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Financial Maths, STD2 F4 2020 HSC 22

Nisa has a credit card on which interest at 17% per annum, compounded daily, is charged on the amount owing.

At the beginning of the month, Nisa owes $500 on her credit card. She makes no other purchases using the credit card, but fifteen days later, she repays $250.

Assuming that interest is charged for the fifteen days, calculate the amount owing on the credit card immediately after the $250 payment is made.   (3 marks)

Show Answers Only

`$253.50`

Show Worked Solution

`text{Days of interest}\ (n) = 15`

`text{Daily interest rate}\ (r) = frac{0.17}{365} = 0.00046575 …`

`text{Amount owing}\ (FV)` `= PV (1 + r)^n-250`
  `= 500 (1.00046575 …)^15-250`
  `= 503.50-250= $253.50`

Financial Maths, STD2 F4 2018* HSC 28d

Yanika opens a new credit card account, with interest and fees as shown.
 

Interest

    • Compound interest calculated daily at the rate 12.41% p.a.
    • No interest-free period

Fees

    • $0 for online repayments
    • $3 for repayments in cash (fee added to balance immediately after repayment)
        

Yanika makes a single purchase of $849 with the credit card.

  1. Show that the balance owing on the credit card 24 days after making the purchase is $855.95.   (2 marks)

  2. Yanika makes her first repayment 24 days after making the purchase. She makes a cash repayment of $450.

     

    What is the balance owing on the credit card immediately after her repayment is made and the repayment fee has been charged?   (1 mark)

Show Answers Only

i.    `text(See Worked Solutions)`

ii.   `$408.95`

Show Worked Solution

i.    `text(Days of interest)\ (n) = 24`

♦ Mean mark part (i) 48%, part (ii) 49%.

`text(Daily interest rate)\ (r) = 0.1241/365 = 0.00034`

`text(Balance Owing)\ (FV)` `= PV(1+r)^n`
  `= 849(1.00034)^24`
  `= 855.954…=$855.95\ \ text{(nearest cent)}`

 

ii.   `text(Balance owing)= 855.95-450 + 3= $408.95`