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Financial Maths, STD2 EQ-Bank 17

Mia wants to buy a tablet with a cash price of $960. She cannot pay for it upfront and is considering two options.
 

Option 1: Buy now, pay later

  • 4 equal payments of $240 over 8 weeks
  • No interest or fees if all payments are made on time

Option 2: Short-term loan

  • Establishment fee: $75
  • Monthly account-keeping fee: $30
  • Weekly repayments of $55 over 5 months (20 weeks)

Assume Mia will make all payments on time under either option.

  1. Calculate the total amount Mia will pay under each option.   (2 marks)

  2. Which option is cheaper, and by how much?   (1 mark)

Show Answers Only

a.    \(\text{Option 1: }\$960,\ \text{Option 2: }\$1325\)

b.    \(\text{Option 1 is cheaper by }\$365\)

Show Worked Solution

a.    \(\text{Option 1: } \)

\(\text{Repayments}=4 \times 240 = \$960\)
  

\(\text{Option 2:}\)

\(\text{Account-keeping} = 30 \times 5 = \$150\)

\(\text{Weekly repayments} = 55 \times 20 = \$1100\)

\(\text{Total} = 75+150+1100 = \$1325\)
  

b.    \(\text{Option 1 is cheaper.}\)

\(\text{Difference} = 1325-960 = \$365\)

Financial Maths, STD2 EQ-Bank 21

Maya uses a buy now, pay later payment option to make a purchase of $120. Her repayments are split across 4 equal payments over 6 weeks. No interest is charged.

Maya misses her final payment on 16 March 2026 and is charged a late fee of $19. Maya's payment schedule is shown, with her balance totalling $49.

\begin{array}{|l|c|c|c|} \hline \textbf{Payment} & \textbf{Due Date} & \textbf{Amount} & \textbf{Status} \\ \hline \text{1st} & \text{2 February 2026} & \$30 & \text{Paid} \\ \hline \text{2nd} & \text{16 February 2026} & \$30 & \text{Paid} \\ \hline \text{3rd} & \text{2 March 2026} & \$30 & \text{Paid} \\ \hline \text{4th} & \text{16 March 2026} & \$30 & \text{Not Paid} \\ \hline \text{Outstanding Due} & \text{30 March 2026} & \$49 \text{ including late fee} & \\ \hline \end{array}
  1. Find the total amount Maya pays for her purchase if repaying in full on 30 March 2026.   (1 mark)
  2. Maya's bank offers short-term loans where simple interest is charged at 16% per annum.
    Suppose Maya had borrowed $120 from the bank to make this purchase on 2 February 2026 and repaid it in full 8 weeks later.
    How much would Maya have saved using this approach instead of the buy now, pay later option?   (2 marks)

Show Answers Only

a.    \(\$139\)

b.    \(\$16.05\)

Show Worked Solution

a.    \(\text{If total owing paid on 30 March:}\)

\(\text{Total paid} = 30+30+30+49 = \$139\)
  

b.    \(r = 16\% = 0.16, \quad n = \dfrac{8 \times 7}{365} = \dfrac{56}{365}\)

\(I= Prn = 120 \times 0.16 \times \dfrac{56}{365}= 2.945\ldots = \$2.95\)

\(\text{Amount saved} = 19-2.95 = \$16.05\)

Financial Maths, STD2 EQ-Bank 20

Kimberley uses a buy now, pay later payment option to make a purchase of $100. Her repayments are split across 4 equal payments over 6 weeks. No interest is charged.

Kimberley misses her final payment and is charged a late fee of $17. Kimberley’s payment schedule is shown, with her balance totalling $42.
 

  1. Find the total amount Kimberley pays for her purchase if repaying in full on 27 July 2024.   (1 mark)
  2. Kimberley’s bank offers short-term loans where simple interest is charged at 18% per annum.
  3. Suppose Kimberley had borrowed $100 from the bank to make this purchase on 1 June 2024 and repaid it in full 8 weeks later.
  4. How much would Kimberley have saved using this approach instead of the buy now, pay later option?   (2 marks)
Show Answers Only

a.    \($117\)

b.    \($14.24\)

Show Worked Solution

a.    \(\text{If total owing paid on 27 July:}\)

\(\text{Total paid} = 25+25+25+42=$117\)
 

b.    \(r=18\%=0.18,\ \ n=\dfrac{8 \times 7}{365} = \dfrac{56}{365}\)

\(I=Prn=100 \times 0.18 \times \dfrac{56}{365} = 2.761… = $2.76 \)

\(\text{Amount saved} = 17-2.76=$14.24\)