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Cars are essential for navigating modern society, but they can be challenging to afford upfront. As a result, many people explore various financial options, such as credit cards, "quick money" schemes, or personal loans from banks. It is crucial to understand the costs, fees, and benefits associated with these financial options to make wise financial decisions (Financial Literacy Foundation, 2007).
When considering loans for purchasing a car, factors such as interest rates, additional repayments, the loan term, and the initial deposit play a significant role in the decision-making process.
Car Sales offers a wide range of affordable cars in the price range of $5,000 to $10,000. The primary objective of this investigation is to select a car within this price range and determine a reasonable loan option. For this study, we have chosen a 2008 Hyundai Elantra SX Manual priced at $5,290 (Carsales, n.d).
We observed that the loan interests compound on a fortnightly basis to ensure consistency in the data.
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Compounding the interest monthly could lead to irregular repayment schedules due to varying numbers of days in different months.
Let's explore the available finance options:
| Finance Option | Interest Rate | Loan Term | Additional Benefits | Annual Fee |
|---|---|---|---|---|
| West Pac Personal Loan | 12.99% p.a. | 1 to 7 years | No additional benefits | N/A |
| American Express Westpac Altitude Platinum Card | 20.24% p.a. | N/A | Additional benefits on eligible purchases | $49 |
| Nimble Medium Loan | 47.6158% p.a. | 62 days to 22 months | No additional benefits | $400 establishment fee |
Now that we have information about the available finance options, we can proceed with our analysis.
Before selecting a financial option for purchasing the car, we need to establish certain assumptions:
This study involves evaluating the three finance options based on interest rates, loan terms, and repayment schedules to determine the most suitable finance option.
We will use mathematical equations to calculate interest rates for each loan and the compounding frequency. The interest rate for each loan will be calculated using the following equation:
A = A₀(1 + (r/100))^n
Where:
We will also calculate the payments required per period using the annuity formula:
P = r(PV) / [1 - (1 + r)^(-n)]
Where:
We will justify these equations using an Excel template and the PMT function. Additionally, we will cross-check our results with an online bank calculator to ensure the accuracy of our calculations.
Using the Compound Interest Formula, we have calculated the variables and inputted them to estimate the final investment value of each loan after the loan period.
For the Westpac Personal Loan:
We can calculate the final investment value (A) as follows:
A = A₀ * (1 + (r/100))^n
Substituting the values:
A = 5000 * (1 + (12.99/100))^2
A ≈ $6,383.37 (rounded to 2 decimal places)
For the American Express Westpac Altitude Platinum Card:
We can calculate the final investment value (A) as follows:
A = A₀ * (1 + (r/100))^n
Substituting the values:
A = 5000 * (1 + (20.24/100))^2
A ≈ $7,228.83 (rounded to 2 decimal places)
For the Nimble Medium Loan:
We can calculate the final investment value (A) as follows:
A = A₀ * (1 + (r/100))^n
Substituting the values:
A = 5000 * (1 + (47.6158/100))^1.83
A ≈ $10,197.25 (rounded to 2 decimal places)
Total Interest for Westpac Personal Loan: $1,383.37
Total Interest for American Express Westpac Altitude Platinum Card: $2,228.83
Total Interest for Nimble Medium Loan: $5,197.25
After the loan period specified in the loans, the total repayment for the $5,000 loan increased due to the additional interest charged. The added interest was calculated by subtracting the initial loan amount from the final investment value, as indicated in the 'Total Interest' above. This provides a clear comparison between the three finance options to determine the lowest interest rate.
It's important to note that the interest calculations mentioned above do not include the establishment fees or other additional fees.
Let's explore the additional fees associated with each finance option:
| Finance Option | Establishment Fee | Monthly Fee | Annual Fee | Total Fees |
|---|---|---|---|---|
| Westpac Personal Loan | $250 | $12 | $0 | $262 |
| American Express Westpac Altitude Platinum Card | $150 | $0 | $49 | $199 |
| Nimble Medium Loan | $400 | $0 | $0 | $400 |
The fortnightly repayment schedule for each finance option was calculated using the annuity formula, as detailed in Appendix 3.
For the Westpac Personal Loan:
We can calculate the fortnightly repayments (P) as follows:
P = r * (PV) / [1 - (1 + r)^(-n)]
Substituting the values:
P = 0.129926 * 5000 / [1 - (1 + 0.129926)^(-52)]
P ≈ $109.42 (rounded to 2 decimal places)
For the American Express Westpac Altitude Platinum Card:
We can calculate the fortnightly repayments (P) as follows:
P = r * (PV) / [1 - (1 + r)^(-n)]
Substituting the values:
P = 0.202426 * 5000 / [1 - (1 + 0.202426)^(-52)]
P ≈ $117.29 (rounded to 2 decimal places)
For the Nimble Medium Loan:
We can calculate the fortnightly repayments (P) as follows:
P = r * (PV) / [1 - (1 + r)^(-n)]
Substituting the values:
P = 0.47615824 * 5000 / [1 - (1 + 0.47615824)^(-48)]
P ≈ $162.48 (rounded to 2 decimal places)
Using the PMT function in Excel spreadsheets, we verified the constant periodic payments of the loans based on the fixed interest rate and duration. The loan data was input in a standard format for the Westpac Personal Loan. The Excel spreadsheet displayed an Amortization Table, which breaks down the loan into a series of fixed payments to completely pay off the loan balance (Pritchard J, 2019). This verification process was repeated for the other two finance options.
The main objective of this task was to explore three loan options suitable for purchasing a car, considering how well these finance options align with my current financial situation. All three finance options met the assumptions stated: a $5,000 loan, fortnightly repayments, a two-year loan term, and minimum repayments.
The Credit Card option had a higher interest rate compared to the personal loan option, resulting in a total cost of $7,228.83, with $2,228.83 in interest. Although this financial option aligns with the assumptions and is a reasonable loan to consider, it is $845.46 more expensive than the first finance option. The interest-free period transitions to a high-interest rate of 20.24%. The fortnightly repayments of $117.29 can be covered with the assumed $200 income. Additional repayments can be made to shorten the loan term. However, the Credit Card's fee of $150 is unreasonable, as it cannot be paid unless the amount is saved before taking out the loan. This makes it less favorable as it doesn't allow any improvements to eliminate the establishment fee.
The Nimble Medium Loan proved to be unrealistic due to its high interest rate. The total interest charged at the end of the loan reaches $5,197.25, exceeding the initial loan amount. While it was assumed that the loan would be taken over a two-year period, Nimble does not offer terms longer than 22 months. With a $200 fortnightly income, it is feasible to repay the medium loan bi-weekly. However, the establishment fee of $400 is unattainable unless more money is saved before starting the loan. The overall cost of the loan is expensive, making it an unreasonable finance option for purchasing the car.
The Westpac Personal Loan totaled $6,383.37, not including monthly fees and establishment fees. It aligns with the assumption of a $5,000 loan amount. The second assumption of earning a $200 fortnightly income is suitable for covering the $109.42 fortnightly repayments required to pay off the loan. Its flexibility allows for additional repayments to be made to shorten the loan term. However, the establishment fee and additional monthly service fees amount to $538. The assumption that $290 was saved before starting the loan and put towards the car payment means there are insufficient funds in my account to cover the $250 establishment fee.
Further calculations, detailed in Appendix 5, were conducted to explore the effects of shortening the loan term to one year to reduce the interest. However, this proved to be an unrealistic possibility, as it would require $205.55 fortnightly repayments, exceeding my financial capability. As shown in Appendix 6, if the loan term was reduced by 6 months, $141.42 fortnightly payments would be required. This would reduce the cost of the loan by $378.13 and align with the financial assumptions. Based on the initial assumptions and calculations, although the Westpac personal loan offers cheaper repayments, the establishment fee is not feasible with my current financial situation. Therefore, the credit card loan is the best option based on fee prices. However, this is not the ideal solution, as further improvements could be made to find a cheaper solution. Based on the Westpac conditions, the establishment fee can be waived if the loan is taken out before the 30th of September. Therefore, applying for a loan on the 9th of September, as opposed to January 1st, would eliminate the establishment fee, making the personal loan a viable option. This would reduce the total fees to $288, only accounting for the monthly fees.
The Amortization Table provided an effective mathematical model for organizing loan repayments. This model allowed consistent calculations to be applied to all three finance options, facilitating clear comparisons. Additionally, the use of the annuity formula helped maintain precision by representing interest rates as fractions rather than relying on excessive decimal places.
However, the Mathematical Model had some limitations. Inconsistent loan terms across the three options resulted in data discrepancies. While the Westpac personal loan and credit card could be taken over two years, the Nimble Quick Money Scheme had a maximum term of 22 months. Additionally, rounding to two decimal places in interest, annuity, and payment calculations introduced minor inaccuracies. For example, rounding 10,197.25101 to $10,197.25 for the Nimble loan. Furthermore, the PMT function, while useful for calculating repayments, did not incorporate establishment and additional fees, which were calculated separately.
After a comprehensive evaluation of the three finance options, the improved Westpac Personal Loan emerges as the most rational choice for purchasing the car. The credit card option proves expensive compared to the personal loan and lacks a price limitation, potentially leading to unaffordable borrowings and increased repayments. The Nimble Medium Loan, with its high interest rate and excessive fees, does not align with the outlined criteria.
The calculations for interest rates and annuity clearly demonstrate that the Westpac Personal Loan offers the most cost-effective option. It features a low-interest rate, affordable fortnightly repayments, and an overall reasonable cost, making it the ideal choice for financing the car purchase.
Comparing Car Loan Options for Wise Financing: A Mathematical Analysis. (2024, Jan 18). Retrieved from https://studymoose.com/document/comparing-car-loan-options-for-wise-financing-a-mathematical-analysis
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