Question

A retired woman has 50,000 to invest but needs to make 6000 a year from the interest to meet certain living expenses one bond investment pays 15% annual interest the rest of it she wants to put in a CD that pays 7%

Answer 1

To meet her annual income goal of $6,000, the retired woman needs to allocate her $50,000 investment between the 15% bond and the 7% CD. Let's use the following variables:

Let X be the amount invested in the 15% bond.

Let Y be the amount invested in the 7% CD.

We can set up a system of equations to represent the situation:

1. X + Y = $50,000 (total investment)

2. 0.15X + 0.07Y = $6,000 (annual interest goal)

Now, we can solve this system of equations. First, solve equation (1) for X:

X = $50,000 - Y

Now, substitute this expression for X into equation (2):

0.15($50,000 - Y) + 0.07Y = $6,000

Now, simplify and solve for Y:

7,500 - 0.15Y + 0.07Y = $6,000

Combine like terms:

0.07Y = $6,000 - $7,500

0.07Y = -$1,500

Now, divide by 0.07 to find Y:

Y = -$1,500 / 0.07

Y ≈ -$21,428.57

Since the amount invested in the CD cannot be negative, this means that she cannot invest any money in the CD at 7% because the bond alone will not generate enough interest to meet her income goal. Therefore, she should invest the entire $50,000 in the 15% bond.

Please note that these calculations assume no taxes on the interest income, and you should consult a financial advisor for more specific advice based on your financial situation.