Credit Cards

Financial Maths, STD2 EQ-Bank 32

Yasmin is planning to purchase a Newcastle Knights corporate box for $5000. She intends to repay the entire amount 90 days after making the purchase.

She is comparing two credit options.

Credit card: compound interest charged daily at 18% per annum, with a 30-day interest-free period from the date of purchase.
Personal loan: simple interest charged at 9.5% per annum.

Determine which option Yasmin should choose, showing calculations to support your answer. (4 marks)

--- 10 WORK AREA LINES (style=lined) ---

Show Answers Only

$\text{Credit card (daily compound interest):}$

$\text{Days accruing interest}\ =90-30=60$

$\text{Amount owing}$	$= 5000\left(1+\dfrac{0.18}{365}\right)^{60}$
	$= 5150.118\ldots$
	$= \$5150.12\ \text{(nearest cent)}$

$\text{Interest} = 5150.12-5000 = \$150.12$

$\text{Personal loan (simple interest):}$

$I = Prn$	$=5000 \times 0.095 \times \dfrac{90}{365}$
	$= 117.123\ldots$
	$= \$117.12\ \text{(nearest cent)}$

$\therefore\ \text{Since \$117.12 < \$150.12, Yasmin should choose the personal loan.}$

Show Worked Solution

$\text{Days accruing interest}\ =90-30=60$

$\text{Credit card (daily compound interest):}$

$\text{Amount owing}$	$= 5000\left(1+\dfrac{0.18}{365}\right)^{60}$
	$= 5150.118\ldots$
	$= \$5150.12\ \text{(nearest cent)}$

$\text{Interest} = 5150.12-5000 = \$150.12$

$\text{Personal loan (simple interest):}$

$I = Prn$	$=5000 \times 0.095 \times \dfrac{90}{365}$
	$= 117.123\ldots$
	$= \$117.12\ \text{(nearest cent)}$

$\therefore\ \text{Since \$117.12 < \$150.12, Yasmin should choose the personal loan.}$

Financial Maths, STD2 EQ-Bank 28

Sam needs to borrow $3000 and plans to repay it in full after 30 days. He is comparing two options.

Credit card: compound interest charged daily at 19.9% per annum, with no interest-free period.
Personal loan: simple interest charged at 11.5% per annum.

Calculate the interest Sam would be charged on the credit card over the 30 days. (2 marks)

--- 4 WORK AREA LINES (style=lined) ---
How much does Sam save by choosing the personal loan. (2 marks)

--- 5 WORK AREA LINES (style=lined) ---

Show Answers Only

a. $\$49.46$

b. $\text{Saving =}\ \$21.10$

Show Worked Solution

a. $\text{Daily interest rate} = \dfrac{0.199}{365}$

$\text{Amount owing}$	$= 3000\left(1+\dfrac{0.199}{365}\right)^{30}$
	$= 3049.458\ldots$
	$= \$3049.46\ \text{(nearest cent)}$

$\therefore \text{Interest} = 3049.46-3000 = \$49.46$

b. $\text{Personal loan (simple interest):}$

$I = Prn$	$=3000 \times 0.115 \times \dfrac{30}{365}$
	$= 28.356\ldots$
	$= \$28.36\ \text{(nearest cent)}$

$\therefore \text{Saving} = 49.46-28.36 = \$21.10$

Financial Maths, STD2 EQ-Bank 26

A credit card has an interest-free period of 55 days from and including the date of purchase. Interest is charged on purchases, compounding daily at a rate of 16.8% per annum. Interest is charged from the day following the interest-free period.

Furniture was purchased for $1200 using this credit card. Full payment was made on the 78th day after the date of purchase. There were no other purchases on this credit card.

For how many days is interest charged on the purchase? Give your answer to the nearest cent. (1 mark)

--- 2 WORK AREA LINES (style=lined) ---
Calculate the total interest charged when the account was paid in full. (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

Show Answers Only

a. $23 \text{ days}$

b. $\$12.77$

Show Worked Solution

a. $\text{Interest is charged after the 55-day interest-free period.}$

$\text{Days charged} = 78-55 = 23 \text{ days}$

b. $\text{Daily interest rate} = \dfrac{0.168}{365}$

$\text{Amount owing} $	$= 1200\left(1+\dfrac{0.168}{365}\right)^{23}$
	$= 1212.768\ldots$
	$= \$1212.77\ \text{(nearest cent)}$

$\therefore\ \text{Interest} = 1212.77-1200 = \$12.77$

Financial Maths, STD2 EQ-Bank 27

A credit card account has no interest-free period. Compound interest is calculated daily at a rate of 18.5% per annum and charged to the account up to and including the statement date.

A single purchase of $1500 was made and interest accrued on the purchase for 28 days, including the statement date. There were no other purchases on the account.

Calculate the closing balance on the statement date. (2 marks)

--- 5 WORK AREA LINES (style=lined) ---
The minimum payment is calculated as $30 or 3% of the closing balance, whichever is greater. Calculate the minimum payment due. (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

Show Answers Only

a. $\$1521.43$

b. $\$45.64$

Show Worked Solution

a. $\text{Daily interest rate} = \dfrac{0.185}{365}$

$\text{Closing balance}$	$= 1500\left(1+\dfrac{0.185}{365}\right)^{28}$
	$= 1521.433\ldots$
	$= \$1521.43$

b. $3\% \text{ of closing balance} = 0.03 \times 1521.43= \$45.64$

$\text{Since } \$45.64 > \$30, \text{ the minimum payment due is } \$45.64.$

Financial Maths, STD2 EQ-Bank 5 MC

A credit card is an example of a reducing balance loan.

Which statement best explains why this is the case?

Interest is charged at a fixed amount each month, regardless of the balance owing.
Interest is charged on the outstanding balance, which decreases as repayments are made.
The interest rate reduces each month as the balance is repaid.
A fixed portion of the amount borrowed is repaid each month, with no interest charged.

Show Answers Only

$B$

Show Worked Solution

B is correct: Like any reducing balance loan, interest is charged on the outstanding balance, which decreases as repayments are made.

Other options:

A is incorrect: the interest is not a fixed amount; it depends on the balance.
C is incorrect: it is the balance that reduces, not the interest rate, which stays fixed.
D is incorrect: interest is charged on a credit card, and repayments are not a fixed portion of the principal.

$\Rightarrow B$

Financial Maths, STD1 EQ-Bank 4 MC

A credit card has the following fees:

annual fee of $\$90$
late payment fee of $\$20$ each time a payment is late
cash advance fee of $\$5$ each time a cash advance is made

During one year, the cardholder made 2 late payments and 3 cash advances.

What is the total amount of fees charged for the year?

$\$55$
$\$90$
$\$130$
$\$145$

Show Answers Only

$D$

Show Worked Solution

$\text{Annual fee} = \$90$

$\text{Late payment fees} = 2 \times \$20 = \$40$

$\text{Cash advance fees} = 3 \times \$5 = \$15$

$\text{Total fees} = 90+40+15 = \$145$

$\Rightarrow D$

Financial Maths, STD1 F3 2025 HSC 21

A credit card has an interest-free period of 45 days from and including the date of purchase. Interest is charged on purchases made, compounding daily at a rate of 13.74% per annum, from and including the day following the interest-free period.

Concert tickets were purchased for a total of $392 using this credit card.

Full payment was made on the 68th day from the date of purchase. There were no other purchases on this credit card.

What was the total interest charged when the account was paid in full? (3 marks)

--- 7 WORK AREA LINES (style=lined) ---

Show Answers Only

$\text{Interest charged}\ =\$ 3.41$

Show Worked Solution

$\text{Day 1-45: no interest is charged}$

$\text{Day 46-68: interest charged (23 days)}$

$\text{Daily interest rate}=\dfrac{13.74}{365} \%=\dfrac{13.74}{365 \times 100}$

$\text{Amount owing}=392\left(1+\dfrac{13.74}{365 \times 100}\right)^{23}=\$ 395.41$

$\text{Interest charged}=395.41-392=\$ 3.41$

♦♦ Mean mark 33%.

Financial Maths, STD1 F3 2024 HSC 26

Bobby has a credit card that has no interest-free period.

Interest is charged at 0.07% per day, compounding daily, on the outstanding balance.

How much interest is Bobby charged on an outstanding balance of $600 for 30 days? (3 marks)

--- 8 WORK AREA LINES (style=lined) ---

Show Answers Only

$$12.73\ \text{(nearest cent)}$

Show Worked Solution

$PV=600,\ \ \ r=\dfrac{0.07}{100},\ \ \ n=30$

$FV$	$=PV(1+r)^n$
	$=600\Big(1+\dfrac{0.07}{100}\Big)^{30}$
	$=612.728\dots$

$\therefore\ \text{Interest}\ =$612.73-$600=$12.73\ \text{(nearest cent)}$

♦♦♦ Mean mark 27%.

Financial Maths, STD1 F3 2023 HSC 5 MC

The following is part of a credit card statement for August, with some figures missing.

What are the amounts for 'New charges' and 'Closing balance'?

	$\text{New charges}$	$\text{Closing balance}$
A.	$$85.97$	$$468.43$
B.	$$85.97$	$$596.66$
C.	$$90.61$	$$473.07$
D.	$$90.61$	$$477.71$

Show Answers Only

$D$

Show Worked Solution

$\text{New Charges}=85.97+4.64=$90.61$

$\text{Closing Balance}=506.05+90.61-(18.95+100)=$477.71$

$\Rightarrow D$

Financial Maths, STD1 F3 2022 HSC 26

A family uses a credit card to purchase a lounge during the month of November.

The credit card has no interest-free period. Interest is charged at a rate of 21% per annum, compounded daily, from and including the date of purchase to the last day of the month.

The table shows the only purchases and payments on the credit card during the month of November.

What is the closing balance owing on the credit card on 30 November? (3 marks)

Show Answers Only

`$5569.34`

Show Worked Solution

`text{Interest calculation:}`

`text{Days = 16 (15th November – 30th November)}`

`text{Daily interest rate} = 21/365 %`

`text{Card Balance (30 Nov)}`	`=7500(1+21/(365 xx100))^16-2000`
	`=7569.339\ …-2000`
	`=$5569.34`

♦♦ Mean mark 23%.

Financial Maths, STD1 F3 2021 HSC 30

Blake opens a new credit card account on 1 May. He uses it, for the first time, on 4 May to buy concert tickets for $850.

He makes no further purchases or repayments during the month of May.

A statement for the credit card is issued on the last day of each month.

The statement for May shows that interest is charged at 19.75% per annum, compounding daily, from 20 May (included) until 31 May (included).

What is the compound interest shown on the statement issued on 31 May? (3 marks)

--- 5 WORK AREA LINES (style=lined) ---
The minimum payment is calculated as 3% of the closing balance on 31 May. Calculate the minimum payment. (1 mark)

--- 1 WORK AREA LINES (style=lined) ---

Show Answers Only

a. `$5.54`

b. `$25.67`

Show Worked Solution

a. `text(Daily interest rate) = 19.75/365 = 0.05411text(%) = 0.0005411`

`text(Days incurring interest = 12)`

♦♦♦ Mean mark part (a) 14%.

`text{Card balance (31 May)}`	`= PV(1+r)^n`
	`= 850 (1 + 0.0005411)^12= $855.54`

`:.\ text(Interest)= 855.54-850= $5.54`

♦♦♦ Mean mark part (b) 15%.

`text(Minimum payment)`

`= 855.54 xx 0.03= $25.67“

Financial Maths, STD1 F3 2019 HSC 32

Ashley has a credit card with the following conditions:

There is no interest-free period.
Interest is charged at the end of each month at 18.25% per annum, compounding daily, from the purchase date (included) to the last day of the month (included).

Ashley's credit card statement for April is shown, with some figures missing.

The minimum payment is calculated as 2% of the closing balance on 30 April.

Calculate the minimum payment. (3 marks)

--- 6 WORK AREA LINES (style=lined) ---

Show Answers Only

`$74.41`

Show Worked Solution

`text(Daily interest)= 18.25/(100 xx 365)= 0.0005`

♦♦♦ Mean mark 12%.

`text(Closing balance)= 3700(1.0005)^11= 3720.40`

`:.\ text(Minimum payment)`	`= 3720.40 xx 0.02`
	`= $74.408…`
	`= $74.41\ \ text{(nearest cent)}`

Financial Maths, STD2 F4 2018* HSC 28d

Yanika opens a new credit card account, with interest and fees as shown.

Interest

- Compound interest calculated daily at the rate 12.41% p.a.
- No interest-free period

Fees

- $0 for online repayments
- $3 for repayments in cash (fee added to balance immediately after repayment)

Yanika makes a single purchase of $849 with the credit card.

Show that the balance owing on the credit card 24 days after making the purchase is $855.95. (2 marks)

--- 4 WORK AREA LINES (style=lined) ---
Yanika makes her first repayment 24 days after making the purchase. She makes a cash repayment of $450.

What is the balance owing on the credit card immediately after her repayment is made and the repayment fee has been charged? (1 mark)

--- 1 WORK AREA LINES (style=lined) ---

Show Answers Only

i. `text(See Worked Solutions)`

ii. `$408.95`

Show Worked Solution

i. `text(Days of interest)\ (n) = 24`

♦ Mean mark part (i) 48%, part (ii) 49%.

`text(Daily interest rate)\ (r) = 0.1241/365 = 0.00034`

`text(Balance Owing)\ (FV)`	`= PV(1+r)^n`
	`= 849(1.00034)^24`
	`= 855.954…=$855.95\ \ text{(nearest cent)}`

ii. `text(Balance owing)= 855.95-450 + 3= $408.95`

Financial Maths, STD2 F4 2016 HSC 17 MC

Ariana is charged compound interest at the rate of 0.036% per day on outstanding credit card balances. She has $780 outstanding for 24 days.

How much compound interest is she charged?

$6.74
$6.77
$786.74
$786.77

Show Answers Only

`B`

Show Worked Solution

`text(Total owing)`

♦ Mean mark 38%.
COMMENT: Credit card problems consistently produce sub-50% mean marks. Important review area.

`= P(1+r)^n`

`= 780(1 + 0.036/100)^24= 786.77`

`:.\ text(Interest charged)= 786.77-780= $6.77`

`=> B`

Financial Maths, STD2 F4 2015* HSC 29a

On 20 August, tickets were purchased for $425 using a credit card. No other purchases were made using this card in August. Compound interest was charged daily at a rate of 18.25% per annum. There was no interest‑free period. The period for which interest was charged included the date of purchase and the date of payment.

What amount was paid when the account was paid in full on 31 August? (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

Show Answers Only

`$427.56`

Show Worked Solution

`text(Days of interest)\ = 12`

♦ Mean mark 35%.

`text(Daily interest rate)\ = 0.1825/365=0.0005`

`text(Total Paid)\ (FV)`	`= PV(1+r)^n`
	`= 425(1.0005)^12`
	`= 427.557…=$427.56\ \ text{(nearest cent)}`

Financial Maths, STD2 F4 2006* HSC 25b

In June, Ms Bigspender received a statement for her credit card account.

The account has no interest-free period. Compound interest is calculated daily and charged to her account on the statement date.

For how many days is she charged interest on her purchase? (1 mark)

--- 2 WORK AREA LINES (style=lined) ---
Calculate the interest charged to her account. (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

Show Answers Only

a. `29`

b. `$8.98`

Show Worked Solution

a. `text(# Days interest charged)`

`=\ text{9 (in May) + 20 (in June)}= 29`

b. `text(Daily interest rate)\ (r) = 0.0498/100=0.000498`

`text(Closing Balance)\ (FV)`	`= PV(1+r)^n`
	`= 617.72(1.000498)^29= $626.703`

`:.\ text(Interest charged)=626.70-617.72=$8.98`

Financial Maths, STD2 F4 2004 HSC 19 MC

Kerry has a credit card. She is charged 0.05% compound interest per day on outstanding balances.

How much interest is Kerry charged on an amount of $250, which is outstanding on her credit card for 30 days?

$3.75
$3.78
$253.75
$253.78

Show Answers Only

`B`

Show Worked Solution

`text(Using)\ A = P(1 + r)^n`

`A`	`= 250 (1 + 0.0005)^30`
	`= 250 (1.0151…)= 253.777…`

`:.\ text(Amount of interest charged)`

`= 253.777…-250= $3.777…`

`=> B`

Financial Maths, STD2 F4 2010* HSC 22 MC

In July, Ms Alott received a statement for her credit card account. The account has no interest free period. Compound interest is calculated daily and charged to her account on the statement date.

What is the minimum payment due on this account?

$23.56
$25.00
$86.08
$87.20

Show Answers Only

`D`

Show Worked Solution

`text(Days of interest)\ (n) =2+23=25`

♦♦♦ Mean mark 20%. Lowest scoring MC question in the 2010 exam.

`text(Daily interest rate)\ (r) = 0.0521/100 = 0.000521`

`text(Closing Balance)\ (FV)`	`=PV(1+r)^n`
	`=1721.50 (1.000521)^25=$1744.06`

`text(5% of closing balance)=5/100xx1744.06=87.20\ text{(nearest cent)}`

`text(S)text(ince)\ $87.20>$25\ , text(minimum payment)=$87.20`

`=>D`

Financial Maths, STD2 F4 2011* HSC 10 MC

A television was purchased for $2100 on 12 April 2011 using a credit card. Compound interest was charged daily at a rate basis 19.71% per annum for purchases on this credit card. There were no other purchases on this credit card account.

There was no interest-free period. The period for which interest was charged included the date of purchase and the date of payment.

What amount was paid when the account was paid in full on 20 May 2011?

$2143.09
$2143.53
$2144.23
$2144.68

Show Answers Only

`D`

Show Worked Solution

♦♦ Mean mark 32%
COMMENT: Make sure you know how to adjust an annual rate to a daily rate, as shown in the Worked Solutions.

`text(Days for interest)\ (n) =19+20=39`

`text(Daily interest rate)\ (r) = 0.1971/365 = 0.00054`

`text{Total paid}\ (FV)`	`= PV (1+r)^n`
	`=2100(1.00054)^39=$2144.68`

`=>D`

Financial Maths, STD2 F4 2012* HSC 26c

Heather used her credit card to purchase a plane ticket valued at $1990 on 28 January 2011. She made no other purchases on her credit card account in January. She paid the January account in full on 19 February 2011.

The credit card account has no interest free period. Compound interest is charged daily at the rate of 21.9% per annum, including the date of purchase and the date the account is paid.

How much interest did she pay, to the nearest cent? (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

Show Answers Only

`$27.64`

Show Worked Solution

`text(Days of interest)\ (n) = 4+19=23`

`text(Daily interest rate)\ (r) = 0.219/365=0.0006`

♦ Mean mark 38%
MARKER’S COMMENT: Too many students calculated the # days as 22 instead of 23!

`text(Total Paid)\ (FV)`	`= PV(1+r)^n`
	`= 1990(1.0006)^23`
	`=2017.644…=$2017.64`

`:.\ text(Interest Paid)=2017.64-1990=$27.64`

\(\text{Amount owing}\)	\(= 5000\left(1+\dfrac{0.18}{365}\right)^{60}\)
	\(= 5150.118\ldots\)
	\(= \$5150.12\ \text{(nearest cent)}\)

\(I = Prn\)	\(=5000 \times 0.095 \times \dfrac{90}{365}\)
	\(= 117.123\ldots\)
	\(= \$117.12\ \text{(nearest cent)}\)

\(\text{Amount owing}\)	\(= 5000\left(1+\dfrac{0.18}{365}\right)^{60}\)
	\(= 5150.118\ldots\)
	\(= \$5150.12\ \text{(nearest cent)}\)

\(I = Prn\)	\(=5000 \times 0.095 \times \dfrac{90}{365}\)
	\(= 117.123\ldots\)
	\(= \$117.12\ \text{(nearest cent)}\)

\(\text{Amount owing}\)	\(= 3000\left(1+\dfrac{0.199}{365}\right)^{30}\)
	\(= 3049.458\ldots\)
	\(= \$3049.46\ \text{(nearest cent)}\)

\(\text{Closing balance}\)	\(= 1500\left(1+\dfrac{0.185}{365}\right)^{28}\)
	\(= 1521.433\ldots\)
	\(= \$1521.43\)

\(FV\)	\(=PV(1+r)^n\)
	\(=600\Big(1+\dfrac{0.07}{100}\Big)^{30}\)
	\(=612.728\dots\)

	\(\text{New charges}\)	\(\text{Closing balance}\)
A.	\($85.97\)	\($468.43\)
B.	\($85.97\)	\($596.66\)
C.	\($90.61\)	\($473.07\)
D.	\($90.61\)	\($477.71\)