Answered

The 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 :

sqdancefan

Answer:

  1583.90 dollars

Step-by-step explanation:

You want the average daily balance of Elliott's account in June with transactions ...

  • day 1: 1223 (starting balance)
  • day 10: 615 deposit
  • day 15: 63 withdrawal
  • day 22: 120 withdrawal

Average daily balance

The most straightforward way to compute the average daily balance might be to list the balances at the end of each day, then average those values. This works well for a spreadsheet, but is a bit tedious for hand calculation.

It is easier to list the balance and the number of days for which it applies. Adding the products of these numbers, and dividing by the total number of days will give the same result.

Balances and Days

Elliott's account had these balances for these days:

  1223 for (10 -1) = 9 days

  (1223 +615) = 1838 for (15 -10) = 5 days

  (1838 -63) = 1775 for (22 -15) = 7 days

  (1775 -120) = 1655 for (31 -22) = 9 days

Then the average daily balance is ...

  [tex]\dfrac{1223(9) +1838(5)+1775(7)+1655(9)}{9+5+7+9}=\dfrac{47517}{30}=1583.90[/tex]

Elliott's average daily balance in June was 1583.90 dollars.

__

Additional comment

Equivalently, one can multiply the value of each transaction by the number of days to the end of the month, and divide the sum of those products by the number of days in the month. This approach can save a bit of arithmetic.

Other Questions