The simple interest on an investment is directly...

The simple interest on an investment is directly proportional to the amount of the investment. An investment of $\$ 6500$ earns $\$ 211.25$ after 1 year. Find a mathematical model that gives the interest $I$ after 1 year in terms of the amount invested $P$.

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Key Concepts

Simple Interest

Simple interest is a method of calculating the interest charge on a loan or investment based solely on the original principal, without taking into account any interest previously earned or accrued. This leads to a linear relationship between the interest earned and the initial amount invested.

Direct Proportionality

Direct proportionality occurs when two variables increase or decrease in constant ratio, meaning the ratio between them remains the same. In the context of the problem, it indicates that the interest earned is a constant multiple of the amount invested, which can be represented by a straightforward linear equation.

Mathematical Modeling

Mathematical modeling involves formulating real-world scenarios into mathematical expressions or equations. In this problem, the relationship between the interest earned and the amount invested is modeled with a linear equation, which effectively captures the constant rate of interest, allowing predictions or further analysis based on changes in the principal.

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