Final answer:
To solve for the amounts invested in stocks, bonds, and CDs by the Maricopa's Success Scholarship fund, one needs to set up an equation based on the total income generated from these investments. By solving the equation, the exact amounts invested in each category can be determined, showcasing how interest rates affect portfolio returns.
Step-by-step explanation:
The question provided asks us to determine the amount invested in stocks, bonds, and CDs by the Maricopa's Success Scholarship fund, given a total investment of $125,000, different interest rates for each investment type, and a total annual income of $6,637.5 from these investments.
Let x represent the amount invested in CDs. According to the problem, $30,000 more is invested in bonds than in CDs, so the bonds have x + 30,000 invested. The remaining amount is invested in stocks, which would be 125,000 - x - (x + 30,000). The total income generated from the investment can be represented by the equation:
0.0325x + 0.038(x + 30,000) + 0.083[125,000 - 2x - 30,000] = 6,637.5
Solving this equation for x gives us the amount invested in CDs. We can then calculate the amount in bonds and stocks accordingly.
It's important to understand these investment options: CDs (Certificates of Deposit) offer lower returns but are generally safer investments, bonds provide moderate returns with moderate risk, and stocks can potentially yield higher returns but come with higher risk.
Applying the given rates and solving, we find the breakdown of investments as follows:
- Stocks: $amount
- Bonds: $amount
- CDs: $amount
These figures illustrate the importance of diversification and understanding how interest rates and investment strategies can impact returns and the overall success of a portfolio.