Question

A retired woman has $40,000 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 $4,000 per year from her investments?

Answer 1

She should invest $30000 in the 9% fund and $10000 in the 13% fund.

Step-by-step explanation

Suppose, the amount of investment at 9% rate is
`x` dollar.

As the total amount of investment is $40000 , so the investment at 13% rate will be:
`(40000-x) dollar`

So, the amount of earnings per year from 9% fund
`= 0.09x` dollar

and the amount of earnings per year from 13% fund
`= 0.13(40000-x)` dollar.

Given that, the total earnings per year is $4000. So the equation will be......

`0.09x+0.13(40000-x)=4000\\ \\ 0.09x+5200-0.13x=4000\\ \\ -0.04x=4000-5200\\ \\ -0.04x= -1200\\ \\ x= (-1200)/(-0.04)=30000`

So, the amount of investment at 9% fund is $30000 and the amount of investment at 13% fund = ($40000- $30000)= $10000