Question

Wade just retired, and has $600,000 to invest. A very safe Certificate of Deposit (CD) account pays 2%, while ariskier bond fund pays 8.5% in interest. Wade figures he needs $27,000 a year in interest to live on. How muchshould he invest in each account to make enough interest while minimizing his risk?$at 2%at 8.5%Round answers to the nearest dollar.

Answer 1

We can write 2 equations from the information given.

Let the amount invested in CD be "x" and the amount invested in bond be "y".

The total amount invested is $600,000. Thus, we can write,

`x+y=600,000`

The CD pays 2% (0.02) and the bond pays 8.5% (0.085). Total interest needed is $27,000. Thus, we can craft another equation,

`0.02x+0.085y=27,000`

Solving the first equation for "x", we can substitute it into the second equation and solve for "y" first. The steps are shown below:

`\begin{gathered} x+y=600,000 \\ or,x=600,000-y \\ -------------- \\ 0.02x+0.085y=27,000 \\ 0.02(600,000-y)+0.085y=27,000 \\ 12000-0.02y+0.085y=27,000 \\ 0.065y=27,000-12,000 \\ 0.065y=15,000 \\ y=230,769.23 \end{gathered}`

Now, we can find "x",

`\begin{gathered} x+y=600,000 \\ x+230,769.23=600,000 \\ x=600,000-230,769.23 \\ x=369,230.77 \end{gathered}`

Rounded to the nearest dollar, we write our answer >>>

$369,231 at 2%$230,769 at 8.5%