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17 June, 03:49

In planning her retirement, Liza deposits some money at 2.5% interest, with twice as much deposited at 4.5%. Find the amount deposited at each rate if the total annual interest income is $1150.

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  1. 17 June, 04:13
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    Let us assume $x is deposit at 2.5% interest.

    At the rate 4.5% deposited amount is twice of the amount deposited at 2.5%.

    Therefore, at the rate 4.5% deposited amount = $2x.

    Total interest earned by both different deposited amount at the rate 2.5% and at the rate 4.5% = $1150.

    We can setup an eqation now,

    Interest earned on $x at 2.5% + interest earned on $2 at 4.5% = $1150.

    2.5% of x + 4.5% of 2x = 1150

    Percentage could be written in decimals by dividing by 100.

    Therefore, 2.5% = 2.5 / 100 = 0.025 and 4.5% = 4.5/100 = 0.045.

    We could rewrite above equation as,

    0.025*x + 0.045 * 2x = 1150

    0.025x + 0.09x = 1150

    Adding 0.025x + 0.09x, we get 0.115x.

    So, 0.115x=1150.

    Dividing both sides by 0.115.

    0.115x/0.115=1150/0.115.

    x = $1000.

    2x = 2 * 1000 = $2000

    Therefore,

    $1000 deposited at 2.5% and $2000 deposited at 4.5%.
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