You deposit $3000 in an account earning 2% interest compounded quarterly. How much will you have in the account in 10 years? Round your answer to the nearest cent.

To calculate the amount of money in an account after a certain period when interest is compounded quarterly, we use the compound interest formula:

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

Where:
- $A$ = the amount of money in the account after $t$ years
- $P$ = the initial principal (deposit) = \$3000
- $r$ = annual interest rate (in decimal form) = 2% = 0.02
- $n$ = number of times the interest is compounded per year = 4 (since it's compounded quarterly)
- $t$ = the number of years = 10

Now, let's plug the values into the formula and calculate the amount.

\[
A = 3000 \left(1 + \frac{0.02}{4}\right)^{4 \times 10}
\]

I'll compute that for you.

After 10 years, with an initial deposit of $3000 at an interest rate of 2% compounded quarterly, the amount in the account will be approximately **$3662.38**.

Would you like further clarification, or do you have any other questions?

Here are 5 related questions to expand your understanding:
1. How would the final amount change if the interest was compounded monthly instead of quarterly?
2. What would the final amount be if the interest rate was 3% instead of 2%?
3. How much interest is earned after 10 years in this account?
4. How long would it take for the account to double at the same interest rate and compounding frequency?
5. What is the difference between simple interest and compound interest?

**Tip:** The more frequently interest is compounded, the faster the investment grows!

Learn how to calculate compound interest for an initial deposit of $3000 at a 2% annual interest rate compounded quarterly over 10 years. Using the compound interest formula, this financial mathematics problem provides a step-by-step solution, with the final amount being approximately $3662.38.

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