Final answer:
To achieve a minimum of $5,000 interest per month, the retiree should invest $50,000 in the stock fund and $50,000 in the bond fund, following the financial advisor's guidance to invest as much as possible in the more stable bond fund.
Step-by-step explanation:
The retiree needs to determine how much to invest in each of the two accounts to meet their goal of earning at least $5,000 in interest each month. To model this, we can use a system of linear equations based on the given interest rates and desired income:
- Let x represent the amount to invest in the stock fund at 7% interest.
- Let y represent the amount to invest in the bond fund at 3% interest.
- The total amount invested is $100,000: x + y = 100,000.
- The total interest earned per month must be at least $5,000: 0.07x + 0.03y ≥ 5,000.
To maximize investment in the bond fund (y), given the guidance from the financial advisor and the constraints, we solve the system:
Step 1: Solve the equation x + y = 100,000 for y, giving us y = 100,000 - x.
Step 2: Substitute y in the second equation and get 0.07x + 0.03(100,000 - x) ≥ 5,000, which simplifies to 0.07x + 3,000 - 0.03x ≥ 5,000. Simplifying further gives 0.04x ≥ 2,000, so x ≥ 50,000.
Step 3: Since we need to maximize y, we should take the lowest value of x that satisfies the condition, which is x = 50,000.
Step 4: Substitute x = 50,000 back into the equation y = 100,000 - x to get y = 100,000 - 50,000, thus y = 50,000.
Therefore, the retiree should invest $50,000 in the stock fund and $50,000 in the bond fund to meet their goals based on the advisor's recommendations.