# 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...

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?

Asked on by cbromm

aruv | High School Teacher | (Level 2) Valedictorian

Posted on

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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