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

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