Unit test

Google Classroom

Problem

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$1	Starting balance	$1223$1223
$10$10	Deposit	$615$615
$15$15	Withdrawal	$-63$minus, 63
$22$22	Withdrawal	$-120$minus, 120

There are $30$30 days in June.

What is the average daily balance of Elliott's account for the month of June?

 dollars

Hint #11 / 4

Let's start by figuring out what the new balance is each time the balance changes, and the number of days with that balance. Then we can take the mean of those balances.

Hint #22 / 4

Day of June	Transaction amount (in dollars)	New balance	Days with that balance
$1$1	$1223$1223	$1223$1223	$10-1=9$10, minus, 1, equals, 9
$10$10	$615$615	$1223+615=1838$1223, plus, 615, equals, 1838	$15-10=5$15, minus, 10, equals, 5
$15$15	$-63$minus, 63	$1838+(-63)=1775$1838, plus, left parenthesis, minus, 63, right parenthesis, equals, 1775	$22-15=7$22, minus, 15, equals, 7
$22$22	$-120$minus, 120	$1775+(-120)=1655$1775, plus, left parenthesis, minus, 120, right parenthesis, equals, 1655	$31-22=9$31, minus, 22, equals, 9

[Why subtract from 31?]

Hint #33 / 4

To find the mean, we first sum all of the daily balances. Then we divide by $30$30, since there are $30$30 days in June.

$\begin{aligned}&\phantom{=}\dfrac{1223 \times 9 + 1838 \times 5 + 1775 \times 7 + 1655 \times 9}{30} \\\\ &=\dfrac{11{,}007 + 9190 + 12{,}425 + 14{,}895}{30} \\\\ &=\dfrac{47{,}517}{30} \\\\ &=1583.90 \end{aligned}$

Hint #44 / 4

The average daily balance of Elliott's account for the month of June is $1583.90$1583, point, 90 dollars.