Final answer:
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.