Final answer:
To find the average amount in the account over a period of several months when depositing $5,000 at the beginning of each month and withdrawing money continuously in a linear fashion, you can use the formula for the sum of an arithmetic series.
Step-by-step explanation:
To find the average amount in the account over a period of several months, we need to determine the average decrease in the amount each month. Since the amount in the account decreases linearly, we can use the formula for the sum of an arithmetic series.
The formula for the sum of an arithmetic series is: S = (n/2)(a + l), where S is the sum, n is the number of terms, a is the first term, and l is the last term.
In this case, the first term (a) is $5,000, the last term (l) is $0, and the number of terms (n) is the number of months over the period.
For example, if we consider a period of 12 months, the sum of the amounts in the account for the 12 months is: S = (12/2)(5000 + 0) = $30,000. The average amount in the account is then calculated by dividing the sum by the number of months, which is $30,000 / 12 = $2,500.