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3 October, 05:18

Last year, Ann had $10,000 to invest. She invested some of it in an account that paid 7% simple interest per year, and she invested the rest in an account that paid 8% simple interest per year. After one year, she received a total of $790 in interest. How much did she invest in each account

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  1. 3 October, 05:43
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    Amount invested at 7% = $1,000

    Amount invested at 8% = $9,000

    Explanation

    Let the amount invested

    at 7% = X

    at 8% = Y

    According to given condition

    X + Y = $10,000 (Eq 1)

    and

    0.07X + 0.08Y = $790 (Eq 2)

    By multiplying (Eq 1) with 0.07

    0.07X + 0.07Y = $700 (Eq 3)

    By subtracting (Eq 3) from (Eq 2)

    0.07X - 0.07X + 0.08Y - 0.07Y = $790 - $700

    0.08Y - 0.07Y = $790 - $700

    0.01Y = $90

    Y = $90 / 0.01

    Y = $9,000

    X + $9,000 = $10,000

    X = $10,000 - $9,000

    X = $1,000

    Check:

    $1,000 x 7% + $9,000 x 8% = $790

    $790 = $790
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