How Much Would \$200 Invested At 5\% Interest Compounded Monthly Be Worth After 9 Years? Round Your Answer To The Nearest Cent.$A(t)=P\left(1+\frac{r}{n}\right)^{nt}$A. \$363.82 B. \$310.27 C. \$313.37 D. \$207.63

Feb 27, 2025 by ADMIN 222 views

Understanding Compound Interest: A Calculation of $200 Invested at 5% Interest Compounded Monthly

Compound interest is a powerful financial concept that allows your savings to grow exponentially over time. It's a crucial aspect of personal finance, and understanding how it works can help you make informed decisions about your investments. In this article, we'll explore how much $200 invested at 5% interest compounded monthly would be worth after 9 years.

The Formula for Compound Interest

The formula for compound interest is given by:

A(t) = P(1 + r/n)^(nt)

Where:

A(t) is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
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 for, in years.

Calculating the Future Value of $200 Invested at 5% Interest Compounded Monthly

Now that we have the formula, let's plug in the values to calculate the future value of $200 invested at 5% interest compounded monthly after 9 years.

P = $200 (the initial amount of money)
r = 0.05 (5% interest rate in decimal form)
n = 12 (monthly compounding)
t = 9 years

Substituting these values into the formula, we get:

A(9) = 200(1 + 0.05/12)^(12*9)

A(9) = 200(1 + 0.0041667)^(108)

A(9) = 200(1.0041667)^108

Using a calculator to compute the value, we get:

A(9) ≈ $313.37

In conclusion, if you invest $200 at 5% interest compounded monthly, it would be worth approximately $313.37 after 9 years. This calculation demonstrates the power of compound interest and how it can help your savings grow over time.

Comparison with Other Options

Let's compare our result with the other options:

A. $363.82: This is higher than our calculated value, indicating that it's not the correct answer.
B. $310.27: This is close to our calculated value, but not exactly the same.
C. $313.37: This is our calculated value, indicating that it's the correct answer.
D. $207.63: This is lower than our calculated value, indicating that it's not the correct answer.

Final Answer

Based on our calculation, the correct answer is:

C. $313.37

This article has demonstrated how to calculate the future value of an investment using the compound interest formula. By understanding this concept, you can make informed decisions about your investments and watch your savings grow over time.
Compound Interest Q&A: Understanding the Power of Your Investments

In our previous article, we explored how much $200 invested at 5% interest compounded monthly would be worth after 9 years. We calculated the future value of the investment using the compound interest formula and found that it would be worth approximately $313.37. In this article, we'll answer some frequently asked questions about compound interest to help you better understand this powerful financial concept.

Q: What is compound interest?

A: Compound interest is the interest earned on both the principal amount and any accrued interest over time. It's a powerful way to grow your savings, as the interest earned in each period is added to the principal, allowing the interest to earn interest in subsequent periods.

Q: How does compound interest work?

A: Compound interest works by applying the interest rate to the principal amount and any accrued interest over a specified period. The interest is then added to the principal, creating a snowball effect that can lead to significant growth in your savings over time.

Q: What are the key factors that affect compound interest?

A: The key factors that affect compound interest are:

Principal amount: The initial amount of money invested.
Interest rate: The rate at which interest is earned.
Compounding frequency: The number of times interest is compounded per year.
Time: The length of time the money is invested for.

Q: How can I maximize my compound interest?

A: To maximize your compound interest, consider the following strategies:

Start early: The earlier you start investing, the more time your money has to grow.
Invest regularly: Consistently investing a fixed amount of money can help you take advantage of compound interest.
Choose a high-interest rate: Look for investments with high interest rates to maximize your earnings.
Avoid withdrawals: Try to avoid withdrawing money from your investment, as this can reduce the interest earned.

Q: What are some common mistakes to avoid when using compound interest?

A: Some common mistakes to avoid when using compound interest include:

Not understanding the interest rate: Make sure you understand the interest rate and how it affects your investment.
Not considering compounding frequency: Ensure you understand how often interest is compounded and how it affects your investment.
Not starting early: Delaying investment can reduce the impact of compound interest.
Not being patient: Compound interest works over time, so be patient and let your investment grow.

Q: Can I use compound interest to pay off debt?

A: Yes, you can use compound interest to pay off debt. Consider consolidating your debt into a single loan with a lower interest rate and a longer repayment period. This can help you take advantage of compound interest and pay off your debt more efficiently.

Q: How can I calculate compound interest?

A: You can calculate compound interest using the formula:

A(t) = P(1 + r/n)^(nt)

Where:

A(t) is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
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 for, in years.

Compound interest is a powerful financial concept that can help your savings grow over time. By understanding how it works and avoiding common mistakes, you can maximize your earnings and achieve your financial goals. Remember to start early, invest regularly, and be patient to take full advantage of compound interest.