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Financial Maths, STD2 EQ-Bank 28

Sam needs to borrow $3000 and plans to repay it in full after 30 days. He is comparing two options.

  • Credit card: compound interest charged daily at 19.9% per annum, with no interest-free period.
  • Personal loan: simple interest charged at 11.5% per annum.
  1. Calculate the interest Sam would be charged on the credit card over the 30 days.   (2 marks)

  2. How much does Sam save by choosing the personal loan.   (2 marks)

Show Answers Only

a.    \(\$49.46\)

b.    \(\text{Saving =}\ \$21.10\)

Show Worked Solution

a.    \(\text{Daily interest rate} = \dfrac{0.199}{365}\)

\(\text{Amount owing}\) \(= 3000\left(1+\dfrac{0.199}{365}\right)^{30}\)
  \(= 3049.458\ldots\)
  \(= \$3049.46\ \text{(nearest cent)}\)

  

\(\therefore \text{Interest} = 3049.46-3000 = \$49.46\)
  

b.    \(\text{Personal loan (simple interest):}\)

\(I = Prn\) \(=3000 \times 0.115 \times \dfrac{30}{365}\)
  \(= 28.356\ldots\)
  \(= \$28.36\ \text{(nearest cent)}\)

 
\(\therefore \text{Saving} = 49.46-28.36 = \$21.10\)

Financial Maths, STD2 EQ-Bank 5 MC

A credit card is an example of a reducing balance loan.

Which statement best explains why this is the case?

  1. Interest is charged at a fixed amount each month, regardless of the balance owing.
  2. Interest is charged on the outstanding balance, which decreases as repayments are made.
  3. The interest rate reduces each month as the balance is repaid.
  4. A fixed portion of the amount borrowed is repaid each month, with no interest charged.
Show Answers Only

\(B\)

Show Worked Solution

B is correct: Like any reducing balance loan, interest is charged on the outstanding balance, which decreases as repayments are made.

Other options:

  • A is incorrect: the interest is not a fixed amount; it depends on the balance.
  • C is incorrect: it is the balance that reduces, not the interest rate, which stays fixed.
  • D is incorrect: interest is charged on a credit card, and repayments are not a fixed portion of the principal.

\(\Rightarrow B\)