Savings accounts and fees | Year 11

01 / LEARN

Understand the idea.

Follow the statement

An account balance records money moving in and out. Credits, such as deposits and interest, increase the balance; debits, such as withdrawals and fees, decrease it. Sort the transactions by direction before combining them with the opening balance.

Interest depends on the supplied timing rule. Money deposited late in a period may earn less interest than money present throughout it. Use the interest actually stated or the specified calculation method instead of assuming a different daily or monthly rule.

A model account statement
Entry	Credit (AUD)	Debit (AUD)
Opening balance	900.00
Deposit	120.00
Withdrawal		75.00
Interest	2.00
Fee		4.00
Closing balance	943.00

Compare net earnings

Compare accounts using the same starting amount and the same time interval. Calculate interest separately from fees, then compare the final balances. A higher interest rate can be outweighed by charges, especially when the opening deposit is small.

For a fixed monthly fee, multiply the charge by the number of months it is collected. Keep those fees distinct from percentage rates: dollars can be subtracted from a balance, but a quoted percentage must first be applied to its stated reference amount.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Worked example

An account opens at AUD 900. It receives AUD 120 and AUD 2 interest, then has a AUD 75 withdrawal and AUD 4 fee. Find the closing balance.

Worked solution

1
Total the credits.
$C = 120 + 2 = AUD 122$
The deposit and interest both add money to the account.
2
Total the debits.
$D = 75 + 4 = AUD 79$
The withdrawal and fee both remove money from the account.
3
Update the opening balance.
$B = 900 + 122 - 79 = AUD 943.00$
Closing balance equals opening balance plus credits minus debits.

Answer

AUD 943.00

EXAMPLE 02

Worked example

For one year, A pays 4% simple interest without fees. B pays 5% simple interest but charges AUD 3 monthly. Compare a AUD 2000 deposit.

Worked solution

1
Calculate Account A's final balance.
$A = 2000 + 2000 (0.04) = AUD 2080$
One year of 4% simple interest adds AUD 80 with no fee.
2
Calculate Account B's interest and yearly fees.
$\begin{aligned} I_{B} & = 2000 (0.05) = 100 \\ F_{B} & = 12 (3) = 36 \end{aligned} (AUD)$
The quoted annual simple-interest amount and twelve monthly fees are separate cash flows.
3
Find B's final balance.
$B = 2000 + 100 - 36 = AUD 2064$
The fees reduce the gross balance after interest is included.
4
Compare the final balances.
$A - B = 2080 - 2064 = AUD 16$
Account A finishes higher despite its lower quoted rate under these supplied rules.

Answer

A finishes AUD 16 higher.

03 / YOUR TURN

Try it yourself.

Check your understanding

Interest is AUD 1.50 and the monthly fee AUD 2. What is the net change?

Show answer & reasoning

AUD 0.50 decrease

Interest is a credit and the fee is a debit, so the net change is $1.50 - 2.00 = - 0.50 (AUD)$ . The balance decreases by AUD 0.50.

Keep practising

6 worksheet questions · 12 marks

Open worksheet Worked solutions

Read the questions online

Opening AUD 650, deposit AUD 80, withdrawal AUD 135. Find closing balance.
2 marks
Find 9 months of AUD 2.50 monthly fees.
2 marks
Opening AUD 420, deposit AUD 150, fee AUD 3, closing AUD 537. Find the withdrawal.
2 marks
AUD 1200 earns 3% simple interest for a year; annual fees are AUD 18. Find net earnings and final balance.
2 marks
Compare AUD 900 at 2% simple interest/no fee with 4% simple interest/AUD 24 yearly fee.
2 marks
Why must a model state when deposits are made?
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Opening AUD 650, deposit AUD 80, withdrawal AUD 135. Find closing balance.
2 marks
$650 + 80 - 135 = 595$ .
AUD 595.00
Find 9 months of AUD 2.50 monthly fees.
2 marks
$9 \times 2.50 = 22.50$ .
AUD 22.50
Opening AUD 420, deposit AUD 150, fee AUD 3, closing AUD 537. Find the withdrawal.
2 marks
$420 + 150 - 3 - W = 537$ .
$W = 30$ .
AUD 30.00
AUD 1200 earns 3% simple interest for a year; annual fees are AUD 18. Find net earnings and final balance.
2 marks
$Interest = 36$ .
$36 - 18 = 18$ .
AUD 18 net; AUD 1218 final
Compare AUD 900 at 2% simple interest/no fee with 4% simple interest/AUD 24 yearly fee.
2 marks
$900 \times 1.02 = 918$ .
$900 \times 1.04 - 24 = 912$ .
First: AUD 918; second: AUD 912. First is higher.
Why must a model state when deposits are made?
2 marks
The time for which each deposit is invested affects its growth.
Different deposit dates can earn different amounts of interest.

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Curriculum reference & lesson scope

SACE Board of South Australia

Stage 1 General Mathematics: investing and borrowing. Supplied educational models cover interest, investment comparisons, shares and credit; they are not recommendations of real products or statements of personal tax liability.

Official curriculum source ↗

In this lesson

Understand the idea.

Follow the statement

Compare net earnings

See the method in action.

Worked example

Total the credits.

Total the debits.

Update the opening balance.

Worked example

Calculate Account A's final balance.

Calculate Account B's interest and yearly fees.

Find B's final balance.

Compare the final balances.

Try it yourself.

Check your understanding

Keep practising