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18 October, 20:00

A retired woman has $180,000 to invest. she has chosen one relatively safe investment fund that has an annual yield of 9% and another, riskier fund that has a 13% annual yield. how much should she invest in each fund if she would like to earn $18,000 per year from her investments?

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  1. 18 October, 20:35
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    Solution:

    Let the amount invested in scheme which yields 9% be x and amount invested in scheme which yields 13% be y.

    x + y = 180000 - - equation 1

    0.09x + 0.13y = 18000 - - equation 2

    Balancing the equations, multiply equation 1 with 0.09 and equation 2 with 1,

    0.09x + 0.09y = 16200 - equation 3

    0.09x + 0.13y = 18000 - - equation4

    Subtracting equation 4 from 3,

    -0.04y = - 1800

    y = 45000

    Now putting value of y in equation 1,

    x + 45000 = 180000

    x = 135000

    The amount to be invested in scheme which yields 9% = $135,000

    The amount to be invested in scheme which yields 13% = $45,000
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