You are given the total annual interest earned from a total...

You are given the total annual interest earned from a total of $$\$ 12,000$$ invested in two funds paying the given rates of simple interest. Write and solve a system of equations to find the amount invested at each rate. See Example 2. $$ \begin{array}{lll} \quad \text { Annual Interest } & \text { Rate I } & \text { Rate 2 } \\ \quad \$ 500 & 3 \% & 5 \% \\ \end{array} $$

You are given the total annual interest earned from a total of $$\$ 12,000$$ invested in two funds paying the given rates of simple interest. Write and solve a system of equations to find the amount invested at each rate. See Example 2.
$$
\begin{array}{lll}
\quad \text { Annual Interest } & \text { Rate I } & \text { Rate 2 } \\ \quad \$ 500 & 3 \% & 5 \% \\
\end{array}
$$

Key Concepts

Simple Interest

Simple interest is a method of calculating the interest charged on a principal amount by applying a constant rate over the period of investment or debt. Unlike compound interest, it does not consider interest on previously earned interest, making it a linear calculation based solely on the initial amount and the given rate.

System of Linear Equations

A system of linear equations consists of multiple equations that are solved together to find the values of unknown variables that satisfy each equation simultaneously. In finance, such systems are used to compute different portions of an investment distributed across various interest rates by equating the sum of the earnings to a known total.

Variable Assignment

Variable assignment involves defining symbols to represent unknown quantities in a problem. This step is fundamental when translating word problems into mathematical expressions, as it allows for the creation of equations that model the relationships between different financial quantities.

Problem Translation

Problem translation is the process of converting a real-world scenario into mathematical expressions or equations. This involves identifying the key components of the problem – such as the total investment, individual interest rates, and total interest earned – and expressing the relationships among them using appropriate mathematical models.

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