The principal represent an amount of money deposited in a savings account subject to compound interest at the given rate. Answer part a of this question. Here is your data: Principal: $3000, Rate: 0.7%, compounded: quarterly, time: 2 years. Find how much money will be in the account after 2 years, rounding to nearest cent if needed.

To calculate the amount of money in the account after 2 years with compound interest, we can use the compound interest formula:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ A $ is the amount of money in the account after the time period.
- $ P $ is the principal amount (initial investment).
- $ r $ is the annual interest rate (in decimal form).
- $ n $ is the number of times the interest is compounded per year.
- $ t $ is the time the money is invested for, in years.

Given:
- $ P = 3000 $ dollars
- $ r = 0.7\% = 0.007 $ (as a decimal)
- $ n = 4 $ (since the interest is compounded quarterly)
- $ t = 2 $ years

Now, plug in the values into the formula:

\[
A = 3000 \left(1 + \frac{0.007}{4}\right)^{4 \times 2}
\]

Let's calculate the amount $ A $.The amount of money in the account after 2 years will be **$3,042.26**, rounded to the nearest cent.

Would you like any more details or have any questions about this calculation?

Here are five related questions:
1. What would the amount be if the interest were compounded monthly instead of quarterly?
2. How does increasing the interest rate to 1% affect the final amount?
3. What would the final amount be if the principal were $5,000 instead of $3,000?
4. How much interest is earned after 2 years at the given rate?
5. How does compound interest compare to simple interest over 2 years?

**Tip:** Understanding how different compounding frequencies affect the final amount can help in choosing the best savings or investment options.

Learn how to calculate compound interest with a principal of $3000, an interest rate of 0.7% compounded quarterly over 2 years. Detailed step-by-step solution provided, rounding to the nearest cent. Understand the impact of compounding frequency on savings.

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