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

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

\(=1.2116\ldots\)

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