We are given the formula for the balance $B(t)$ after $t$ months:

$B(t) = 400400 \times (0.9894)^t$

We need to find the balance after 6 months, so substitute $t = 6$ into the formula:

$B(6) = 400400 \times (0.9894)^6$

Now, let's calculate $B(6)$:

$B(6) = 400400 \times (0.9894)^6 \approx 400400 \times 0.9362 = 374835.48$

After 6 months, the balance is approximately $374,835.48.

Would you like more details or have any questions? Here are some follow-up questions to expand on this problem:

1. What is the balance after 12 months?
2. How does the interest rate affect the balance after each month?
3. How would the balance change if the interest rate were 20% instead of 22%?
4. How does the formula $B(t) = 400400 \times (0.9894)^t$ reflect the concept of compound interest?
5. What would the minimum payment be after the first month?

Tip: When calculating the balance with compound interest, the power in the formula shows how many periods (months) have passed and how the interest accumulates.