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You have lost the benefit of an interest free period on your credit card. The balance of your credit card is $1,200 for the first 5 days of the statement period then $2,000 for the next 22 days and finally $2,300 for the last 3 days of the statement period. The annual interest rate on the credit card is 19%. There are 365 days in a year.Calculate the interest charged at the end of the statement period. [Express your result with 2 decimal places] Do not type any $ sign.

Question

You have lost the benefit of an interest free period on your credit card. The balance of your credit card is 1,200forthefirst5daysofthestatementperiodthen1,200 for the first 5 days of the statement period then 2,000 for the next 22 days and finally 2,300forthelast3daysofthestatementperiod.Theannualinterestrateonthecreditcardis192,300 for the last 3 days of the statement period. The annual interest rate on the credit card is 19%. There are 365 days in a year.Calculate the interest charged at the end of the statement period. [Express your result with 2 decimal places] Do not type any sign.

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Solution

To calculate the interest charged at the end of the statement period, we need to calculate the average daily balance and then apply the daily interest rate.

  1. Calculate the average daily balance:

    For the first 5 days, the balance is 1,200.Forthenext22days,thebalanceis1,200. For the next 22 days, the balance is 2,000. For the last 3 days, the balance is $2,300.

    So, the average daily balance is: [(12005) + (200022) + (2300*3)] / 30 = $1,910

  2. Calculate the daily interest rate:

    The annual interest rate is 19%, so the daily interest rate is 19% / 365 = 0.05205%

  3. Calculate the interest charged at the end of the statement period:

    The interest charged is the average daily balance * daily interest rate * number of days in the statement period.

    So, the interest charged is: 1910 * 0.0005205 * 30 = $29.83

Therefore, the interest charged at the end of the statement period is $29.83.

This problem has been solved

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