Jose just retired

Question

Jose just retired, and has $610,000 to invest. A very safe Certificate of Deposit (CD) account

pays 1%, while a riskier bond fund pays 4.5% in interest. Jose figures he needs $18,000 a year

in interest to live on. How much should he invest in each account to make enough interest

while minimizing his risk?

Answer 1

Hi, Amanda!

This sort of depends on whether you're calculating simple or compound interest. Given that Jose is expecting to take a fixed amount of money out of his account each year without expecting a larger return, we should probably us simple interest for this.

The equation to calculate the amount of money that you get from simple interest is as follows:

A = P*(1+rt).

P refers to the principal, which is the amount of money that starts in the account.

r refers to the interest rate itself.

t refers to the number of time periods in which interest builds up. Given that the problem suggests that he'll be withdrawing his money once per year, it's safe to say that t, here, is equal to one.

So that leaves us with

A = P * (1+r)

So with that out of the way, let's move onto the problem.

Setting up the problem itself

There are going to be 2 bank accounts that Jose uses, namely the secure CD and the riskier bond fund.

The rate for the CD is 1%, or .01 . So the equation for it will be equal to P * 1.01

The rate for the bond fund is 4.5%, or .045. The equation for it will be P * 1.045

Now, let's represent the amount of money in the CD with the letter "x," and the amount of money in the bond fund with "y". Our result will be

A = x*1.01 + y* 1.045

To make things possible to calculate, remember that every dollar in x is one fewer dollar in y, and we're starting off with $610,000. So, x + y=610,000, which means that y = 610,000-x. We can plug this back into our equation, to get

A = x*1.01 + (610,000-x) * 1.045

Simplifying, this takes us to

A = 1.01x + 637,450 - 1.045x

Now, Jose needs $18,000 each year. This will be on top of the $610,000 dollars he already has in the bank (remember that A includes both the principal and the interest!). So, A will be equal to $628,000.

628,000 = 1.01x + 637,450 -1.045x.

Simplifying, we get

628,000 = 637,450 - 0.035x.

To solve for x, we can subtract 637,450 from both sides.

-9450 = -.035x

Now, we can divide each side by -.035 to get

x = 270,000.

Jose will need to put $270,000 into the CD. The rest he will need to put into the bond fund.

$610,000 - $270,000 = $340,000

I always recommend double checking your work!

Plug your answers back into your original equation.

$270,000 * 1.01 + $340,000 * 1.045 = $628,000.

It looks like we have our answer. Jose will need to invest $270,000 at 1%, and $340,000 at 4.5%

Hope this helps!