An investor will invest a total of 15,000 in two accounts,...

An investor will invest a total of $\$ 15,000$
in two accounts, one paying $4 \%$ annual simple interest and the other $3 \%$. If he wants to earn $\$ 550$ annual interest, how much should he invest at each rate?

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Key Concepts

Simple Interest

Simple interest is a method for calculating the interest charge on a loan or investment based on the original principal. It involves multiplying the principal amount by the interest rate and the time period. This concept is crucial for understanding how interest earnings accumulate in financial investments that do not compound over time.

System of Linear Equations

A system of linear equations is a collection of two or more equations with the same set of unknowns that can be solved simultaneously. In investment and mixture problems, forming equations based on the total amount invested and the total interest earned allows one to determine the individual amounts allocated to different interest rates.

Mixture Problems

Mixture problems involve combining two or more components with different properties to achieve a desired overall characteristic. In the context of investments, this means allocating a total sum across accounts with different interest rates so that the total return meets a specified target. Solving such problems typically requires setting up and solving a system of equations.

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