The sum of $3,000 is deposited into an account paying 10% annually. If $1,206 is withdrawn at the end of years 1 and 2, how much then remain

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The sum of $3,000 is deposited into an account paying 10% annually. If $1,206 is withdrawn at the end of years 1 and 2, how much then remains in the account?”

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    2021-09-10T20:25:44+00:00

    What we have so far: 
    INITIAL CASH AMOUNT IN THE BANK: USD3,000
    ANNUAL INCREASE OF THE CASH AMOUNT IN THE BANK: 10%
    YEARS THE CASH STAYED IN THE BANK: 2 years.
    AMOUNT WITHDRAWN AT THE END OF YEAR 1: USD1,206
    AMOUNT WITHDRAWN AT THE END OF YEAR 2: USD1,206

    First, we need to solve for YEAR 1:
    FOR YEAR 1: 
    Initial Deposit * Annual Increase Rate = Annual Increase
    3,000 * 0.10 = Year 1’s Annual Increase
    Year 1’s  Annual Increase = USD300
    ∴The YEAR 1’S ANNUAL INCREASE IS USD300.
    ∴The NEW AMOUNT is now USD3,300.

    BUT NOT SO FAST! After the year, you took out USD1,206.
    New Amount – USD1,206 = Year 1 Amount
    3,300 – 1,206 = Year 1 Amount
    Year 1 Amount = USD2094
    ∴The YEAR 1 AMOUNT which will carry over to YEAR 2 is USD2094.

    Now, let us solve for the REMAINING BALANCE.
    FOR YEAR 2’s Annual Increase: 
    YEAR 1 AMOUNT * Annual Increase = Year 2’s Annual Increase
    2094*0.10 = Year 2’s Annual Increase
    Year 2’s Annual Increase = USD209.4
    ∴The YEAR 1’S ANNUAL INCREASE IS USD209.4.
    ∴The NEW AMOUNT is now USD2,303.4.

    But you took out USD1,206
    USD2,303.4 – USD1,206 = Remaining Balance
    Remaining Balance = USD1097.4

    ∴The Answer is: USD1097.4

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