Question

A retired woman has $140,000 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 $14,000 per year from her investments?.

Answer 1

The retired woman should invest $35,000 in the riskier fund with a 13% yield and $105,000 in the safer fund with a 9% yield to earn $14,000 per year from her investments.

Step-by-step explanation:

The question asks how to distribute $140,000 between two investment funds to achieve a desired annual income of $14,000. We can set up a system of equations to solve this problem. Let x be the amount invested in the safe fund (9% yield), and y be the amount invested in the riskier fund (13% yield). The equations will be as follows:

• 
  
• x + y = $140,000 (total investment)
• 
  
• 0.09x + 0.13y = $14,000 (desired annual income)

To solve these equations, we can use substitution or elimination methods. Multiplying the second equation by 100 to clear decimals:

• 
  
• 9x + 13y = 1,400,000
• 
  
• x = 140,000 - y

Substitute the second equation into the first:

• 
  
• 9(140,000 - y) + 13y = 1,400,000
• 
  
• 1,260,000 - 9y + 13y = 1,400,000
• 
  
• 4y = 140,000
• 
  
• y = $35,000

Therefore, she should invest $35,000 in the riskier fund, and the rest:

• 
  
• x = 140,000 - 35,000 = $105,000

in the safe fund to achieve her goal.