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Assuming an interest rate of 2.25% per annum, a monthly compounding period, and the following account information for the month of June 2022, find the amount of interest that will be credited to the client's savings account for the month of June 2022. (Use the equivalence 1 year = 365 days.)Date Balance06/01/2022 Php75,00006/06/2022 Php60,00006/13/2022 Php50,00006/25/2022 Php65,000 Group of answer choicesPhp110.03Php121.03Php99.03Php88.03

Question

Assuming an interest rate of 2.25% per annum, a monthly compounding period, and the following account information for the month of June 2022, find the amount of interest that will be credited to the client's savings account for the month of June 2022. (Use the equivalence 1 year = 365 days.)Date Balance06/01/2022 Php75,00006/06/2022 Php60,00006/13/2022 Php50,00006/25/2022 Php65,000 Group of answer choicesPhp110.03Php121.03Php99.03Php88.03

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Solution

To calculate the interest that will be credited to the client's savings account for the month of June 2022, we need to calculate the daily balance of the account and then apply the interest rate.

  1. First, calculate the number of days for each balance:

    • From 06/01/2022 to 06/06/2022: 5 days with a balance of Php75,000
    • From 06/06/2022 to 06/13/2022: 7 days with a balance of Php60,000
    • From 06/13/2022 to 06/25/2022: 12 days with a balance of Php50,000
    • From 06/25/2022 to the end of the month (06/30/2022): 5 days with a balance of Php65,000
  2. Calculate the total balance for the month by multiplying each balance by the number of days it was held, then summing these amounts:

    • (5 days * Php75,000) + (7 days * Php60,000) + (12 days * Php50,000) + (5 days * Php65,000) = Php1,770,000
  3. Divide this total by the number of days in June to get the average daily balance:

    • Php1,770,000 / 30 days = Php59,000
  4. Calculate the monthly interest rate by dividing the annual interest rate by 12:

    • 2.25% / 12 = 0.1875%
  5. Finally, apply this monthly interest rate to the average daily balance to find the interest for June:

    • Php59,000 * 0.1875% = Php110.63

So, the amount of interest that will be credited to the client's savings account for the month of June 2022 is approximately Php110.63. This is not an exact match to any of the provided answer choices, but it is closest to Php110.03.

This problem has been solved

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