The sum of money invested in two savings accounts is 1000 ....

The sum of money invested in two savings accounts is $\$ 1000 .$ If both accounts pay $4 \%$ interest compounded annually, is it possible to earn a total of $\$ 50$ in interest in the first year?
(a) Explain your answer in words.
(b) Explain your answer using a system of equations.

Key Concepts

Compound Interest

Compound interest refers to the method of calculating interest where the interest earned during a period is added to the principal, and in subsequent periods, interest is earned on the increased principal. In a scenario where the interest is compounded annually, the calculation at the end of one year is effectively the same as simple interest. This concept is crucial for understanding how interest accrues over time in various financial products.

System of Equations

A system of equations is a set of equations with multiple variables that are solved together to find a common solution for all variables. In financial contexts, such as allocating investments among accounts, one equation might represent the sum of the invested amounts, while another equation represents the total interest earned. This approach provides a structured method to analyze and solve problems involving multiple interdependent quantities.

Feasibility Analysis

Feasibility analysis involves determining whether a desired outcome is achievable given the constraints and parameters of a problem. In interest calculation problems, this concept is applied by comparing the theoretical maximum interest earned from an investment at a given rate to the target amount. If the maximum possible interest does not meet the target, the desired outcome is deemed unfeasible. This reasoning is fundamental in evaluating financial scenarios and ensuring realistic expectations.

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