Suppose you deposit $8800 into a savings account that earns 8.88% interest, compounded monthly.

Fill in the following table, rounding to the nearest cent.

Month	Interest Amount	Balance
1	$
$
2	$
$
3	$
$
4	$
$


We can solve this problem using the compound interest formula:

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

Where:
- $A$ is the amount of money in the account after $t$ years (final balance).
- $P$ is the principal amount (initial deposit) = \$8800.
- $r$ is the annual interest rate = 8.88% = 0.0888.
- $n$ is the number of times the interest is compounded per year = 12 (monthly compounding).
- $t$ is the time in years.

For each month, the formula for the new balance is:
\[
A_{\text{new}} = A_{\text{old}} \left(1 + \frac{r}{n}\right)
\]
The interest earned in each month is the difference between the new and old balances:
\[
\text{Interest} = A_{\text{new}} - A_{\text{old}}
\]

### Step-by-step calculation:

**Month 1:**
\[
A_{\text{new}} = 8800 \times \left(1 + \frac{0.0888}{12}\right) = 8800 \times 1.0074 = 8865.12
\]
Interest earned in Month 1:
\[
\text{Interest} = 8865.12 - 8800 = 65.12
\]

**Month 2:**
\[
A_{\text{new}} = 8865.12 \times 1.0074 = 8930.90
\]
Interest earned in Month 2:
\[
\text{Interest} = 8930.90 - 8865.12 = 65.78
\]

**Month 3:**
\[
A_{\text{new}} = 8930.90 \times 1.0074 = 8997.36
\]
Interest earned in Month 3:
\[
\text{Interest} = 8997.36 - 8930.90 = 66.46
\]

**Month 4:**
\[
A_{\text{new}} = 8997.36 \times 1.0074 = 9064.52
\]
Interest earned in Month 4:
\[
\text{Interest} = 9064.52 - 8997.36 = 67.16
\]

### Filled Table:

| Month | Interest Amount | Balance  |
|-------|-----------------|----------|
| 1     | $65.12          | $8865.12 |
| 2     | $65.78          | $8930.90 |
| 3     | $66.46          | $8997.36 |
| 4     | $67.16          | $9064.52 |

Would you like any further details, or have any questions?

### 5 Related Questions:
1. What happens to the balance if the interest rate changes to 10%?
2. How is the balance affected if compounding is done quarterly instead of monthly?
3. What is the formula for continuous compounding, and how would the balance change if used?
4. How does the time period affect the amount of interest earned?
5. How would different initial deposit amounts change the outcomes?

**Tip**: The more frequent the compounding periods, the faster your balance grows due to the effect of interest on interest!

Suppose you deposit $8800 into a savings account that earns 8.88% interest, compounded monthly. Fill in the following table, rounding to the nearest cent.

Month	Interest Amount	Balance
1	$	$
2	$	$
3	$	$
4	$	$

Learn how to calculate compound interest on a $8800 deposit at 8.88% interest compounded monthly. This problem provides a step-by-step solution with interest earned and balance updates for the first four months. Suitable for Grades 9-12.

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