Select The Correct Answer.Walter Took Out A \$6,000 Loan For Six Years. He Is Being Charged 6 Percent Interest, Compounded Annually. Calculate The Total Amount He Will Pay. The Total Amount Is Given By The Formula: \[ \text{Total Amount} =

Understanding Compound Interest

Compound interest is a type of interest that is calculated on both the initial principal and the accumulated interest from previous periods. In other words, it's interest on top of interest. This type of interest is commonly used in loans, investments, and savings accounts. In this article, we will calculate the total amount that Walter will pay on his loan using the formula for compound interest.

The Formula for Compound Interest

The formula for compound interest is given by:

${ \text{Total Amount} = P \left(1 + \frac{r}{n}\right)^{nt} }$

Where:

• P is the principal amount (the initial amount borrowed)
• r is the annual interest rate (in decimal form)
• n is the number of times that interest is compounded per year
• t is the time the money is invested or borrowed for, in years

Applying the Formula to Walter's Loan

In Walter's case, the principal amount (P) is $6,000, the annual interest rate (r) is 6% or 0.06 in decimal form, the interest is compounded annually (n = 1), and the loan is for six years (t = 6).

Plugging these values into the formula, we get:

${ \text{Total Amount} = 6000 \left(1 + \frac{0.06}{1}\right)^{1 \times 6} }$

${ \text{Total Amount} = 6000 \left(1 + 0.06\right)^{6} }$

${ \text{Total Amount} = 6000 \left(1.06\right)^{6} }$

Calculating the Total Amount

To calculate the total amount, we need to calculate the value of (1.06)^6.

Using a calculator or a computer program, we get:

${ \left(1.06\right)^{6} \approx 1.419067 }$

Now, we can multiply this value by the principal amount to get the total amount:

${ \text{Total Amount} = 6000 \times 1.419067 }$

${ \text{Total Amount} \approx 85104.02 }$

Conclusion

Therefore, the total amount that Walter will pay on his loan is approximately $85,104.02. This is the amount that he will pay after six years, assuming that the interest is compounded annually at a rate of 6%.

Example Use Cases

This formula can be used to calculate the total amount of a loan with compound interest in various scenarios, such as:

• Calculating the total amount of a mortgage
• Determining the total amount of a car loan
• Calculating the total amount of a personal loan
• Determining the total amount of a business loan

Tips and Variations

• To calculate the total amount of a loan with compound interest, you can use a financial calculator or a computer program.
• You can also use a formula to calculate the total amount of a loan with compound interest, such as the formula above.
• To calculate the total amount of a loan with compound interest, you need to know the principal amount, the annual interest rate, the number of times that interest is compounded per year, and the time the money is invested or borrowed for.
• You can also use a formula to calculate the total amount of a loan with compound interest, such as the formula above.

Common Mistakes

• Not using the correct formula to calculate the total amount of a loan with compound interest
• Not knowing the principal amount, the annual interest rate, the number of times that interest is compounded per year, and the time the money is invested or borrowed for
• Not using a financial calculator or a computer program to calculate the total amount of a loan with compound interest
• Not checking the calculations for errors

Conclusion

Q: What is compound interest?

A: Compound interest is a type of interest that is calculated on both the initial principal and the accumulated interest from previous periods. In other words, it's interest on top of interest.

Q: How do I calculate the total amount of a loan with compound interest?

A: To calculate the total amount of a loan with compound interest, you can use the formula:

${ \text{Total Amount} = P \left(1 + \frac{r}{n}\right)^{nt} }$

Where:

• P is the principal amount (the initial amount borrowed)
• r is the annual interest rate (in decimal form)
• n is the number of times that interest is compounded per year
• t is the time the money is invested or borrowed for, in years

Q: What is the principal amount (P)?

A: The principal amount (P) is the initial amount borrowed. For example, if you borrow $10,000, the principal amount is $10,000.

Q: What is the annual interest rate (r)?

A: The annual interest rate (r) is the rate at which interest is charged on the loan. For example, if the interest rate is 6%, the annual interest rate is 0.06.

Q: What is the number of times that interest is compounded per year (n)?

A: The number of times that interest is compounded per year (n) is the number of times that interest is calculated and added to the principal amount in a year. For example, if interest is compounded monthly, n = 12.

Q: What is the time the money is invested or borrowed for (t)?

A: The time the money is invested or borrowed for (t) is the number of years that the money is invested or borrowed for. For example, if you borrow money for 5 years, t = 5.

Q: How do I calculate the total amount of a loan with compound interest using a financial calculator or a computer program?

A: To calculate the total amount of a loan with compound interest using a financial calculator or a computer program, you can enter the principal amount, the annual interest rate, the number of times that interest is compounded per year, and the time the money is invested or borrowed for. The calculator or program will then calculate the total amount.

Q: What are some common mistakes to avoid when calculating the total amount of a loan with compound interest?

A: Some common mistakes to avoid when calculating the total amount of a loan with compound interest include:

• Not using the correct formula to calculate the total amount of a loan with compound interest
• Not knowing the principal amount, the annual interest rate, the number of times that interest is compounded per year, and the time the money is invested or borrowed for
• Not using a financial calculator or a computer program to calculate the total amount of a loan with compound interest
• Not checking the calculations for errors

Q: How can I use the total amount of a loan with compound interest to make informed decisions about my finances?

A: You can use the total amount of a loan with compound interest to make informed decisions about your finances by:

• Calculating the total amount of a loan with compound interest to determine the total cost of the loan
• Comparing the total amount of a loan with compound interest to other loan options to determine the best option for your financial situation
• Using the total amount of a loan with compound interest to determine the monthly payment amount
• Using the total amount of a loan with compound interest to determine the total interest paid over the life of the loan

Q: What are some real-world examples of calculating the total amount of a loan with compound interest?

A: Some real-world examples of calculating the total amount of a loan with compound interest include:

• Calculating the total amount of a mortgage to determine the total cost of the loan
• Determining the total amount of a car loan to determine the total cost of the loan
• Calculating the total amount of a personal loan to determine the total cost of the loan
• Determining the total amount of a business loan to determine the total cost of the loan

Q: How can I calculate the total amount of a loan with compound interest using a spreadsheet?

A: You can calculate the total amount of a loan with compound interest using a spreadsheet by:

• Creating a spreadsheet with the principal amount, the annual interest rate, the number of times that interest is compounded per year, and the time the money is invested or borrowed for
• Using a formula to calculate the total amount of a loan with compound interest
• Using a financial function to calculate the total amount of a loan with compound interest
• Checking the calculations for errors