Select The Correct Answer.Jenny Borrowed $ \$500 $ For Five Years At 4 Percent Interest, Compounded Annually. What Is The Total Amount She Will Have Paid When She Pays Off The Loan?Total Amount $= P(1+i)^t$A. $ \$608.33 $ B.

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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. It is a key concept in finance and is used to calculate the total amount paid on loans and investments. In this article, we will explore how to calculate the total amount paid on a loan with compound interest.

The Formula for Compound Interest

The formula for compound interest is given by:

A = P(1 + i)^t

Where:

  • A is the total amount paid on the loan
  • P is the principal amount (the initial amount borrowed)
  • i is the interest rate (expressed as a decimal)
  • t is the time period (in years)

Calculating the Total Amount Paid

Let's use the given values to calculate the total amount paid on the loan:

  • P = $500 (the initial amount borrowed)
  • i = 4% = 0.04 (the interest rate)
  • t = 5 years (the time period)

Plugging these values into the formula, we get:

A = 500(1 + 0.04)^5

Using a Calculator to Calculate the Total Amount Paid

Using a calculator to calculate the total amount paid, we get:

A ≈ 608.33

Evaluating the Answer Choices

Now that we have calculated the total amount paid, let's evaluate the answer choices:

A. $608.33 B. $600 C. $620 D. $640

Based on our calculation, the correct answer is:

A. $608.33

Conclusion

In this article, we explored how to calculate the total amount paid on a loan with compound interest. We used the formula A = P(1 + i)^t to calculate the total amount paid, and we evaluated the answer choices to determine the correct answer. We hope this article has provided you with a better understanding of compound interest and how to calculate the total amount paid on a loan.

Additional Examples

Here are a few additional examples to help you practice calculating the total amount paid on a loan with compound interest:

  • Example 1: A person borrows $1,000 for 3 years at 6% interest, compounded annually. What is the total amount they will have paid when they pay off the loan?
  • Example 2: A business borrows $10,000 for 5 years at 8% interest, compounded annually. What is the total amount they will have paid when they pay off the loan?

Solving Example 1

To solve example 1, we can use the formula A = P(1 + i)^t:

A = 1000(1 + 0.06)^3

Using a calculator to calculate the total amount paid, we get:

A ≈ 1105.06

Solving Example 2

To solve example 2, we can use the formula A = P(1 + i)^t:

A = 10000(1 + 0.08)^5

Using a calculator to calculate the total amount paid, we get:

A ≈ 14491.03

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. It is a key concept in finance and is used to calculate the total amount paid on loans and investments.

Q: How is compound interest calculated?

A: Compound interest is calculated using the formula A = P(1 + i)^t, where:

  • A is the total amount paid on the loan
  • P is the principal amount (the initial amount borrowed)
  • i is the interest rate (expressed as a decimal)
  • t is the time period (in years)

Q: What is the difference between simple interest and compound interest?

A: Simple interest is calculated only on the initial principal, while compound interest is calculated on both the initial principal and the accumulated interest from previous periods. This means that compound interest grows faster than simple interest over time.

Q: How does the frequency of compounding affect the total amount paid?

A: The frequency of compounding affects the total amount paid by increasing the number of times interest is calculated and added to the principal. For example, if interest is compounded monthly, the total amount paid will be higher than if interest is compounded annually.

Q: Can compound interest be negative?

A: Yes, compound interest can be negative. This occurs when the interest rate is negative, meaning that the borrower is actually paying the lender to borrow money. This is often seen in situations where the borrower is trying to avoid paying interest on a loan.

Q: How can I calculate compound interest manually?

A: To calculate compound interest manually, you can use the formula A = P(1 + i)^t. You can also use a financial calculator or a spreadsheet to make the calculation easier.

Q: What are some real-world examples of compound interest?

A: Compound interest is used in many real-world situations, including:

  • Savings accounts: Many savings accounts offer compound interest, which means that the interest earned is added to the principal and earns interest in subsequent periods.
  • Loans: Compound interest is used to calculate the total amount paid on loans, including mortgages and car loans.
  • Investments: Compound interest is used to calculate the growth of investments, including stocks and bonds.

Q: How can I minimize the impact of compound interest on my finances?

A: To minimize the impact of compound interest on your finances, you can:

  • Pay off high-interest loans and credit cards as quickly as possible.
  • Consider consolidating debt into a lower-interest loan or credit card.
  • Build an emergency fund to avoid going into debt when unexpected expenses arise.
  • Take advantage of compound interest by saving and investing regularly.

Q: Can I use compound interest to my advantage?

A: Yes, you can use compound interest to your advantage by:

  • Saving and investing regularly to take advantage of compound interest.
  • Using a high-yield savings account or certificate of deposit (CD) to earn compound interest.
  • Considering a tax-advantaged retirement account, such as a 401(k) or IRA, to earn compound interest on your investments.

Conclusion

In this article, we answered some frequently asked questions about compound interest. We covered topics such as how compound interest is calculated, the difference between simple interest and compound interest, and how to minimize the impact of compound interest on your finances. We also discussed how to use compound interest to your advantage by saving and investing regularly.