Ann Invested $ 9000 \$9000 $9000 In An Account That Earns 4.7 % 4.7\% 4.7% Interest, Compounded Annually. The Formula For Compound Interest Is A ( T ) = P ( 1 + I ) T A(t) = P(1 + I)^t A ( T ) = P ( 1 + I ) T .How Much Did Ann Have In The Account After 5 Years?A. $ 13 , 230.00 \$13,230.00 $13 , 230.00 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 powerful tool for growing investments over time. In this article, we will explore how to calculate compound interest using the formula $A(t) = P(1 + i)^t$, where $A(t)$ is the amount of money accumulated after $t$ years, $P$ is the principal amount (initial investment), $i$ is the annual interest rate (in decimal form), and $t$ is the time the money is invested for in years.

The Formula for Compound Interest

The formula for compound interest is given by:

$$A(t) = P(1 + i)^t$$

Where:

• $A(t)$ is the amount of money accumulated after $t$ years
• $P$ is the principal amount (initial investment)
• $i$ is the annual interest rate (in decimal form)
• $t$ is the time the money is invested for in years

Calculating Ann's Investment After 5 Years

Ann invested $\$9000$ in an account that earns $4.7\%$ interest, compounded annually. We need to calculate how much she will have in the account after 5 years. To do this, we will use the formula for compound interest.

First, we need to convert the annual interest rate from a percentage to a decimal. We can do this by dividing the percentage by 100:

$$i = \frac{4.7}{100} = 0.047$$

Now, we can plug in the values we know into the formula:

$$A(5) = 9000(1 + 0.047)^5$$

To calculate this, we need to raise $1 + 0.047$ to the power of 5:

$$(1 + 0.047)^5 = 1.2475$$

Now, we can multiply this by the principal amount:

$$A(5) = 9000 \times 1.2475 = 11217.5$$

So, after 5 years, Ann will have $\$11,217.50$ in the account.

Conclusion

In this article, we have seen how to calculate compound interest using the formula $A(t) = P(1 + i)^t$. We have also used this formula to calculate how much Ann will have in the account after 5 years, given an initial investment of $\$9000$ and an annual interest rate of $4.7\%$. The result is $\$11,217.50$.

Calculating Compound Interest: A Step-by-Step Guide

If you want to calculate compound interest for yourself, here is a step-by-step guide:

1. Convert the annual interest rate to a decimal: Divide the percentage by 100.
2. Plug in the values into the formula: Use the formula $A(t) = P(1 + i)^t$ and plug in the values you know.
3. Raise $1 + i$ to the power of $t$: Use a calculator or a computer program to raise $1 + i$ to the power of $t$.
4. Multiply the result by the principal amount: Multiply the result by the principal amount to get the final amount.

Common Mistakes to Avoid

When calculating compound interest, there are several common mistakes to avoid:

• Forgetting to convert the annual interest rate to a decimal: Make sure to divide the percentage by 100.
• Rounding errors: Make sure to use a calculator or a computer program to avoid rounding errors.
• Forgetting to multiply the result by the principal amount: Make sure to multiply the result by the principal amount to get the final amount.

Real-World Applications

Compound interest has many real-world applications, including:

• Savings accounts: Many savings accounts earn compound interest, which can help your money grow over time.
• Investments: Compound interest can be used to calculate the return on investment for stocks, bonds, and other investments.
• Loans: Compound interest can be used to calculate the interest on loans, including credit card debt and mortgages.

Conclusion

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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 powerful tool for growing investments over time. In this article, we will answer some frequently asked questions about compound interest.

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 $A(t) = P(1 + i)^t$, where $A(t)$ is the amount of money accumulated after $t$ years, $P$ is the principal amount (initial investment), $i$ is the annual interest rate (in decimal form), and $t$ is the time the money is invested for 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.

Q: How does compound interest work?

A: Compound interest works by adding the interest earned in previous periods to the principal amount, so that the interest earned in the next period is calculated on the new, higher principal amount.

Q: What are the benefits of compound interest?

A: The benefits of compound interest include:

• Higher returns: Compound interest can earn higher returns than simple interest.
• Long-term growth: Compound interest can help your money grow over time.
• Flexibility: Compound interest can be used to calculate the return on investment for stocks, bonds, and other investments.

Q: What are the risks of compound interest?

A: The risks of compound interest include:

• Inflation: Compound interest may not keep pace with inflation.
• Market volatility: Compound interest may be affected by market volatility.
• Interest rate changes: Compound interest may be affected by changes in interest rates.

Q: How can I calculate compound interest?

A: You can calculate compound interest using the formula $A(t) = P(1 + i)^t$, where $A(t)$ is the amount of money accumulated after $t$ years, $P$ is the principal amount (initial investment), $i$ is the annual interest rate (in decimal form), and $t$ is the time the money is invested for in years.

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

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

• Forgetting to convert the annual interest rate to a decimal: Make sure to divide the percentage by 100.
• Rounding errors: Make sure to use a calculator or a computer program to avoid rounding errors.
• Forgetting to multiply the result by the principal amount: Make sure to multiply the result by the principal amount to get the final amount.

Q: How can I use compound interest in real-world applications?

A: Compound interest can be used in a variety of real-world applications, including:

• Savings accounts: Many savings accounts earn compound interest, which can help your money grow over time.
• Investments: Compound interest can be used to calculate the return on investment for stocks, bonds, and other investments.
• Loans: Compound interest can be used to calculate the interest on loans, including credit card debt and mortgages.

Conclusion

In conclusion, compound interest is a powerful tool for growing investments over time. By understanding how compound interest works and how to calculate it, you can make informed decisions about your finances and achieve your long-term goals.