NSW Mathematics Standard 11 - 2020 Edition
9.03 On-road and running costs of a car
Lesson

On-road costs include all of the expenses necessary to get a new car ready to drive on the road. Previously, we covered two of these on-road costs:

• The purchase price of the vehicle, including the cost of a car loan
• Stamp duty

Here we cover two further on-road costs: car insurance and registration.

### Types of car insurance

Whenever we drive a vehicle, there is always the risk of an accident that could result in injury or death, as well as damage to vehicles or property.

Accidents can be unexpected. If we are at-fault in an accident, we will be held liable (i.e. it is our responsibility) for any accident related expenses. This is where an appropriate level of insurance can help.

Car insurance comes in four main levels of cover:

• Compulsory Third Party (CTP), also know as a 'green slip', is the only level of insurance that is compulsory by law. It provides covers for injury or death to other people involved in an accident. It may not cover injury to ourselves and does not cover any damage to vehicles or property.

• Third Party Property is the most basic non-compulsory form of car insurance. It provides cover for damages caused by our vehicle to other vehicles or property. It does not cover damage to our own vehicle.

• Third Party, Fire and Theft is an intermediate level of non-compulsory insurance. It provides all of the cover of Third Party Property Damage, as well as loss or damage to our own car by fire, or if our car is stolen. This type of insurance is sometimes offered as an additional option on Third Party Property Insurance, rather than as a separate policy.

• Comprehensive is the most expensive level of insurance, but as its name suggests, it provides the most cover. It is the only insurance type that covers damage or loss to our own car, whether or not we are at fault. In addition, It includes all of the cover provided by the two non-compulsory insurance types mentioned above.

The following table summarises the level of cover offered by these four insurance types:

Insurance Type Injury or death to other people? Damage to other people's property? Damage or loss to your own car from fire or theft? Damage to your own car in an accident?
Comprehensive (CTP) Yes No No No
Third Party Property No Yes No No
Third Party, Fire and Theft No Yes Yes No
Comprehensive No Yes Yes Yes

For peace of mind, most people buy the best level of insurance cover they can afford. While CTP is the only insurance that is compulsory, it doesn't cover for loss or damage to any cars or property.

Did you know?

In the language of insurance, the insured person who is at fault in an accident is known as the 'first party', The insurance company (or insurer) is the 'second party'. Any person or persons making a claim against the 'first party' for injury/death, loss or damage is known as the 'third party'.

CTP and other types of car insurance are purchased from an insurance company. The details and level of cover provided are outlined in an insurance policy.

The annual cost of insurance is called a premium. For CTP, the least expensive insurance, the premium is normally paid annually when the vehicle is registered. For other types of insurance, the premium may be divided over a series of regular payments, usually on a fortnightly or monthly basis.

### Making a claim

If a car is involved in an incident, with the potential expense for loss or damage, the insured person may wish to report the incident to their insurance company. This is called making a claim.

When a claim is made, the insurance company will assess the nature of the incident and cover the cost of any loss or damage, according to the details of the policy.

If the insured person is at-fault in an incident, they normally pay a fee called an excess, when they make a claim. The amount of excess to be paid is outlined on their insurance policy.

If an insured person does not make any at-fault claims over an entire year, their insurance company will normally award them a discount, called a no-claim bonus, on the cost of their insurance premium.

### Factors affecting the cost of insurance

There is no one-size-fits-all cost for car insurance. Insurance premiums are based on individual circumstances and vary considerably depending on a range of factors, including:

• Age and gender of the driver
• Driving history and experience
• Claims history
• Type of car being driven
• Postcode of the driver
• How often the car is driven
• Whether or not the car is garaged

#### Worked example

Lisa buys a second-hand car for $\$12580$$12580. Her Compulsory Third Party insurance is \455$$455 per year and her Comprehensive insurance premium is $\$42$$42 per fortnight. 1. What is her annual insurance cost? Lisa was involved in an accident where her car ran into the back of another car causing \3750$$3750 damage, as well as $\$2390$$2390 damage to her own car. Her Comprehensive insurance policy states that she must pay an excess of 7.5%7.5% of the repair costs, if she is at fault. 1. How much does Lisa pay in excess for this accident? 2. How much does the insurance company pay out in repair costs? Solution 1. There are 2626 fortnights in a year, so her annual Comprehensive premium is 2626 \times× 4242. We add this result to her CTP premium, to find her total annual insurance.  Annual insurance cost == 455+26\times42455+26×42 == 455+1092455+1092 == \1547$$1547
2. The excess is $7.5%$7.5% of the total repair costs.
 Total repair costs $=$= $3750+2390$3750+2390 $=$= $\$6140$$6140 Excess == 7.5%7.5% of \6140$$6140 $=$= $0.075\times6140$0.075×6140 $=$= $\$460.50$$460.50 3. The insurance company will pay the balance remaining after the excess has been deducted from the total repair costs.  Amount insurance company pays == \6140$$6140 $-$− $\$460.50$$460.50 == \5679.50$$5679.50

### Vehicle registration

Registering a vehicle ensures it is roadworthy and identifiable. In NSW all vehicles including caravans, trailers and motorcycles must be registered with Roads and Maritime Services (RMS).

Registration is valid for one year. Most of the annual cost of registration is a motor vehicle tax, based on the tare (unladen) mass of the car. The greater the car's mass, the higher the tax.

The following table from the RMS outlines the motor vehicle tax for light private use vehicles with various tare masses (as of January 1, 2019).

Tare mass of vehicle (kg) Motor vehicle tax
Up to $975$975 $\$215$$215 976976 to 11541154 \250$$250
$1155$1155 to $1504$1504 $\$305$$305 15051505 to 25042504 \466$$466

Registration costs will also include an annual fee. As of January 1, 2019, the RMS annual registration fee is $\$66$$66 Additional registration fees may be charged depending on individual circumstances. Registering a used car, for example, may include a fee for a Vehicle Safety Check (formerly called a 'pink slip'), a registration transfer fee or a registration renewal fee. Remember too that stamp duty (based on the value of the car) is normally paid as part of vehicle registration. In addition, CTP insurance is required as a minimum level of cover, for the driver of a registered vehicle. In some cases, consumers may be able to organise registration, stamp duty and CTP insurance through their car dealership. ### Other on-road costs Another on-road cost that may be compulsory is a dealer delivery charge. This is an amount charged by the car dealership to prepare the car for leaving their premises. It may include the cost of preparing documentation, detailing the car, performance and safety checks, cleaning costs or transporting the car prior to purchase. The amount is often negotiable. Did you know? In Australia, there is an additional compulsory government tax on 'luxury' vehicles. For the 2018-19 financial year, the luxury car tax is 33%33% of every dollar of a car's purchase price over \66331$$66331 (or $\$75526$$75526 if the vehicle meets certain fuel-efficient criteria). Summary of on-road costs On top of the purchase price and any costs associated with a car loan, there are compulsory expenses that need to be paid before a new car can be driven on the road. The first three apply in all situations and must be paid within 1414 days of purchasing a car: • Stamp duty • CTP insurance • Vehicle registration • Dealer delivery charges (if applicable) • Luxury car tax (for 'luxury' vehicles only) Important but non-compulsory on-road costs include: • Additional insurance coverage (i.e. Third Party Property, Comprehensive). ### Running costs for a car In addition to on-road costs, there will be a number of regular expenses related to keeping a car running and well maintained. These could include: • Fuel costs • Regular service • Cost of spare parts (i.e. new tyres) • Road-side assistance • Tolls, parking fees and fines • Washing and cleaning Depreciation, the amount by which a vehicle declines in value over a period of time, may also be considered a 'running cost'. Registration and insurance are often considered as 'running costs', since they are ongoing regular expenses necessary to keep a car 'running' and on the road. #### Practice questions ##### Question 1 The average monthly cost of running a particular model of car has been estimated to be \964.44$$964.44.

1. What is the yearly cost of running this car?

Assume that there are $52$52 weeks in a year, and give your answer correct to the nearest cent.

2. Harry owns this particular model of car and finds that the fortnightly running costs are in fact $\$660.42$$660.42. By how much more does Harry pay in running costs compared to the estimated running costs, per year? Assume that there are 5252 weeks in a year, and give your answer correct to the nearest cent. ##### Question 2 Lisa bought a new car for \22000$$22000. She is told that the running cost of the car will be $291.10$291.10 cents per km. Lisa travels $14000$14000 km per year.

1. What is her yearly running costs in dollars? Give your answer to the nearest cent.

2. What is the monthly running costs for Lisa? Give your answer to the nearest cent.

##### Question 3

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

1. What is his weekly running costs to the nearest cent?

Assume that there are $52$52 weeks in a year.

Cost
Fuel $\$3769$$3769 CTP Insurance and Comprehensive Car Insurance \1393$$1393
Price of Servicing $\$348$$348 for the first service and \369$$369 for the second service.
Cost of Tyres $\$201$$201 each NRMA Gold Membership \150$$150
Tolls and Parking Fees $\$720$$720 Parking Fines \320$$320
2. If the depreciation on Xavier's car amounted to $\$55005500 and is also considered as a running cost, calculate the new weekly running cost of the car to the nearest cent.

### Outcomes

#### MS11-2

represents information in symbolic, graphical and tabular form

#### MS11-5

models relevant financial situations using appropriate tools