You deposit $300 each month into an account earning 8% interest compounded monthly. How much will you have in the account in 30 years?

$358,105.19
$447,107.83
$442,012.45
$356,190.12

To calculate the future value of a series of regular monthly deposits into an account that earns compound interest, we can use the **Future Value of an Annuity Formula**:

\[
FV = P \times \frac{(1 + r)^n - 1}{r}
\]

Where:
- $FV$ is the future value (the amount of money you will have in the account after 30 years).
- $P$ is the monthly deposit amount ($300).
- $r$ is the monthly interest rate (annual rate divided by 12 months, so $ r = \frac{0.08}{12} = 0.00667 $).
- $n$ is the total number of deposits (30 years × 12 months = 360 months).

Now, let's compute it step by step:

1. **Monthly Interest Rate (r):**
   \[
   r = \frac{0.08}{12} = 0.00667
   \]

2. **Total Number of Deposits (n):**
   \[
   n = 30 \times 12 = 360 \text{ months}
   \]

3. **Apply the Formula:**
   \[
   FV = 300 \times \frac{(1 + 0.00667)^{360} - 1}{0.00667}
   \]
   \[
   FV = 300 \times \frac{(1.00667)^{360} - 1}{0.00667}
   \]

Using a calculator, we find:

\[
(1.00667)^{360} \approx 10.93557
\]
\[
FV = 300 \times \frac{10.93557 - 1}{0.00667} \approx 300 \times 1490.36 = 447,107.83
\]

Thus, the amount you will have in the account after 30 years is **$447,107.83**.

### Correct answer: $447,107.83

Would you like further explanation or details on any step?

### Related Questions:
1. What is the formula for calculating compound interest on a single deposit?
2. How would the result change if the interest was compounded quarterly instead of monthly?
3. What if the interest rate was 6% instead of 8%—how would that affect the future value?
4. How does the duration of the investment impact the total amount earned?
5. What happens if you stop making deposits after 20 years instead of 30?

**Tip:** Small changes in the interest rate or deposit frequency can significantly affect the future value due to the compound effect.

You deposit $300 each month into an account earning 8% interest compounded monthly. How much will you have in the account in 30 years?

Learn how to calculate the future value of monthly deposits into an account earning 8% interest compounded monthly. This example involves a $300 deposit each month over 30 years, using the Future Value of an Annuity formula. The final amount after 30 years is $447,107.83.

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