Bailey uses his credit card to purchase accessories for his classic car. The only purchase he will make on his credit card is for the $3000 worth of accessories. He has a credit limit of $5000 with a 55-day interest-free period and interest of 17.65% p.a. His minimum payment is $25 or 3% of the balance, whichever is greater.
a) Bailey makes a regular payment of $250 at the end of each month with interest calculated daily and added to his balance at the end of month. How many months it will take him to pay off his credit card balance?
b) Bailey also has the option of taking out a personal loan for $3000 with flat rate interest of 15.40% p.a. for 2 years and regular monthly repayments of $163.50. Which option is the most cost effective for Bailey? Justify your answer using calculations.
Just need help with a, then should be able to figure out b, thanks.
To calculate how many months it will take Bailey to pay off his credit card balance, we'll need to consider his monthly payment, interest rate, and minimum payment requirements.
Given information:
- Credit card balance: $3000
- Credit limit: $5000
- Interest-free period: 55 days
- Interest rate: 17.65% p.a.
- Minimum payment: $25 or 3% of the balance, whichever is greater
First, let's determine the minimum payment. Since 3% of the balance ($3000) is $90, which is greater than $25, Bailey's minimum payment would be $90.
Now, let's calculate the interest to be added to the balance at the end of each month. The interest rate of 17.65% p.a. can be converted to a daily interest rate by dividing it by the number of days in a year (365):
Daily interest rate = 17.65% / 365 ≈ 0.04824%
Next, we'll calculate the interest accumulated during the 55-day interest-free period. Since we know the interest rate is calculated daily, the interest for this period can be calculated as follows:
Interest = (Credit card balance) x (Daily interest rate) x (Number of days)
= $3000 x 0.04824% x 55
≈ $0.7906
Therefore, the balance at the end of the interest-free period would be:
Balance = (Credit card balance) + (Interest)
= $3000 + $0.7906
≈ $3000.79
Now, let's calculate how many months it will take Bailey to pay off his credit card balance with his regular monthly payment of $250.
Month 1:
- Opening balance = $3000.79 (from the previous calculation)
- Payment = $250
- Interest for the month = (Opening balance) x (Daily interest rate) x (Number of days in the month)
- Closing balance = (Opening balance) + (Interest for the month) - (Payment)
Repeat this calculation for each subsequent month until the closing balance is zero or less than the minimum payment of $90. Keep track of the months it takes to reach this point. This will give you the answer to part a).
Note: Do not forget to recalculate the daily interest rate each month based on the number of days in that particular month.
Once you have the number of months it takes to pay off the credit card balance, you can move on to part b) to compare it with the personal loan option.