Select The Correct Answer.Alisha Has A $15,000 Car Loan With A 6 Percent Interest Rate Compounded Annually. How Much Will She Have Paid At The End Of The Five-year Term?The Formula To Use Is: $\text{total Amount} = P(1 + R)^t$A. $19,500.25 B.

Feb 26, 2025 by ADMIN 244 views

**Calculating the Total Amount Paid on a Car Loan**

Understanding the Problem

Alisha has a car loan of $15,000 with an interest rate of 6 percent compounded annually. The problem asks us to calculate the total amount she will have paid at the end of a five-year term. To solve this problem, we will use the formula for compound interest: $\text{total amount} = P(1 + r)^t$ .

Breaking Down the Formula

Before we dive into the calculation, let's break down the formula:

$P$ represents the principal amount, which is the initial amount borrowed. In this case, it's $15,000.
$r$ represents the interest rate, which is 6 percent in this case.
$t$ represents the time period, which is 5 years in this case.
$(1 + r)^t$ represents the compound interest factor.

Calculating the Compound Interest Factor

To calculate the compound interest factor, we need to raise $(1 + r)$ to the power of $t$ . In this case, we have:

$(1 + r)^t = (1 + 0.06)^5$

Using a calculator, we get:

$(1 + 0.06)^5 ≈ 1.338225$

Calculating the Total Amount

Now that we have the compound interest factor, we can calculate the total amount using the formula:

$\text{total amount} = P(1 + r)^t$

Substituting the values, we get:

$\text{total amount} = 15000(1.338225)$

Using a calculator, we get:

$\text{total amount} ≈ 20071.875$

Rounding the Answer

The problem asks us to choose the correct answer from the options provided. However, the calculated answer is not among the options. We need to round the answer to the nearest cent.

Rounding $20,071.875$ to the nearest cent, we get:

$20,071.88$

Choosing the Correct Answer

Now that we have the calculated answer, we can choose the correct answer from the options provided. However, the calculated answer is not among the options. We need to choose the closest answer.

Comparing the calculated answer with the options, we can see that the closest answer is:

$A. $19,500.25$

However, this is not the correct answer. The correct answer is not among the options provided.

Conclusion

In this problem, we calculated the total amount paid on a car loan using the formula for compound interest. We broke down the formula, calculated the compound interest factor, and calculated the total amount. We then rounded the answer to the nearest cent and chose the correct answer from the options provided. However, the calculated answer is not among the options. We need to choose the closest answer.

Final Answer

The final answer is not among the options provided. However, the closest answer is:

$A. $19,500.25$

Note: This answer is not correct. The correct answer is not among the options provided.

Additional Information

To calculate the total amount paid on a car loan, you can use the formula for compound interest: $\text{total amount} = P(1 + r)^t$ . You can also use a calculator or a spreadsheet to calculate the total amount.

References

[1] Compound Interest Formula. (n.d.). Retrieved from https://www.investopedia.com/terms/c/compoundinterest.asp
[2] Car Loan Calculator. (n.d.). Retrieved from https://www.bankrate.com/calculators/loans/car-loan-calculator.aspx

Calculating the Total Amount Paid on a Car Loan
Breaking Down the Formula
Calculating the Compound Interest Factor
Calculating the Total Amount
Rounding the Answer
Choosing the Correct Answer
Conclusion
Final Answer
Additional Information
References
Table of Contents
Frequently Asked Questions (FAQs) About Calculating the Total Amount Paid on a Car Loan =====================================================================================

Q: What is compound interest?

A: Compound interest is the interest earned on both the principal amount and any accrued interest over time. In the case of a car loan, compound interest is calculated on the outstanding balance of the loan, including any interest that has already been added.

Q: How is compound interest calculated?

A: Compound interest is calculated using the formula: $\text{total amount} = P(1 + r)^t$ , where:

$P$ is the principal amount (the initial amount borrowed)
$r$ is the interest rate (as a decimal)
$t$ is the time period (in years)

Q: What is the principal amount (P)?

A: The principal amount (P) is the initial amount borrowed, which in this case is $15,000.

Q: What is the interest rate (r)?

A: The interest rate (r) is 6 percent, which as a decimal is 0.06.

Q: What is the time period (t)?

A: The time period (t) is 5 years.

Q: How do I calculate the compound interest factor?

A: To calculate the compound interest factor, you need to raise $(1 + r)$ to the power of $t$ . In this case, you would calculate $(1 + 0.06)^5$ .

Q: What is the compound interest factor?

A: The compound interest factor is approximately 1.338225.

Q: How do I calculate the total amount paid on the car loan?

A: To calculate the total amount paid on the car loan, you need to multiply the principal amount (P) by the compound interest factor. In this case, you would calculate $15,000 \times 1.338225$ .

Q: What is the total amount paid on the car loan?

A: The total amount paid on the car loan is approximately $20,071.88.

Q: Why is the calculated answer not among the options provided?

A: The calculated answer is not among the options provided because the options are rounded to the nearest cent, while the calculated answer is not.

Q: What is the closest answer among the options provided?

A: The closest answer among the options provided is $A. $19,500.25$ . However, this is not the correct answer.

Q: What is the correct answer?

A: The correct answer is not among the options provided. However, the closest answer is $A. $19,500.25$ .

Q: How can I calculate the total amount paid on a car loan?

A: You can calculate the total amount paid on a car loan using the formula for compound interest: $\text{total amount} = P(1 + r)^t$ . You can also use a calculator or a spreadsheet to calculate the total amount.

Q: What are some common mistakes to avoid when calculating the total amount paid on a car loan?

A: Some common mistakes to avoid when calculating the total amount paid on a car loan include:

Not using the correct formula for compound interest
Not rounding the interest rate to the correct decimal place
Not using the correct time period
Not calculating the compound interest factor correctly

Q: How can I avoid these mistakes?

A: To avoid these mistakes, you should:

Use the correct formula for compound interest
Round the interest rate to the correct decimal place
Use the correct time period
Calculate the compound interest factor correctly

Q: What are some additional resources that can help me calculate the total amount paid on a car loan?

A: Some additional resources that can help you calculate the total amount paid on a car loan include:

Online calculators, such as the Bankrate Car Loan Calculator
Spreadsheets, such as Microsoft Excel
Financial software, such as Quicken
Online resources, such as Investopedia's Compound Interest Calculator

Q: How can I use these resources to calculate the total amount paid on a car loan?

A: To use these resources to calculate the total amount paid on a car loan, you should:

Enter the principal amount, interest rate, and time period into the calculator or spreadsheet
Use the formula for compound interest to calculate the total amount
Round the answer to the correct decimal place
Use the result to determine the total amount paid on the car loan

Q: What are some common applications of compound interest?

A: Some common applications of compound interest include:

Calculating the total amount paid on a car loan
Calculating the total amount paid on a mortgage
Calculating the total amount paid on a savings account
Calculating the total amount paid on an investment

Q: How can I use compound interest to my advantage?

A: You can use compound interest to your advantage by:

Using a high-yield savings account to earn interest on your savings
Investing in a certificate of deposit (CD) to earn interest on your investment
Using a compound interest calculator to calculate the total amount paid on a car loan or mortgage
Using a financial software to track your finances and calculate compound interest

Q: What are some common misconceptions about compound interest?

A: Some common misconceptions about compound interest include:

Compound interest is only used for loans
Compound interest is only used for savings accounts
Compound interest is only used for investments
Compound interest is only used for short-term financial planning

Q: How can I avoid these misconceptions?

A: To avoid these misconceptions, you should:

Understand the formula for compound interest
Understand how compound interest is used in different financial applications
Use a compound interest calculator or spreadsheet to calculate compound interest
Consult with a financial advisor to determine the best use of compound interest for your financial situation.