Leticia has been tracking two volatile stocks. Stock A over...

Leticia has been tracking two volatile stocks. Stock A over the last year has increased $10 \%,$ and stock $\mathrm{B}$ has increased $14 \%$ (using a simple interest model). She has $\$ 10,000$ to invest and would like to split it between these two stocks. If the stocks continue to perform at the same rate, how much should she invest in each to result in a balance of $\$ 11,260 ?$

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Key Concepts

System of Linear Equations

This key concept involves setting up and solving equations that have multiple unknown variables. In the investment problem, one equation represents the total investment sum while the other links the invested amounts to the overall return after applying the respective percentage increases. Solving these simultaneously helps determine the precise allocation to each stock.

Percentage Increase

This concept involves calculating the increase in value of an investment by a given percentage. In the context of the problem, each stock’s future value is determined by multiplying the invested amount by a factor corresponding to its percentage growth (e.g., 1.10 for a 10% increase), which is typical in simple interest scenarios.

Investment Allocation

Investment allocation is the process of dividing a total available sum among different securities or assets to achieve specific financial outcomes. In the problem, the investor must determine how much to invest in each stock, taking into account their different rates of return, so that the combined future value meets a target amount.

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