Suppose you owe ​$400400 on your credit card and you decide to make no new purchases and to make the minimum monthly payment on the account. Assuming that the interest rate on your card is 22​% per month on the unpaid balance and that the minimum payment is 33​% of the total​ (balance plus​ interest), your balance after t months is given by ​B(t)equals=400400​(0.98949894 Superscript t​). Find your balance at each of the given times. Complete parts​ (a) through​ (e) below.
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Part 1
​(a) six months
After six​ months, the balance is ​$enter your response here.
​(Round to the nearest cent as​ needed.)

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.

Suppose you owe $400400 on your credit card and you decide to make no new purchases and to make the minimum monthly payment on the account. Assuming that the interest rate on your card is 22​% per month on the unpaid balance and that the minimum payment is 33​% of the total​ (balance plus​ interest), your balance after t months is given by ​B(t) = 400400​(0.9894^t​). Find your balance at each of the given times. Complete parts​ (a) through​ (e) below.

Calculate your credit card balance over time using the formula B(t) = 400400 * (0.9894^t). This problem explores the impact of a 22% monthly interest rate and minimum payments. Learn how to find the balance after 6 months, and how interest affects your total over time. Suitable for high school students.

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