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 $\$ 3250$ earns $\$ 113.75$ 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

Direct Proportionality

Direct proportionality is a mathematical relationship between two variables in which one is a constant multiple of the other. This concept implies that if one variable increases, the other increases at a rate determined by the constant of proportionality, and vice versa. It is essential in understanding relationships in various fields, including finance, where interest earned is directly linked to the principal invested.

Simple Interest

Simple interest refers to the calculation of interest on the original principal amount of an investment or loan, without accounting for interest on accumulated interest. It is determined by multiplying the principal, the rate of interest, and the time period. This concept is foundational in financial mathematics and helps in understanding how investments grow over a specified period.

Proportionality Constant

The proportionality constant in a direct proportionality relationship is the fixed number that relates the two variables. In the context of simple interest, it represents the interest rate per time period. Determining this constant from known values allows for constructing a mathematical model that can predict or calculate interest for any given principal amount.

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