A lottery winner plans to invest part of her $1,880,000 in utility bonds paying 13% per year and the rest in  savings account paying 6% per year.  How much should be allocated to each investment...

A lottery winner plans to invest part of her $1,880,000 in utility bonds paying 13% per year and the rest in  savings account paying 6% per year.  How much should be allocated to each investment if the yearly income from the savings account is to be twice the income from the utility bonds?

Asked on by cbromm

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llltkl | College Teacher | (Level 3) Valedictorian

Posted on

Let the amount of money invested by the lottery winner in the utility bonds be x.

Then amount of money invested in savings account= (1,880,000-x).

Yearly income from utility bonds=`13/100*x=(13x)/100`

Yearly income from savings account=`6/100*(1,880,000-x)`

According to the given condition:

`6/100*(1,880,000-x)=2*(13x)/100`

`rArr 3(1,880,000-x)=13x`

`rArr5,640,000-3x=13x`

`rArr 16x=5,640,000`

`rArr x=352,500`

Therefore, amount of money invested by the lottery winner in the utility bonds =$352,500.

Amount of money invested in savings account= $(1,880,000-x)

=$(1,880,000-352,500)=$1,527,500.

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