Financial Planning A recently retired couple needs 12,000...

Financial Planning A recently retired couple needs 12,000 dollar per year to supplement their Social Security. They have 150,000 dollar to invest to obtain this income. They have decided on two investment options: AA bonds yielding $10 \%$ per annum and a Bank Certificate yielding $5 \%$. (a) How much should be invested in each to realize exactly 12,000 dollar ? (b) If, after 2 years, the couple requires 14,000 dollar per year in income, how should they reallocate their investment to achieve the new amount?

Financial Planning A recently retired couple needs 12,000 dollar per year to supplement their Social Security. They have 150,000 dollar to invest to obtain this income. They have decided on two investment options: AA bonds yielding $10 \%$ per annum and a Bank Certificate yielding $5 \%$.
(a) How much should be invested in each to realize exactly 12,000 dollar ?
(b) If, after 2 years, the couple requires 14,000 dollar per year in income, how should they reallocate their investment to achieve the new amount?

Key Concepts

Financial Modeling

Financial modeling applies algebra and mathematical techniques to represent real-world financial situations. By translating investment goals and constraints into mathematical formulas, it becomes possible to analyze and determine the optimal investment strategy to achieve specific outcomes.

Rebalancing Investments

Rebalancing involves adjusting the distribution of investments over time in response to changes in financial goals or market conditions. In scenarios where income needs change, reallocation of funds between investment options becomes necessary to align the portfolio with the new targets.

System of Linear Equations

This concept involves creating and solving equations that contain multiple variables. In financial planning problems, systems of linear equations are used to represent constraints such as total investment amounts and the income generated from different rates of return in order to achieve a specific target.

Interest Rates and Yields

Understanding interest rates is crucial for calculating the income produced by each investment option. Yields indicate the percentage return on each investment vehicle, and they are essential for determining how much money needs to be allocated to each option in order to meet a desired income.

Portfolio Allocation

This concept relates to how an investor distributes available funds among different investment options. It is a fundamental aspect of financial planning aimed at achieving income goals while balancing risk and return according to the yield rates of the various investments.

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