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9.03 On-road and running costs of a car

Worksheet
Car insurance
1

Ned bought a new 4-wheel drive for \$25\,880. His CTP Insurance is \$549 per year and his comprehensive insurance is \$80.46 per month. Find the total cost of insurance per year.

2

Third party property insurance costs \$33.34 a month. What is the cost per week?

3

John was going to pay \$690.90 for a new comprehensive insurance policy, but he has been offered a 18\% discount for buying online. Determine the discount that John received.

4

An insurer uses the following decision tree to estimate the cost of CTP Insurance (Green Slip) for drivers:

Lisa is a 55-year old driver who owns a scooter, which was made 17 years ago. If she has previously incurred no traffic fines, then what is her resulting cost of CTP Insurance (Green Slip)?

5

Xanthe bought a motor scooter. Her annual CTP Green Slip was \$378 and her comprehensive vehicle insurance was \$18.44 per month. She also agreed to pay the first 6.5\% of a claim if she had an accident that was her fault.

a

What was her yearly insurance cost, excluding the cost of at-fault claims?

b

She had an accident that was her fault and the damage bill to the other car was \$6790. How much did she contribute to the claim?

c

In the same accident, her scooter suffered \$1020 worth of damage. How much did Xanthe pay towards this claim?

6

The following table shows the third party property insurance premiums for the RIGHT4U insurance company:

Car makeDriver genderDriver ageSuburb where vehicle is garagedPlace where car is normally keptThird party property premium
\text{Fiarello}\text{Male}19\text{North Haverbrook}\text{On street}\$326
\text{Chryslus}\text{Female}53\text{North Haverbrook}\text{Carport}\$186
\text{Ferrini}\text{Male}49\text{Ogdenville}\text{Driveway}\$280
\text{VMW}\text{Female}25\text{Ogdenville}\text{Locked garage}\$220
\text{Potomac}\text{Female}89\text{Brockway}\text{On street}\$335
\text{Lamborgotti}\text{Male}65\text{Brockway}\text{Security compound}\$306

Determine the third party property insurance premium for:

a

The female from North Haverbrook who gets a 10\% no claim discount.

b

The driver who has the car in a locked garage and gets a 4.5\% discount.

c

The driver under 20 years of age who must pay a 14.7\% surcharge as he lives in a high theft area.

d

The Potomac driver from Brockway who pays a 26\% age levy but also gets a 5.6\% loyalty discount.

7

Construct a graph that demonstrates a likely relationship between the number of accidents in different suburbs and the cost of a third party property damage insurance premium.

8

Sally bought a small second-hand car for \$18\,700. Her compulsory third party insurance was \$296 and she took out comprehensive insurance at \$49.81 per month.

a

What was her yearly insurance cost?

b

She ran into the back of a car which had stopped at traffic lights and did \$6240 damage to the car as well as \$3040 damage to her own car. If Sally had to pay an excess of 9.5\% of the repair costs, how much did the insurance company pay?

c

Sally's comprehensive insurance premium will increase by 14.5\% next year. How much will she now pay for this premium per month?

Running costs
9

Lisa bought a new car for \$22\,000. She is told that the running cost of the car will be 291.10 cents per kilometre. Lisa travels 14\,000 \text{ km} per year.

a

Find her yearly running costs.

b

Find her monthly running costs.

10

The average monthly cost of running a particular model of car has been estimated to be \$964.44. Assume that there are 52 weeks in a year.

a

What is the yearly cost of running this car?

b

Harry owns this particular model of car and finds that the fortnightly running costs are in fact \$660.42. By how much more does Harry pay in running costs compared to the estimated running costs, per year?

11

The diagram shows three towns labelled A, B and C. The corresponding road tolls between each town are also displayed:

Kenneth starts at town B and drives to town C for work, leaving his car parked for 8 hours. The parking in the area costs \$1.77 per hour. He later travels to town A to buy dinner. On his way home, there are delays from town A to town B, so he decides to drive back to town B via town C.

How much was his total running costs for the day?

12

Ursula is due to service her car and takes it to the local mechanic. She is told that she needs to replace all four wheels, each pricing at \$330. Her break pads are also out of alignment and need fixing, costing \$520, along with other general services costing \$210. As a regular customer, the mechanic provides the option of regular weekly payments of \$293.

How many payments will she need to make?

13

The purchase price of two cars and their on-road costs are given below:

  • The price of Car A is \$5076 and the price of Car B is \$8308.

  • The total on-road costs excluding stamp duty for the next several years is \$10\,001 and \$8059, for Car A and Car B respectively.

  • The NSW rate on stamp duty is 3\% of the car’s market value up to \$45\,000.

Given that all other extraneous costs are the same for each car, which car will cost the least over the next several years?

14

Ellie purchased a second-hand motorcycle with on-road costs shown in the table:

a

Given that stamp duty is 3\% of the purchase price, complete the table.

b

Hence, calculate the total cost Ellie must pay.

Purchase price (including GST)\$10\,000
Stamp duty
Transfer of registration\$20
Renewal of registration\$240
CTP Insurance (Green Slip)\$110
15

The table below displays a list of on-road costs for two car brands:

Type of carRegistrationCTP Insurance (Green Slip)Stamp duty Additional compulsory costs
\text{Holden}\$550\$510\$220
\text{Ford}\$350\$640\$220
a

Given that the total of the on-road costs for a Holden car is \$1840, what is the cost due for CTP Insurance (Green Slip)?

b

The total costs of a Holden car, including purchase price and on-road costs, is \$18\,840.

Given that the purchase price of the Ford car is 70\% of the price of the Holden car, what is the cost of stamp duty for the Ford car? Note that stamp duty is 3\% of the purchase price of a vehicle, up to \$45\,000.

16

Mario purchased a new motorbike with on-road costs. The following table summarises the costs related to the purchase:

a

Determine the total cost of stamp duty.

b

Hence, what is the cost of registration?

Purchase price (excluding GST)\$65\,000
GST\$6500
Stamp duty3\% \text{ of the first} \\ \$45\,000 \text{ and an} \\ \text{additional } 5\% \\ \text{over } \$45\,000
Registration
CTP Insurance (Green Slip)\$658
Total costs\$75\,558
17

Tom purchased a new station wagon with on-road costs. The following table summarises the costs related to the purchase:

a

Find the cost of the goods and services tax (GST).

b

Hence, find the total cost of stamp duty.

c

Find the total cost that Tom must pay.

Purchase price (excluding GST)\$61\,000
GST10\% \text{ of the} \\ \text{purchase price}
Stamp Duty3\% \text{ of the first} \\ \$45\,000 \text{ and an} \\ \text{additional } 5\% \\ \text{over } \$45\,000
Registration\$719
CTP Insurance (Green Slip)\$691
18

Considering all the annual on-road costs, Bob wants to work out whether he can continue to afford owning a car. The following table summarises the annual on-road costs:

a

If Bob's fortnightly savings is \$95, does Bob have enough savings to afford owning a car?

b

Bob only uses his car to drive to work every day of the week. Alternatively, he could take public transport, with each one-way fare costing him \$2.75.

If Bob works every day of the year, how much will he save in a year if he took public transport and no longer had to pay any on-road costs?

Registration\$310
CTP Insurance (Green Slip)\$380
Fuel\$1320
Additional on-road costs\$360
Total
19

The table shows the sources of average yearly running costs for three people:

SkyeHermioneBrad
Servicing and maintenance\$970\$966\$981
Registration and insurance\$1104\$1079\$1196
Parking and tolls\$106\$188\$119
Fines\$67\$133\$117
Petrol\$2209\$2047\$1867
Average weekly running costs
a

Complete the given table to find the average weekly running costs for each individual. Assume that there are 52 weeks in a year.

b

What is the difference between the total annual running costs of Skye and Brad?

20

A particular dealership is offering 10\% off on brand new cars for those who return and replace a used car. However, the discount only applies to the purchase price (including GST) and excludes all on-road costs. The price of all necessary on-road costs are tabulated in the given table:

Purchase price (including GST) \$28\,000
Stamp duty\$840
Registration\$360
CTP Insurance (Green Slip)\$450

If the dealership agrees to pay \$5700 for a returned car, then what is the total cost all together?

21

Xavier wanted to know how much of his savings were spent on his car. His yearly sources of running costs are given in the table below:

Cost
Fuel\$3769
CTP Insurance and comprehensive car insurance \$1393
Price of servicing\$348 \text{ for the first service and } \$369 \text{ for the second service}
Cost of tyres\$201 \text{ each}
NRMA gold membership\$150
Tolls and parking fees\$720
Parking fines\$320
a

What is his weekly running costs? Assume that there are 52 weeks in a year.

b

If the depreciation on Xavier's car amounted to \$5500 and is also considered as a running cost, calculate the new weekly running cost of the car.

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Outcomes

MS11-2

represents information in symbolic, graphical and tabular form

MS11-5

models relevant financial situations using appropriate tools

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