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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 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

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

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

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

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

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

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