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Financial Maths, STD2 EQ-Bank 27

A credit card account has no interest-free period. Compound interest is calculated daily at a rate of 18.5% per annum and charged to the account up to and including the statement date.

A single purchase of $1500 was made and interest accrued on the purchase for 28 days, including the statement date. There were no other purchases on the account.

  1. Calculate the closing balance on the statement date.   (2 marks)

  2. The minimum payment is calculated as $30 or 3% of the closing balance, whichever is greater. Calculate the minimum payment due.   (2 marks)

Show Answers Only

a.    \(\$1521.43\)

b.    \(\$45.64\)

Show Worked Solution

a.    \(\text{Daily interest rate} = \dfrac{0.185}{365}\)
  

\(\text{Closing balance}\) \(= 1500\left(1+\dfrac{0.185}{365}\right)^{28}\)
  \(= 1521.433\ldots\)
  \(= \$1521.43\)

  

b.    \(3\% \text{ of closing balance} = 0.03 \times 1521.43= \$45.64\)

\(\text{Since } \$45.64 > \$30, \text{ the minimum payment due is } \$45.64.\)

Financial Maths, STD1 F3 2021 HSC 30

Blake opens a new credit card account on 1 May. He uses it, for the first time, on 4 May to buy concert tickets for $850.

He makes no further purchases or repayments during the month of May.

A statement for the credit card is issued on the last day of each month.

The statement for May shows that interest is charged at 19.75% per annum, compounding daily, from 20 May (included) until 31 May (included).

  1. What is the compound interest shown on the statement issued on 31 May?   (3 marks)

  2. The minimum payment is calculated as 3% of the closing balance on 31 May. Calculate the minimum payment.   (1 mark)

Show Answers Only

a.    `$5.54`

b.    `$25.67`

Show Worked Solution

a.   `text(Daily interest rate) = 19.75/365 = 0.05411text(%) = 0.0005411`

`text(Days incurring interest = 12)`

♦♦♦ Mean mark part (a) 14%.
`text{Card balance (31 May)}` `= PV(1+r)^n`
  `= 850 (1 + 0.0005411)^12= $855.54`

  
`:.\ text(Interest)= 855.54-850= $5.54`

♦♦♦ Mean mark part (b) 15%.
b.    `text(Minimum payment)` `= 855.54 xx 0.03= $25.67“

Financial Maths, STD2 F4 2010* HSC 22 MC

In July, Ms Alott received a statement for her credit card account. The account has no interest free period. Compound interest is calculated daily and charged to her account on the statement date.
 

2010 22 mc

What is the minimum payment due on this account? 

  1. $23.56
  2. $25.00
  3. $86.08
  4. $87.20
Show Answers Only

`D`

Show Worked Solution

`text(Days of interest)\ (n) =2+23=25`

♦♦♦ Mean mark 20%. Lowest scoring MC question in the 2010 exam.

`text(Daily interest rate)\ (r) = 0.0521/100 = 0.000521`

`text(Closing Balance)\ (FV)` `=PV(1+r)^n`
  `=1721.50 (1.000521)^25=$1744.06`

  
`text(5% of closing balance)=5/100xx1744.06=87.20\ text{(nearest cent)}`
   

`text(S)text(ince)\ $87.20>$25\ , text(minimum payment)=$87.20`
  

`=>D`