The given amount of annual interest is earned from a total...

The given amount of annual interest is earned from a total of $\$ 12,000$ invested in two funds paying simple interest. Write and solve a system of equations to find the amount invested at each given rate. $$\begin{array}{lll}\text { Annual Interest } & \text { Rate } \mathbf{1} & \text { Rate } \mathbf{2} \\\text { S500 } & 2 \% & 6 \% \end{array}$$

The given amount of annual interest is earned from a total of $\$ 12,000$ invested in two funds paying simple interest. Write and solve a system of equations to find the amount invested at each given rate.

$$\begin{array}{lll}\text { Annual Interest } & \text { Rate } \mathbf{1} & \text { Rate } \mathbf{2} \\\text { S500 } & 2 \% & 6 \% \end{array}$$

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Key Concepts

Investment Allocation

Investment allocation involves dividing a total sum among different financial instruments or funds, each with its own rate of return. By setting up equations that represent both the total investment and the overall returns earned, one can determine the amount allocated to each option.

Methods for Solving Linear Systems

Techniques such as substitution or elimination are used to solve systems of linear equations. These methods allow for the systematic determination of individual variable values that satisfy all constraints, making them essential for solving many financial and algebraic modeling problems.

Simple Interest

Simple interest is calculated on the principal alone using a constant rate over a given period, without compounding effects. It is commonly applied in scenarios like loans or fixed-income investments where the interest for each period is straightforward to compute.

Systems of Linear Equations

A system of linear equations consists of two or more equations with multiple variables that are solved simultaneously. In finance, these systems can model relationships such as the total amount invested and the corresponding earnings from different interest rates.

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