Optimizing Financial Investments for Maximum Income: A Numerical Example

In the realm of financial planning, one often encounters scenarios where the allocation of funds at different interest rates is required to achieve a targeted return. This article explores such a scenario, where an individual has a specific budget to invest and aims to maximize their income as a percentage of the total investment. By applying numerical methods and logical reasoning, we will solve a practical investment problem and provide insights into effective financial management strategies.

Problem Statement

A man has P16,000 to invest. He can allocate part of this amount at 8% and the other at 12%. To achieve an income of 9% on his total investment, we need to determine the optimal allocation of funds between the two interest rates.

Objective

The objective is to identify the amounts that should be invested at each rate to meet the financial goal of earning 9% of the total investment.

Solution

Let's denote the amount invested at 12% as x and the amount invested at 8% as 16000 - x. The total income from these investments after one year should be 9% of P16,000, which is P1,440.

The equation for the total income can be formulated as:

[12% times x 8% times (16000 - x) 9% times 16000]
(1)

First, let's expand and simplify the equation:

[0.12x 0.08(16000 - x) 0.09 times 16000]
[0.12x 1280 - 0.08x 1440]
[0.04x 160]
[x 4000]

From this, we conclude that P4,000 should be invested at 12%.

Consequently, the remaining amount will be invested at 8%:

[16000 - 4000 12000]

Verification

To verify our solution, we calculate the interest earned from each investment:

(1) Interest from P4,000 at 12%:

[0.12 times 4000 480]

(2) Interest from P12,000 at 8%:

[0.08 times 12000 960]

Adding these amounts:

[480 960 1440]

This verifies that the total income is indeed P1,440, which is 9% of P16,000.

Conclusion

By dividing the P16,000 investment into P4,000 at 12% and P12,000 at 8%, the individual can achieve the desired income. This example highlights the importance of strategic fund allocation in achieving financial goals, particularly in investments with varying interest rates.

Additional Insights

This scenario, while hypothetical, provides valuable lessons in financial planning. It demonstrates how numerical methods can be used to solve real-world investment problems. Effective financial planning often involves making calculated decisions based on available data and goals. By understanding these principles, one can make more informed financial choices and optimize their investments for better returns.

Key Takeaways

Investment Strategy: Identifying the right allocation of funds based on different interest rates. Financial Planning: Calculating the optimal amounts to invest at different rates to achieve a specific income goal. Optimal Investment: Verifying the calculations to ensure the investment plan meets the financial objectives.

Further Reading

For a deeper dive into financial planning and investment strategies, consider exploring resources such as Investopedia and Forbes. These platforms offer a wealth of information on financial management and investment techniques.