Greta opens a savings account with $2,719.27.  The account offers 1.8% interest compounded quarterly for 29 years.  Calculate the account balance assuming no additional deposits nor withdrawals were made to this account.  *Round your answer to the nearest penny.* 

We can solve this problem using the formula for compound interest:

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

Where:
- $ A $ is the final amount (the account balance).
- $ P $ is the initial principal (the amount initially deposited).
- $ r $ is the annual interest rate (expressed as a decimal).
- $ n $ is the number of times the interest is compounded per year.
- $ t $ is the number of years the money is invested or borrowed.

### Given:
- $ P = 2719.27 $
- $ r = 1.8\% = 0.018 $
- $ n = 4 $ (quarterly compounding)
- $ t = 29 $ years

Now, we plug these values into the formula to calculate the balance.

\[
A = 2719.27 \left(1 + \frac{0.018}{4}\right)^{4 \times 29}
\]

Let's calculate this.The account balance after 29 years, with no additional deposits or withdrawals, will be **$4,577.68**.

Would you like more details or have any questions?

Here are some related questions:
1. How would the balance change if the interest were compounded monthly instead of quarterly?
2. What if the interest rate increased to 2.5%? How would that impact the final balance?
3. How does the number of compounding periods per year affect the growth of savings?
4. How long would it take to double the initial deposit at the current interest rate and compounding frequency?
5. What happens to the balance if the initial deposit was larger, say $5,000, but the interest rate and terms remain the same?

**Tip:** The more frequently interest is compounded, the faster your savings grow, even with the same interest rate!

Greta opens a savings account with $2,719.27. The account offers 1.8% interest compounded quarterly for 29 years. Calculate the account balance assuming no additional deposits nor withdrawals were made to this account. Round your answer to the nearest penny.

Learn how to calculate the compound interest on a $2,719.27 savings account with 1.8% interest compounded quarterly over 29 years. This problem covers key financial mathematics concepts, including the compound interest formula, and is suitable for students in Grades 10-12.

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