Question

Let y(t) represent your bank account balance, in dollars, after t years, starting with $30,000 in the account. Each year, the account earns 5% interest, and you withdraw _______.

Answer 1

Let y(t) = $30,000 * (1.05)^t represent the bank account balance after t years. Each year, the account earns 5% interest, and you withdraw $0 annually.

Step-by-step explanation:

In this scenario, the bank account balance, y(t), is modeled by the exponential growth formula y(t) = P * (1 + r)^t, where P is the initial principal, r is the interest rate per period, and t is the time in years. In this case, P is $30,000, r is 5% (or 0.05), and t represents the number of years.

The formula for the bank account balance over time becomes y(t) = $30,000 * (1.05)^t. This formula accounts for the initial amount of $30,000 and the 5% interest earned each year. Notably, there is no withdrawal term in the formula (i.e., no subtracting term) as the question specifies that no money is withdrawn annually.

The absence of a withdrawal term implies that, despite the annual interest, you do not withdraw any money from the account each year. Therefore, your bank account balance only grows due to the 5% interest compounded annually. This decision results in a continually increasing balance without any reduction, and the direct answer is that you withdraw $0 annually.