Michael Perez deposited a total of $2000 with two savings institutions. Bank A pays interest at the rate of 6%/year, whereas Bank B pays int

Question

Michael Perez deposited a total of $2000 with two savings institutions. Bank A pays interest at the rate of 6%/year, whereas Bank B pays interest at the rate of 8%/year. If Michael earned a total of $136 in interest during a single year, how much did he deposit in each institution?

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Kennedy 4 weeks 2021-12-26T09:13:38+00:00 1 Answer 0 views 0

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    2021-12-26T09:15:26+00:00

    Answer: He invested $1200 in bank A and $800 in bank B.

    Step-by-step explanation:

    Let x represent the amount deposited in bank A.

    Let y represent the amount deposited in bank B

    Michael Perez deposited a total of $2000 with two savings institutions. This means that

    x + y = 2000

    The formula for determining simple interest is expressed as

    I = PRT/100

    Where

    I represents interest paid on the loan.

    P represents the principal or amount taken as loan

    R represents interest rate

    T represents the duration of the loan in years.

    Considering the amount invested in bank A,

    P = x

    R = 6%

    T = 1 year

    I = (x × 6 × 1)/100 = 0.06x

    Considering the amount invested in bank B,

    P = y

    R = 8%

    T = 1 year

    I = (y × 8 × 1)/100 = 0.08y

    If Michael earned a total of $136 in interest during a single year, it means that

    0.06x + 0.08y = 136 – – – – – – – – – – -1

    Substituting x = 2000 – y into equation 1, it becomes

    0.06(2000 – y) + 0.08y = 136

    120 – 0.06y + 0.08y = 136

    – 0.06y + 0.08y = 136 – 120

    0.02y = 16

    y = 16/0.02 = 800

    x = 2000 – y = 2000 – 800

    x = 1200

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