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15 November, 01:27

A bank loaned out $19 comma 00019,000 , part of it at the rate of 7 %7% per year and the rest at 15 %15% per year. If the interest received in one year totaled $20002000 , how much was loaned at 7 % question mark7%? How much of the $19 comma 00019,000 did the bank loan out at 7 % question mark

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  1. 15 November, 04:21
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    Let x be the amount loaned at 7% and ($19,000 - x) be the amount loaned at 15%

    Given:

    Interest incurred at 7%, I1 + Interest incurred at 15%, I2 = $2000

    Interest, I = amount * rate

    I1 = 7/100 * x

    I2 = 15/100 * ($19,000 - x)

    From the above expressions,

    (0.07) x + (0.15) * ($19,000 - x) = $2,000

    Solving for x,

    0.07x + 2850 - 0.15x = 2000

    Collecting like terms,

    0.08x = 850

    x = $10625

    The amount loaned at 7% interest is

    $10625

    The amount loaned at 15% interest is ($19000 - $10625)

    = $8375
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