 km. At $1.90/L, calculate the annual fuel-cost difference.
$1368/year
Car X: 6.2/100 × 20 000 × 1.90 = $2356. Car Y: 9.8/100 × 20 000 × 1.90 = $3724. Difference = $1368/year.
Two cars are driven 16 000 km per year. Car X uses 5.5 L/100 km and Car Y uses 8.5 L/100 km. At $2.00/L, calculate the annual fuel-cost difference.
$960/year
Car X: 5.5/100 × 16 000 × 2.00 = $1760. Car Y: 8.5/100 × 16 000 × 2.00 = $2720. Difference = $960/year.
Two cars are driven 25 000 km per year. Car M uses 7 L/100 km and Car N uses 11 L/100 km. At $1.80/L, calculate the annual fuel-cost difference.
$1800/year
Car M: 7/100 × 25 000 × 1.80 = $3150. Car N: 11/100 × 25 000 × 1.80 = $4950. Difference = $1800/year.
Level 3 · Further Application
Car A uses 7.2 L/100 km and Car B uses 5.8 L/100 km. Both are driven 18 000 km/year at $1.95/L.
$491.40/year
(a) Car A: 7.2/100 × 18 000 × 1.95 = $2527.20. Car B: 5.8/100 × 18 000 × 1.95 = $2035.80.
(b) Saving = $491.40/year.
Car C uses 8.4 L/100 km and Car D uses 6.5 L/100 km. Both are driven 22 000 km/year at $2.05/L.
$856.90/year
(a) Car C: 8.4/100 × 22 000 × 2.05 = $3788.40. Car D: 6.5/100 × 22 000 × 2.05 = $2931.50.
(b) Saving = $856.90/year.
Car E uses 9 L/100 km and Car F uses 6.2 L/100 km. Both are driven 15 000 km/year at $1.90/L.
$798/year
(a) Car E: 9/100 × 15 000 × 1.90 = $2565. Car F: 6.2/100 × 15 000 × 1.90 = $1767.
(b) Saving = $798/year.
Level 1 · Fluency
A car’s price is in cell A2 and it loses 15% of its value each year. Write a formula for its value after 1 year.
=A2*0.85.
A car’s price is in cell A2 and it loses 20% of its value each year. Write a formula for its value after 1 year.
=A2*0.80.
A car’s price is in cell A2 and it loses 12% of its value each year. Write a formula for its value after 1 year.
=A2*0.88.
Level 2 · Application
Two cars are priced $24 000 and $31 000 and each depreciates 15% p.a. Calculate the value of each after 5 years.
$13 754.87
24 000 × 0.85⁵ = $10 648.42; 31 000 × 0.85⁵ = $13 754.87.
Two cars are priced $28 000 and $36 000 and each depreciates 18% p.a. Calculate the value of each after 4 years.
$16 276.38
28 000 × 0.82⁴ = $12 659.41; 36 000 × 0.82⁴ = $16 276.38.
Two cars are priced $22 000 and $30 000 and each depreciates 10% p.a. Calculate the value of each after 6 years.
$15 943.23
22 000 × 0.9⁶ = $11 691.70; 30 000 × 0.9⁶ = $15 943.23.
Level 3 · Further Application
Describe how to set up a spreadsheet to compare the total purchase cost (sale price + on-road costs) of three vehicles.
(a) Columns: Vehicle, Sale price, Stamp duty, Registration, Insurance, Total cost.
(b) With sale price in B2, duty C2, rego D2, insurance E2: =B2+C2+D2+E2, filled down for each vehicle.
Describe how to set up a spreadsheet to compare the drive-away cost (sale price + stamp duty + registration) of three vehicles.
(a) Columns: Vehicle, Sale price, Stamp duty, Registration, Total cost.
(b) With sale price in B2, duty C2, rego D2: =B2+C2+D2, filled down for each vehicle.
Describe how a spreadsheet could rank four cars by total purchase cost (sale price + on-road costs).
(a) Columns: Vehicle, Sale price, On-road costs, Total cost.
(b) With sale price in B2 and on-road costs in C2: =B2+C2, filled down; then use =MIN(...) over the total-cost column (or sort it ascending) to identify the cheapest car.
Level 1 · Fluency
A car needs a $320 service every 15 000 km. If it is driven 30 000 km in a year, what is the annual servicing cost?
$640
30 000 ÷ 15 000 = 2 services → 2 × 320 = $640.
A car needs a $280 service every 10 000 km. If it is driven 30 000 km in a year, what is the annual servicing cost?
$840
30 000 ÷ 10 000 = 3 services → 3 × 280 = $840.
A car needs a $360 service every 12 000 km. If it is driven 24 000 km in a year, what is the annual servicing cost?
$720
24 000 ÷ 12 000 = 2 services → 2 × 360 = $720.
Level 2 · Application
A car owner budgets $150/month for running costs. Actual yearly costs were: servicing $600, tyres $480, registration $780 and repairs $340. Compare the actual monthly average with the budget.
$33.33/month over
Actual = 600 + 480 + 780 + 340 = $2200/year = $183.33/month. This is $33.33/month over the $150 budget.
A car owner budgets $180/month for running costs. Actual yearly costs were: servicing $720, tyres $560, registration $840 and repairs $520. Compare the actual monthly average with the budget.
$40/month over
Actual = 720 + 560 + 840 + 520 = $2640/year = $220/month. This is $40/month over the $180 budget.
A car owner budgets $200/month for running costs. Actual yearly costs were: servicing $640, tyres $600, registration $910 and repairs $250. Compare the actual monthly average with the budget.
exactly on budget
Actual = 640 + 600 + 910 + 250 = $2400/year = $200/month, which is exactly on budget (a $0 difference).
Level 3 · Further Application
A car needs a $320 service every 15 000 km and a $680 set of tyres every 40 000 km. It is driven 20 000 km per year.
$766.67/year
(a) 20 000/15 000 × 320 = $426.67.
(b) Tyres: 20 000/40 000 × 680 = $340. Combined ≈ $766.67/year.
A car needs a $290 service every 12 000 km and a $640 set of tyres every 32 000 km. It is driven 24 000 km per year.
$1060/year
(a) 24 000/12 000 × 290 = 2 × 290 = $580.
(b) Tyres: 24 000/32 000 × 640 = 0.75 × 640 = $480. Combined = $1060/year.
A car needs a $350 service every 15 000 km and a $720 set of tyres every 45 000 km. It is driven 18 000 km per year.
$708/year
(a) 18 000/15 000 × 350 = 1.2 × 350 = $420.
(b) Tyres: 18 000/45 000 × 720 = 0.4 × 720 = $288. Combined = $708/year.
Level 1 · Fluency
What does compulsory third-party (CTP / “green slip”) insurance cover?
people
Injury to people caused by the vehicle in an accident (not damage to property or vehicles).
What does comprehensive car insurance cover that CTP (green slip) does not?
your own car
Comprehensive covers damage to your own car and to other people’s property (plus theft/fire), whereas CTP covers only injury to people.
Does third-party property insurance cover damage to your own car?
No
No — it covers damage your car causes to other people’s property, not your own vehicle.
Level 2 · Application
A driver with a $15 000 car chooses third-party property insurance ($450/year) over comprehensive ($980/year). Describe the financial risk they take if they cause an accident that damages their own car.
Third-party property covers damage to other people’s property but not their own car, so they would have to pay to repair or replace their own $15 000 car themselves — a large potential loss to save $530/year.
A driver with a $22 000 car chooses third-party property insurance ($520/year) over comprehensive ($1150/year). Describe the financial risk they take if they cause an accident that damages their own car.
Third-party property does not cover damage to their own car, so they would have to pay to repair or replace their own $22 000 car themselves — a large potential loss to save $630/year.
A driver insures a $9000 car with CTP only. Describe the financial risk they take if the car is stolen or written off in a single-vehicle crash.
CTP covers only injury to people, not loss of the vehicle, so the driver bears the full $9000 loss themselves; comprehensive insurance would have covered theft or damage to their own car.
Level 3 · Further Application
Explain the difference between CTP and comprehensive insurance, and describe a scenario where having only CTP leaves a driver with a significant loss.
(a) CTP covers injury to people only; comprehensive covers damage to your own car and others’ property as well.
(b) E.g. a driver at fault writes off their own $20 000 car — with only CTP, none of that repair/replacement is covered, so they bear the full loss.
Explain the difference between CTP and third-party property insurance, and describe a scenario where having only third-party property leaves a driver with a significant loss.
(a) CTP covers injury to people; third-party property covers damage the driver causes to other people’s property (but not their own car).
(b) E.g. an at-fault driver damages their own $25 000 car — third-party property pays nothing toward their own vehicle, so they bear that loss.
Explain what comprehensive insurance covers, and describe a scenario where it is clearly worth its higher premium.
(a) Comprehensive covers damage to the driver’s own car and to others’ property, plus theft and fire (injury to people is covered by the separate CTP).
(b) E.g. a driver at fault writes off their own $30 000 car — comprehensive covers the replacement, avoiding a $30 000 out-of-pocket loss.
Level 1 · Fluency
DIY servicing costs $200/year in parts; professional servicing costs $650/year. Which is cheaper, and by how much?
$450/year
DIY is cheaper by $450/year.
DIY servicing costs $180/year in parts; professional servicing costs $560/year. Which is cheaper, and by how much?
$380/year
DIY is cheaper by 560 − 180 = $380/year.
DIY servicing costs $240/year in parts; professional servicing costs $700/year. Which is cheaper, and by how much?
$460/year
DIY is cheaper by 700 − 240 = $460/year.
Level 2 · Application
Over a year, Car A costs $1400 fuel, $600 servicing and $480 tyres; Car B costs $1150 fuel, $560 servicing and $520 tyres. Which car is cheaper to run in that year, and by how much?
$250
Car A = 2480; Car B = 2230. Car B is cheaper by $250.
Over a year, Car A costs $1600 fuel, $700 servicing and $520 tyres; Car B costs $1350 fuel, $620 servicing and $560 tyres. Which car is cheaper to run in that year, and by how much?
$290
Car A = 1600 + 700 + 520 = $2820; Car B = 1350 + 620 + 560 = $2530. Car B is cheaper by $290.
Over a year, Car A costs $1250 fuel, $540 servicing and $460 tyres; Car B costs $1500 fuel, $500 servicing and $420 tyres. Which car is cheaper to run in that year, and by how much?
$170
Car A = 1250 + 540 + 460 = $2250; Car B = 1500 + 500 + 420 = $2420. Car A is cheaper by $170.
Level 3 · Further Application
Both cars are driven 15 000 km/year for 5 years (75 000 km total).
| Car A | Car B | |
|---|---|---|
| Fuel (per year) | $1400 | $1150 |
| Service | $320 / 15 000 km | $280 / 10 000 km |
| Tyres | $680 / 40 000 km | $720 / 45 000 km |
Car B
(a) Car A: fuel 5 × 1400 = 7000; services 75 000/15 000 × 320 = 1600; tyres 75 000/40 000 × 680 = 1275 → ≈ $9875. Car B: fuel 5 × 1150 = 5750; services 75 000/10 000 × 280 = 2100; tyres 75 000/45 000 × 720 = 1200 → ≈ $9050.
(b) Car B is cheaper by about $825 over 5 years.
Both cars are driven 12 000 km/year for 5 years (60 000 km total).
| Car A | Car B | |
|---|---|---|
| Fuel (per year) | $1300 | $1500 |
| Service | $300 / 12 000 km | $260 / 10 000 km |
| Tyres | $640 / 40 000 km | $700 / 50 000 km |
Car A
(a) Car A: fuel 5 × 1300 = 6500; services 60 000/12 000 × 300 = 1500; tyres 60 000/40 000 × 640 = 960 → ≈ $8960. Car B: fuel 5 × 1500 = 7500; services 60 000/10 000 × 260 = 1560; tyres 60 000/50 000 × 700 = 840 → ≈ $9900.
(b) Car A is cheaper by about $940 over 5 years.
Both cars are driven 15 000 km/year for 4 years (60 000 km total).
| Car A | Car B | |
|---|---|---|
| Fuel (per year) | $1450 | $1250 |
| Service | $350 / 15 000 km | $300 / 12 000 km |
| Tyres | $700 / 50 000 km | $680 / 40 000 km |
Car B
(a) Car A: fuel 4 × 1450 = 5800; services 60 000/15 000 × 350 = 1400; tyres 60 000/50 000 × 700 = 840 → ≈ $8040. Car B: fuel 4 × 1250 = 5000; services 60 000/12 000 × 300 = 1500; tyres 60 000/40 000 × 680 = 1020 → ≈ $7520.
(b) Car B is cheaper by about $520 over 4 years.
Level 1 · Fluency
In a spreadsheet, annual fuel is in B2, servicing in B3 and insurance in B4. Write a formula for the total annual running cost.
=B2+B3+B4.
In a spreadsheet, annual fuel is in B2, servicing in B3, tyres in B4 and registration in B5. Write a formula for the total annual running cost.
=B2+B3+B4+B5.
In a spreadsheet, the total annual running cost is in B6. Write a formula for the average monthly running cost.
=B6/12.
Level 2 · Application
For a 3-year comparison, annual running cost is in B5. Write a formula for the total 3-year running cost.
=B5*3.
For a 5-year comparison, the annual running cost is in B5. Write a formula for the total 5-year running cost.
=B5*5.
Car 1’s total cost is in B10 and Car 2’s total cost is in C10. Write a formula that returns the cheaper of the two totals.
=MIN(B10,C10).
Level 3 · Further Application
Describe how a spreadsheet could compare the total 5-year running cost of two vehicles, including services and tyre changes that do not occur every year.
(a) Convert to an annual figure: services per year = (km per year)/(km per service) = 15 000/15 000 = 1, then × cost per service; multiply by 5 for the total. Tyres are handled the same way (km/year ÷ km per tyre-set × cost).
(b) Sum each car’s 5-year fuel, service, tyre and insurance costs in a total cell, then compare the two totals (e.g. with a formula that flags the smaller one).
Describe how a spreadsheet could compare the total 4-year running cost of two vehicles, including a service every 20 000 km at 20 000 km/year.
(a) Services per year = (km per year)/(km per service) = 20 000/20 000 = 1 per year, then × cost per service; multiply by 4 for the total.
(b) Sum each car’s 4-year costs in a total cell and compare the two totals, e.g. with =MIN(...) or an IF that flags the smaller one.
Describe how a spreadsheet could compare the total 5-year running cost of two vehicles whose tyres are replaced every 40 000 km at 16 000 km/year.
(a) Tyre-sets per year = (km per year)/(km per set) = 16 000/40 000 = 0.4, then × cost per set; multiply by 5 for the 5-year total.
(b) Add each car’s 5-year fuel, service, tyre and insurance totals, then compare the two totals (e.g. =MIN(...) or an IF flag).
Level 1 · Fluency
A person earns $980/week and has fixed costs of $520/week. How much is left before any saving?
$460
980 − 520 = $460.
A person earns $1150/week and has fixed costs of $680/week. How much is left before any saving?
$470
1150 − 680 = $470.
A person earns $845/week and has fixed costs of $500/week. How much is left before any saving?
$345
845 − 500 = $345.
Level 2 · Application
A person earns $980/week, has fixed costs of $520/week, and wants to save 15% of income. Calculate the discretionary spending money left each week.
$313/week
Saving = 15% × 980 = $147. Discretionary = 980 − 520 − 147 = $313/week.
A person earns $1200/week, has fixed costs of $640/week, and wants to save 20% of income. Calculate the discretionary spending money left each week.
$320/week
Saving = 20% × 1200 = $240. Discretionary = 1200 − 640 − 240 = $320/week.
A person earns $1050/week, has fixed costs of $580/week, and wants to save 12% of income. Calculate the discretionary spending money left each week.
$344/week
Saving = 12% × 1050 = $126. Discretionary = 1050 − 580 − 126 = $344/week.
Level 3 · Further Application
A young worker earns $920/week after tax. Fixed expenses are $480/week and they want to save 15% of income.
$62
(a) Saving = 15% × 920 = $138; discretionary = 920 − 480 − 138 = $302/week.
(b) Extra saving = 200 − 138 = $62, so discretionary falls by $62 to $240/week.
A worker earns $1080/week after tax. Fixed expenses are $560/week and they want to save 15% of income.
$88
(a) Saving = 15% × 1080 = $162; discretionary = 1080 − 560 − 162 = $358/week.
(b) Extra saving = 250 − 162 = $88, so discretionary falls by $88 to $270/week.
A worker earns $760/week after tax. Fixed expenses are $410/week and they want to save 10% of income.
$74
(a) Saving = 10% × 760 = $76; discretionary = 760 − 410 − 76 = $274/week.
(b) Extra saving = 150 − 76 = $74, so discretionary falls by $74 to $200/week.