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George purchased a laptop on his credit card for $2500. Interest is charged at 0.04% per day. He decided to transfer the balance to a new card with a 0% balance transfer for 90 days. How much does he save in the first 180 days on the following new cards? Answer to the nearest cent.
a Interest rate of 0.03% per day c Interest rate of 0.05% per day e Interest rate of 0.07% per day
b Interest rate 0.04% per day d Interest rate 0.06% per day f Interest rate 0.08% per day

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By transferring the credit card balance, George can calculate his potential savings by comparing the total interest accrued at each card's respective daily interest rate over 90 days. Savings are computed as the difference between the total interest on the original card and the total interest on the new card for each rate, considering the first 90 days have 0% interest.

Explanation:

George is considering transferring his laptop purchase balance to various new credit cards with different interest rates. To calculate the savings George would make on each card over the first 180 days after the initial 90 days of 0% interest balance transfer, we apply the daily interest rate to the original balance of $2500 for 90 days since the first 90 days have no interest. We then sum up the interest for each day to obtain the total interest that would have been charged over 90 days.



For example, the calculation for a card with a 0.03% daily interest rate is:

  1. Calculate the daily interest: $2500 Ă— 0.0003 = $0.75 per day.
  2. Multiply the daily interest by the number of days: $0.75 Ă— 90 = $67.50.



Repeat this process for each interest rate:

  • a) 0.03%: $67.50 total interest
  • b) 0.04%: $90.00 total interest
  • c) 0.05%: $112.50 total interest
  • d) 0.06%: $135.00 total interest
  • e) 0.07%: $157.50 total interest
  • f) 0.08%: $180.00 total interest



George saves the total interest that would have occurred from the original card's daily interest rate of 0.04% per day. As the first 90 days have no interest, those savings apply only to the remaining 90 days:

  • a) Savings: $90.00 - $67.50 = $22.50
  • b) Savings: $90.00 - $90.00 = $0.00
  • c) Savings: $90.00 - $112.50 = -$22.50 (George would not save but spend more)
  • d) Savings: $90.00 - $135.00 = -$45.00 (George would not save but spend more)
  • e) Savings: $90.00 - $157.50 = -$67.50 (George would not save but spend more)
  • f) Savings: $90.00 - $180.00 = -$90.00 (George would not save but spend more)

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