Simple Interest The simple interest on an investment is...

Simple Interest The simple interest on an
investment is directly proportional to the amount of
the investment. An investment of $\$ 3250$ will earn
$\$ 113.75$ 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

Simple Interest

Simple interest is a method for calculating the interest earned or paid on a principal amount where the interest rate is applied only once per time period, without compounding. It models the linear growth of an investment or loan over time by multiplying the principal by a constant rate and the time period.

Direct Proportionality

Direct proportionality describes a relationship between two variables in which one variable is a constant multiple of the other. In the context of simple interest, the interest earned is directly proportional to the amount invested, meaning if the investment increases, the interest increases by the same fixed factor.

Interest Rate Calculation

The interest rate in simple interest calculations is the constant factor that relates the principal to the interest earned. It can be determined by dividing the interest by the principal, establishing a fixed rate that applies uniformly over each time period.

Mathematical Modeling

Mathematical modeling involves creating algebraic expressions to describe real-world phenomena. In this context, it means formulating an equation that represents the relationship between the amount invested and the interest earned, such as I = kP, where k is the per annum interest rate.

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