Anger needs $300000 in 5 years for a down payment for a house. They are planning to deposit a regular amount every 2 weeks into an account that pays 6.5%, compounded bi-weekly. How much do they need to deposit every 2 weeks to reach their goal?

To find out how much Anger needs to deposit every 2 weeks, we can use the formula for the future value of an ordinary annuity, which accounts for regular deposits, interest rate, and the number of periods.

The formula for the future value of an ordinary annuity is:

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

Where:
- $ FV $ is the future value (the amount Anger wants to have in 5 years, $300,000).
- $ P $ is the amount deposited every period (this is what we need to find).
- $ r $ is the interest rate per period.
- $ n $ is the total number of periods.

### Given:
- Future Value, $ FV = 300,000 $ dollars.
- Annual interest rate, $ 6.5\% $.
- Compounded bi-weekly (every 2 weeks).
- Time period = 5 years.

### Steps to solve:

1. **Calculate the number of periods (n):**

   Since the deposits are made every 2 weeks and there are 52 weeks in a year:

   \[
   n = 5 \times \frac{52}{2} = 5 \times 26 = 130 \text{ periods}
   \]

2. **Determine the interest rate per period (r):**

   The annual interest rate is 6.5%, but it is compounded bi-weekly, so we divide by the number of bi-weekly periods in a year:

   \[
   r = \frac{6.5\%}{26} = \frac{0.065}{26} \approx 0.0025
   \]

3. **Plug the values into the annuity formula and solve for $ P $:**

   \[
   300,000 = P \times \frac{(1 + 0.0025)^{130} - 1}{0.0025}
   \]

Let's calculate $ P $. 

Anger needs to deposit approximately **$1,955.83** every 2 weeks to reach their goal of $300,000 in 5 years, given a 6.5% interest rate compounded bi-weekly.

Would you like more details or have any questions? Here are some related questions:

1. How would the required deposit change if the interest rate were higher or lower?
2. What would be the total amount of interest earned over the 5 years?
3. How does the frequency of compounding affect the final amount?
4. What if Anger could only save $1,500 bi-weekly? How much would they have in 5 years?
5. How does this calculation change if the deposits are made monthly instead of bi-weekly?

**Tip:** When saving for large financial goals, it's crucial to account for the interest rate's effect over time, as even small

Learn how to calculate bi-weekly deposits required to save $300,000 for a house down payment in 5 years, compounded bi-weekly at 6.5% interest rate. Detailed solution using the future value of an ordinary annuity formula.

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