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How much was invested at each rate?

You invested $8000 in 2 funds paying 4% and 7% annual interest, respectively At the end of the year, the total interest from these investments was $554. How much was invested at each rate?

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  • 9 years ago
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    Let x = amount invested at 4% , or in decimal terms 0.04

    Then (8000 - x) = amount invested at 7% , in decimal terms 0.07

    Using the interest earned information, we have the equation

    (0.04)x + (0.07)(8000 - x) = 554

    0.04x + 560 - 0.07x = 554 . . . . . . . . . . [ multiplied out second terms on left-side ]

    - 0.03x + 560 = 554 . . . . . . . . . . . . . . .[ simplified the x terms on left-side ]

    - 0.03x = - 6 . . . . . . . . . . . . . . . . . . . . [ subtracted 560 from both sides ]

    x = ( - 6 / - 0.03 ) . . . . . . . . . . . . . . . . .[ divided both sides by - 0.03 ]

    x = 200

    -----------------

    $ 200 was invested at 4%

    and

    ($ 8,000 - $ 200) = $ 7,800 was invested at 7%.

    -----------------

    Check:

    One year of interest on $ 200 @ 4% = ($ 200 x 0.04) = $ 8

    One year of interest on $ 7,800 @ 7% = ($ 7,800 x 0.07) = $ 546

    Total interest = ($ 8 + $ 546) = $ 554

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