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Financial Maths, STD2 EO-Bank 5 MC

Omar purchased a laptop for $1680 on 15 May using a credit card. Compound interest was charged daily at a rate of 18.98% per annum. 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 21 June?

  1. $1711.74
  2. $1712.63
  3. $1713.52
  4. $1714.41
Show Answers Only

\(C\)

Show Worked Solution

\(\text{Days for interest}\ (n)=17+21=38\)

\(\text{Daily interest rate}\ (r)=\dfrac{0.1898}{365}=0.00052\)

\(\text{Total paid}\ (FV)\) \(=PV(1+r)^n\)
  \(=1680(1.00052)^{38}\)
  \(=\$1713.52\)

 

\(\Rightarrow C\)

Financial Maths, STD2 EO-Bank 34

Farah wants to buy a commercial espresso machine for her cafe at a cost of $4200. She has decided to pay off whatever she owes in a single amount 75 days after the purchase, and is weighing up two ways to fund it.

  • A credit card that compounds interest daily at 17% per annum, but does not charge interest during the first 25 days after a purchase.
  • A personal loan on which simple interest is charged at 8.9% per annum.

Advise Farah on the cheaper option, backing up your recommendation with the relevant calculations.   (4 marks)

Show Answers Only

\(\text{Credit card interest}=\$98.93\)

\(\text{Personal loan interest}=\$76.81\)

\(\text{As }\$76.81\lt\$98.93,\text{ Farah should choose the personal loan.}\)

Show Worked Solution

\(\text{Days accruing interest}=75-25=50\)

\(\text{Credit card option (interest compounds daily):}\)

\(\text{Amount owing}\) \(=4200\left(1+\dfrac{0.17}{365}\right)^{50}\)
  \(=4298.931\ldots\)
  \(=\$4298.93\ \text{(nearest cent)}\)

 
\(\therefore\ \text{Interest}=4298.93-4200=\$98.93\)
  

\(\text{Personal loan option (simple interest applies):}\)

\(I=Prn\) \(=4200\times 0.089\times\dfrac{75}{365}\)
  \(=76.808\ldots\)
  \(=\$76.81\ \text{(nearest cent)}\)

  
\(\therefore\ \text{As }\$76.81\lt\$98.93,\text{ the personal loan}\)

\(\text{is cheaper, so Farah should choose it.}\)

Financial Maths, STD2 2023 HSC 32 (Adapted)

Theo’s credit card charges interest at 15.9% per annum, compounded daily, on any balance owing and has no interest-free period.

His only transaction for the month was a single purchase of $680, which he paid off completely 28 days afterwards.

  1. Assuming interest applied across all 28 days, calculate the amount of interest to be charged to the purchase.   (2 marks)
  2. Express this interest as a percentage of the total amount Theo repaid, rounding to two decimal places.   (2 marks)
Show Answers Only

a.    \(\text{Interest}=\$8.34\)

b.    \(1.21\%\)

Show Worked Solution

a.    \(\text{Daily interest rate}\ (r)=\dfrac{0.159}{365}\)

\(n=28\ \text{days}\)

\(FV\) \(=PV(1+r)^n\)
  \(=680\left(1+\dfrac{0.159}{365}\right)^{28}\)
  \(=\$688.34\)

 
\(\therefore\ \text{Interest}=688.34-680=\$8.34\)

 

b.    \(\text{Interest as % of total repaid}\)

\(=\dfrac{8.34}{688.34}\times 100\)

\(=1.2116\ldots\)

\(=1.21\%\ \text{(to 2 d.p.)}\)

Financial Maths, STD2 2016 HSC 17 MC (Adapted)

A credit card balance of $920 is outstanding for 20 days. Compound interest is charged at 0.041% per day, with no interest-free period.

Which calculation gives the amount of interest charged on this balance?

  1. \(920\times 0.00041\times 20\)
  2. \(920(1.00041)^{20}\)
  3. \(920(1.00041)^{20}-920\)
  4. \(920(1+0.00041\times 20)\)
Show Answers Only

\(C\)

Show Worked Solution
  • C is correct: compound interest \(=\) total owing \(-\) principal \(=920(1.00041)^{20}-920\).

Other options:

  • A is incorrect: this is simple interest \((Prn)\), not compound interest.
  • B is incorrect: this gives the total amount owing, not the interest.
  • D is incorrect: this gives the total owing using simple interest.

\(\Rightarrow C\)

Financial Maths, STD2 2019 HSC 27 (Adapted)

Bianca has a credit card that offers no interest-free period. At the end of each month, interest is added to the account at 19.5% per annum, compounded daily. Interest is worked out from the day a purchase is made (included) through to the last day of the month (included).

Part of Bianca’s June statement is shown below, with two figures left blank.
  

 

For this account, the minimum payment is set at 3% of the closing balance on 30 June.

Find the minimum payment, giving your answer to the nearest cent.   (3 marks)

Show Answers Only

\(\text{Minimum payment}=\$78.42\)

Show Worked Solution

\(\text{Days of interest}\ (n)=\ \text{21 June – 30 June}=10\)

\(\text{Daily interest rate}\ (r)=\dfrac{0.195}{365}=0.0005342\ldots\)

\(\text{Closing balance}=2600(1+0.0005342\ldots)^{10}=\$2613.92\)

\(\text{Minimum payment}\) \(=\dfrac{3}{100}\times 2613.92\)
  \(=78.4176\ldots\)
  \(=\$78.42\ \text{(nearest cent)}\)

Financial Maths, STD2 EO-Bank 26

Kiara wants to purchase a used motorbike selling for $2500 and will be in a position to settle the whole debt in a single payment 40 days after the purchase.

Two methods of financing the purchase are open to her.

  • Using a credit card, where interest of 20.5% per annum is compounded daily. There is no interest-free period, so interest is charged from the day after the purchase.
  • Taking out a 40-day personal loan, where simple interest is charged at 12% per annum.
  1. Determine the interest that would build up under each method across the 40 days.   (2 marks)
  2. A friend insists that the personal loan will leave Kiara better off by more than $25 compared with the credit card. Decide whether the friend is correct, justifying your answer with calculations.   (2 marks)
Show Answers Only

a.    \(\text{Credit card: }\$56.78\ \text{, Personal loan: }\$32.88\)

b.    \(\text{Difference}=\$23.90\)

\(\text{As }\$23.90\lt\$25,\text{ the friend’s claim is incorrect.}\)

Show Worked Solution

a.    \(\text{Credit card option (compounding daily):}\)

\(\text{Amount owing}\) \(=2500\left(1+\dfrac{0.205}{365}\right)^{40}\)
  \(=2556.784\ldots\)
  \(=\$2556.78\ \text{(nearest cent)}\)

 
\(\therefore\ \text{Interest}=2556.78-2500=\$56.78\)
 

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

\(I=Prn\) \(=2500\times 0.12\times\dfrac{40}{365}\)
  \(=32.876\ldots\)
  \(=\$32.88\ \text{(nearest cent)}\)

 

b.    \(\text{Difference}=56.78-32.88=\$23.90\)

\(\text{As }\$23.90\lt\$25,\text{ the friend’s claim is incorrect.}\)

Financial Maths, STD2 2025 HSC 27 (Adapted)

Noor buys a lounge suite for $650 on 3 April using a credit card. The card has an interest-free period of 30 days from and including the date of purchase. Interest is charged on purchases, compounding daily at a rate of 16.8% per annum, from and including the day following the interest-free period.

No other purchases were made on this credit card.

The account was paid in full on 20 May.

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

Show Answers Only

\(\text{Interest charged}=\$5.41\)

Show Worked Solution

\(\text{Total days (3 April to 20 May)}=28+20=48\)

\(\text{Interest-free days}=30\)

\(\text{Days accruing interest}\ (n)=48-30=18\)

\(\text{Daily interest rate}\ (r)=\dfrac{0.168}{365}=0.00046027\ldots\)

\(\text{Amount owing}=650(1+0.00046027\ldots)^{18}=\$655.41\)

\(\therefore\ \text{Interest charged}=655.41-650=\$5.41\)

Financial Maths, STD2 2020 HSC 22 (Adapted)

Diego pays a $600 car repair bill using his credit card. The card charges interest at 18.6% per annum, compounded daily, and has no interest-free period.

Twenty days after the purchase, Diego makes a part-payment of $300.

Determine how much Diego still owes after making the $300 part-payment.   (3 marks)

Show Answers Only

\(\text{Amount owing}=\$306.14\)

Show Worked Solution

\(\text{Days of interest}\ (n)=20\)

\(\text{Daily interest rate}\ (r)=\dfrac{18.6\%}{365}=\dfrac{0.186}{365}=0.00050959\ldots\)

\(\text{Amount owing}\ (FV)\) \(=PV(1+r)^n-300\)
  \(=600(1+0.00050959\ldots)^{20}-300\)
  \(=606.14-300\)
  \(=\$306.14\)