Jill opened a savings account and deposited $100.00 as principal. The account earns 10% interest, compounded quarterly. What is the balance after 10 years?

To calculate the balance after 10 years in a savings account with compounded interest, we use the compound interest formula:

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

Where:
- $A$ is the final amount (balance after interest),
- $P$ is the principal amount (initial deposit),
- $r$ is the annual interest rate (in decimal form),
- $n$ is the number of times interest is compounded per year,
- $t$ is the time in years.

For this problem:
- $P = 100$,
- $r = 10\% = 0.10$,
- $n = 4$ (since interest is compounded quarterly),
- $t = 10$ years.

Now, plug these values into the formula:

\[
A = 100 \left(1 + \frac{0.10}{4}\right)^{4 \times 10}
\]
\[
A = 100 \left(1 + 0.025\right)^{40}
\]
\[
A = 100 \left(1.025\right)^{40}
\]

Now, calculate:

\[
A = 100 \times 2.685
\]
\[
A \approx 268.50
\]

So, the balance after 10 years is approximately **$268.50**.

Would you like a more detailed breakdown, or do you have any other questions?

Here are 5 related questions:
1. How would the final amount change if the interest was compounded monthly instead of quarterly?
2. What would happen to the balance if the interest rate were 5% instead of 10%?
3. How does the frequency of compounding affect the overall growth of an investment?
4. Can you calculate the balance after 5 years with the same interest rate and compounding period?
5. How does the compound interest formula differ from simple interest?

**Tip:** The more frequently interest is compounded, the greater the final balance will be, even if the interest rate stays the same!

Find out how to calculate the balance of a savings account after 10 years with 10% interest compounded quarterly. Using the compound interest formula, this example demonstrates exponential growth and is suitable for students in Grades 9-12.

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