Question

He average daily balance is the mean of the balance in an account at the end of each day in a month. The following table gives the dates and amounts of the transactions in Elliott's account in June.

Day of June Transaction type Transaction amount (in dollars)
\[1\] Starting balance
\[1223\]
\[10\] Deposit
\[615\]
\[15\] Withdrawal
\[-63\]
\[22\] Withdrawal
\[-120\]
There are
\[30\] days in June.
What is the average daily balance of Elliott's account for the month of June?

Answer 1

The average daily balance of Elliott's account for the month of June is calculated by determining the balance on each day of the month, summing these balances, and then dividing by the number of days in June, which results in an average balance of $1581.90.

Step-by-step explanation:

To calculate the average daily balance of Elliott's account for the month of June, we start by figuring out the balance at the end of each day and then find the mean of these daily balances. The transaction history provided helps to determine the account balance at the end of each day. Here are the steps to calculate the average daily balance:

• From June 1 to June 9, the balance is $1223.
• On June 10, a deposit of $615 is made, so the new balance from June 10 to June 14 is $1223 + $615 = $1838.
• On June 15, a withdrawal of $63 occurs, making the balance from June 15 to June 21 $1838 - $63 = $1775.
• Another withdrawal of $120 happens on June 22, changing the balance from June 22 to June 30 to $1775 - $120 = $1655.
• To find the average, we'll calculate the sum of daily balances and then divide by the total number of days in June.

We calculate the sum of daily balances as follows:

(9 days * $1223) + (5 days * $1838) + (7 days * $1775) + (9 days * $1655) = $10947 + $9190 + $12425 + $14895 = $47457

Now, to find the average:

Average daily balance = Total sum of daily balances ÷ Number of days in June

Average daily balance = $47457 ÷ 30 = $1581.90

Therefore, the average balance for June is $1581.90.