To determine the formula for the balance in the account $n$ years after December 1996, we need to check if the balance follows a geometric sequence.

Step 1: Check the growth factor

From the table:

$\text{Balance in 1997} = 22,000$ $\text{Balance in 1998} = 24,200$ $\text{Balance in 1999} = 26,620$ $\text{Balance in 2000} = 29,282$

Dividing consecutive balances:

$\frac{22,000}{20,000} = 1.1$

$\frac{24,200}{22,000} = 1.1$

$\frac{26,620}{24,200} = 1.1$

$\frac{29,282}{26,620} = 1.1$

Since the balance grows by a consistent factor of 1.1, it follows the geometric sequence formula:

$B_n = B_0 \times r^n$

where:

• $B_0 = 20,000$ (initial balance)
• $r = 1.1$ (growth factor)
• $n$ is the number of years after 1996

Thus, the formula is:

$B_n = 20,000(1.1)^n$

Step 2: Match with the given options

The correct option is:

$\mathbf{A. \ 20,000(1.1)^n}$

Would you like further clarification or additional details?

Related Questions:

1. What is the balance in 2005 using the formula?
2. How long will it take for the balance to exceed $50,000?
3. If the interest rate changed to 8%, what would be the new formula?
4. How does this compare to a linear growth model?
5. Can this be derived using logarithms to find the time needed to reach a certain balance?

Tip: In compound interest, the exponent $n$ represents the number of time periods, ensuring exponential growth.