Brian opens a savings account that has a 3.72% annual interest rate, compounded weekly.
He deposits $300 into the account each week. How much will be in the account after 10 years?

To solve this problem, we need to account for the weekly deposits and the weekly compounding interest. This involves using the future value of an annuity formula combined with the compound interest formula.

### Given:
- **Interest rate (annual):** 3.72%
- **Compounding period:** Weekly
- **Deposit per week:** $300
- **Time period:** 10 years

### Steps:

1. **Convert the annual interest rate to a weekly interest rate:**

\[
\text{Weekly interest rate} = \frac{3.72\%}{52} = \frac{0.0372}{52} \approx 0.0007154
\]

2. **Calculate the number of weeks in 10 years:**

\[
\text{Total weeks} = 10 \times 52 = 520 \text{ weeks}
\]

3. **Use the future value of an annuity formula:**

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

where:
- $ P $ is the weekly deposit ($300),
- $ r $ is the weekly interest rate ($ 0.0007154 $),
- $ n $ is the total number of weeks (520).

4. **Calculate the future value (FV):**

\[
FV = 300 \times \frac{(1 + 0.0007154)^{520} - 1}{0.0007154}
\]

Let's calculate this.The total amount in the account after 10 years will be approximately **$188,894.22**.

Would you like more details on any part of this calculation, or do you have any other questions?

Here are 5 related questions you might find interesting:

1. How would the final amount change if the interest rate were 5% instead of 3.72%?
2. What would be the effect of making monthly deposits instead of weekly?
3. How much interest is earned over the 10 years?
4. What if Brian started with an initial deposit of $5,000?
5. How long would it take for the account to reach $250,000 with the current weekly deposits?

**Tip:** Regular deposits, combined with compounding interest, can significantly increase savings over time. The more frequently you compound, the greater the benefit.

Learn how to calculate the growth of a savings account with weekly deposits and compound interest. This problem involves an annual interest rate of 3.72% compounded weekly and weekly deposits of $300 over a 10-year period. Discover the total amount accumulated in the account and explore related scenarios. Suitable for advanced high school and college students.

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