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.
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 borrowed (initial amount)
- i is the annual interest rate (in decimal form)
- t is the number of years the loan is borrowed for
Calculating the Total Amount Paid
In this example, Jenny borrowed $500 for five years at 4 percent interest, compounded annually. We can use the formula above to calculate the total amount she will have paid when she pays off the loan.
Step 1: Convert the Interest Rate to Decimal Form
The interest rate is given as 4 percent, which is equivalent to 0.04 in decimal form.
Step 2: Plug in the Values into the Formula
We can now plug in the values into the formula:
A = 500(1 + 0.04)^5
Step 3: Calculate the Total Amount Paid
Using a calculator, we can calculate the total amount paid:
A = 500(1.04)^5 A = 500(1.21664) A = 608.32
Rounding the Answer
Rounding the answer to two decimal places, we get:
A = $608.32
Conclusion
In this article, we calculated the total amount paid on a loan with compound interest using the formula A = P(1 + i)^t. We applied this formula to a real-world example, where Jenny borrowed $500 for five years at 4 percent interest, compounded annually. The total amount she will have paid when she pays off the loan is $608.32.
Comparison with the Given Options
The total amount paid on the loan is $608.32, which is closest to option A, $608.33.
Final Answer
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.
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 borrowed, i is the annual interest rate, and t is the number of years the loan is borrowed for.
Q: What is the difference between simple interest and compound interest?
A: Simple interest is calculated only on the initial principal amount, while compound interest is calculated on both the initial principal and the accumulated interest from previous periods.
Q: How does the frequency of compounding affect the total amount paid?
A: The frequency of compounding affects the total amount paid. For example, if the interest is compounded monthly, the total amount paid will be higher than if the 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, or when the principal amount is negative.
Q: How can I calculate compound interest manually?
A: You can calculate compound interest manually using a calculator or by using a formula. However, it's often easier to use a financial calculator or a spreadsheet to calculate compound interest.
Q: What are some real-world examples of compound interest?
A: Compound interest is used in many real-world examples, such as:
- Savings accounts: Many savings accounts offer compound interest, which means that the interest earned is added to the principal amount, and then the interest is calculated on the new principal amount.
- Loans: Compound interest is used to calculate the total amount paid on loans, such as mortgages and car loans.
- Investments: Compound interest is used to calculate the returns on investments, such as stocks and bonds.
Q: How can I avoid paying too much in compound interest?
A: To avoid paying too much in compound interest, you can:
- Pay off your loans quickly
- Make extra payments towards your loans
- Choose a loan with a lower interest rate
- Consider consolidating your loans into a single loan with a lower interest rate
Q: Can I use compound interest to my advantage?
A: Yes, you can use compound interest to your advantage by:
- Investing in a savings account or a certificate of deposit (CD) that offers compound interest
- Using a credit card with a low interest rate and paying off the balance in full each month
- Investing in a retirement account, such as a 401(k) or an IRA, that offers compound interest
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 use compound interest to your advantage. We hope that this article has been helpful in understanding compound interest and how it can be used in real-world examples.