 Lesson

Whether we are using them for Sunday drives, commuting to and from work/school or going on extended road trips, cars play a big role in how we get around.

For many people, a car will be their most expensive asset. Yet most cars are not an investment and will depreciate in value over time. In addition, there are ongoing regular expenses to keep a car on the road.

### The cost of purchase

After deciding to purchase a car, there are several initial costs to consider:

• Purchase price: how much does the car cost? Do we need a loan?
• Stamp duty: a state government tax on new and used car purchases
• Insurance: cover provided by an insurance broker if the car is damaged or involved in an accident
• Registration: the cost of registering the car so that it can be driven on Australian roads

In this section we will look at car loans and stamp duty. Insurance and registration will be considered in the next section. ### Car loans

Cars tend to be expensive compared to most other things we buy. Depending on how much we have saved, it may be necessary to take out a loan.

Car loans are typically organised through a financial institution such as a bank or even the car dealership itself.

Remember!

A loan is a contract between the consumer and the lender to borrow an amount of money. The consumer pays back the amount plus interest over the term of the loan, through regular repayments.

Typically, a car loan has monthly repayments over a term from one to five years. Car loan interest rates are usually fixed (a flat rate) over the term of the loan, so each repayment will remain the same.

Loans may also come with additional fees.

Before applying for a loan, we need to know how much we can comfortably afford to pay in loan repayments.

Simple interest is an easy and effective way to model a car loan and determine the amount of each repayment.

#### Worked example

Marie takes out a car loan for $\$14000$$14000 at a fixed simple interest rate of 10.5%10.5% p.a. and a loan period of 55 years. Calculate the following: 1. The total interest paid. 2. The total loan amount paid. 3. The size of repayments if they are made 1. monthly. 2. fortnightly. Solution 1. For a simple interest loan, the total interest paid, II, is found by multiplying the principal, PP, by the interest rate per time period as a decimal, RR, and the number of time periods, NN Interest rate == 10.5%10.5% per year == 0.1050.105 as a decimal.  II == PRNPRN == 14000\times0.105\times514000×0.105×5 == \7350.00$$7350.00
2. The total loan amount is found by adding the principal, $P$P, and the interest, $I$I.
 Total loan amount $=$= $P+I$P+I $=$= $14000+7350$14000+7350 $=$= $\$21350.00$$21350.00 3. The repayment amount is found by dividing the total loan amount by the number of repayment periods. For example, if repayments are made monthly: Number of repayment periods over a 55 year term == 12\times512×5 == 6060 repayments. 1.  Monthly repayment amount == \frac{21350}{12\times5}2135012×5​ == 355.833355.833... == \355.83$$355.83
2.  Fortnightly repayment amount $=$= $\frac{21350}{26\times5}$2135026×5​ $=$= $164.230$164.230... $=$= $\$164.23$$164.23 Online car loan calculators Most financial institutions have a car loan calculator available online. We can enter the details of the loan to calculate the repayment amount and the total interest. Try entering the loan details from example 1 into this online car loan calculator, and compare the results. Keep in mind that loan calculators use a more accurate, but also more complicated, financial model than the simple interest model we have used. While total interest can be significantly different, the simple interest model tends to provide reasonable estimates for the repayment amount. ### Stamp duty Whenever we register a new or used car in our name, we will need to pay a one-off levy or tax to the state government. This is known as stamp duty, and in NSW, it is collected by Roads and Maritime Services on behalf of the Office of State Revenue. The amount of stamp duty paid depends on the value of the vehicle. Usually this is the purchase price, but for some used cars, it is the vehicle's market value (i.e. what the vehicle is actually worth). Rates for stamp duty differ across all Australian states and territories. In NSW, stamp duty is calculated on the value of the vehicle as follows: Value of vehicle Stamp duty payable Up to \45000$$45000 $\$3$$3 for every \100$$100, or part thereof.
Over $\$45000$$45000 \1350$$1350 plus $\$5$$5 for every \100$$100, or part thereof, over $\$45000$$45000 Note: In the table above, stamp duty is calculated on every \100$$100, or part thereof. This means we may have to round the vehicle's value up to the next $\$100$$100, to account for the part thereof (part of \100$$100). This will be the case if either of the last two digits of the vehicle's value are non-zero (see example 2 below).

#### Worked example

Use the NSW stamp duty table above to calculate the stamp duty for a vehicle with a sale price of:

1. $\$700$$700 2. \12630$$12630
3. $\$48000$$48000 4. \62374$$62374

Solution

1. The value of this vehicle is not greater than $\$45000$$45000, therefore:  Stamp duty == \frac{700}{100}\times3700100​×3 == \21$$21
2. In this case $\$12630$$12630 must first be rounded up to \12700$$12700 because $\$30$$30 is part of the next \100$$100. Since the vehicle's value is not greater than $\$45000$$45000 :  Stamp duty == \frac{12700}{100}\times312700100​×3 == \381$$381
3. The value of this vehicle is greater than $\$45000$$45000 by an amount equal to (\48000$$48000 $-$ $\$45000$$45000), therefore:  Stamp duty == 1350+\frac{48000-45000}{100}\times51350+48000−45000100​×5 == 1350+\frac{3000}{100}\times51350+3000100​×5 == 1350+1501350+150 == \1500$$1500
4. In this case $\$62374$$62374 must first be rounded up to \62400$$62400 because $\$74$$74 is part of the next \100$$100. The value of the vehicle is greater than $\$45000$$45000 by an amount equal to (\62400$$62400 $-$ $\$45000$$45000), therefore:  Stamp duty == 1350+\frac{62400-45000}{100}\times51350+62400−45000100​×5 == 1350+\frac{17400}{100}\times51350+17400100​×5 == 1350+8701350+870 == \2220$$2220

Sometimes, NSW vehicle stamp duty is written in terms of percentages:

$3%$3% of the car's value up to $\$45000$$45000, plus 5%5% of the car's value over \45000$$45000.

#### Worked example

You are given that NSW vehicle stamp duty rate is calculated as follows:

"$3%$3% of the car's market value up to $\$45000$$45000 plus 5%5% of the car's market value that exceeds \45000$$45000."

Calculate the stamp duty for a car with a market value of:

1. $\$20000$$20000 2. \60000$$60000

Solution

1. The market value of the car is not greater than $\$45000$$45000, so the stamp duty will be 3%3% of \20000$$20000.

 Stamp duty $=$= $3%$3% of $\$20000$$20000 == 0.03\times200000.03×20000 == \600$$600
2. Here the market value is greater than $\$45000$$45000 so we add 3%3% of \45000$$45000 to $5%$5% of ($\$60000$$60000 - \45000$$45000).

 Stamp duty $=$= $3%$3% of $\$45000$$45000 plus 5%5% of ((\60000$$60000 $-$− $\$45000$$45000)) == 0.03\times45000+0.05\times150000.03×45000+0.05×15000 == 1350+7501350+750 == \2100$$2100

Keep in mind that there are different formulas for calculating stamp duty and the formula will be given in the question. You may not always be asked questions based on NSW calculations, so it is important to read each question carefully and understand exactly how the stamp duty is to be calculated.

#### Practice questions

##### Question 1

You are given that the NSW car stamp duty rate is calculated as:

"3% of the car’s market value up to $\$45000$$45000 PLUS 5% of the car’s market value that exceeds \45000$$45000".

Find the stamp duty levied on a car worth:

1. $16000? 2.$59000?

3. $64000? 4.$97000?

##### Question 2

Vehicle stamp duty is $2%$2% of the purchase price up to $\$30000$$30000 plus 14%14% for every dollar between \30000$$30000 and $\$40000$$40000 plus 5%5% for every dollar over \40000$$40000.

1. Complete the table below:

Vehicle Value $\$0$$0 \30000$$30000 $\$45000$$45000 \60000$$60000 $\$75000$$75000 Stamp Duty (\$$$)$\editable{}600$600$\editable{}\editable{}3750$3750 2. The piecewise graph below shows the stamp duty for cars from$\$0$$0 to \100000$$100000: Loading Graph... Use the graph to find the following, to the nearest$\$100$$100: i. the stamp duty on a \80000$$80000 car$=$=$\editable{}$dollars. ii. The cost of a car if stamp duty is$\$5000$$5000$=$=$\editable{}\$ dollars.

### Outcomes

#### MS11-2

represents information in symbolic, graphical and tabular form

#### MS11-5

models relevant financial situations using appropriate tools