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Financial Maths, STD2 EQ-Bank 26

A credit card has an interest-free period of 55 days from and including the date of purchase. Interest is charged on purchases, compounding daily at a rate of 16.8% per annum. Interest is charged from the day following the interest-free period.

Furniture was purchased for $1200 using this credit card. Full payment was made on the 78th day after the date of purchase. There were no other purchases on this credit card.

  1. For how many days is interest charged on the purchase? Give your answer to the nearest cent.   (1 mark)

  2. Calculate the total interest charged when the account was paid in full.   (2 marks)

Show Answers Only

a.    \(23 \text{ days}\)

b.    \(\$12.77\)

Show Worked Solution

a.    \(\text{Interest is charged after the 55-day interest-free period.}\)

\(\text{Days charged} = 78-55 = 23 \text{ days}\)
 

b.    \(\text{Daily interest rate} = \dfrac{0.168}{365}\)

\(\text{Amount owing} \) \(= 1200\left(1+\dfrac{0.168}{365}\right)^{23}\)
  \(= 1212.768\ldots\)
  \(= \$1212.77\ \text{(nearest cent)}\)

  

\(\therefore\ \text{Interest} = 1212.77-1200 = \$12.77\)

Financial Maths, STD2 F4 2025 HSC 27

A credit card has an interest-free period of 45 days from and including the date of purchase. Interest is charged on purchases made, compounding daily at a rate of 13.74% per annum, from and including the day following the interest-free period.

Concert tickets were purchased for a total of $392 using this credit card.

Full payment was made on the 68th day from the date of purchase. There were no other purchases on this credit card.

What was the total interest charged when the account was paid in full?   (3 marks)

Show Answers Only

\(\text{Interest charged}\ =\$ 3.41\)

Show Worked Solution

\(\text{Day 1-45: no interest is charged}\)

\(\text{Day 46-68: interest charged (23 days)}\)

\(\text{Daily interest rate}=\dfrac{13.74}{365} \%=\dfrac{13.74}{365 \times 100}\)
  

\(\text{Amount owing}=392\left(1+\dfrac{13.74}{365 \times 100}\right)^{23}=\$ 395.41\)
  

\(\text{Interest charged}=395.41-392=\$ 3.41\)