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A lottery winner plans to invest part of her $540,000 in utility bonds paying 20% per...

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cbromm | (Level 1) Honors

Posted July 11, 2013 at 3:13 AM via web

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A lottery winner plans to invest part of her $540,000 in utility bonds paying 20% per year and the rest in a savings account paying 6% per year.  How much should be allocated to each investment if the yearly income from utility bonds it to be $10,900 more than the income from the savings account?

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aruv | High School Teacher | (Level 2) Valedictorian

Posted July 11, 2013 at 3:30 AM (Answer #1)

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Let winner invest $ x in utility bonds ,so $(540000-x) invested in saving.

Thus

annual income from utility bonds = `(xx20)/100=.2x `

annual income from saving =`((540000-x)xx6)/100` =`.06(540000-x)`

By given condition

`.2x-.06(540000-x)=10900`

`.2x+.06x-32400=10900`

`.26x=10900+32400`

`.26x=43300`

`x=43300/.26=166538.46`

Thus investment in utility bond= $166538.46

and in saving =540000-166538.46=$373461.54

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