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?

llltkl | Student

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.