Simple Interest

Section 2.1 Simple Interest

To determine the amount of interest one should pay for the use of someone else's money, one model is to base the amount of interest according to two conditions:

interest should be directly proportional to the length of time over which the money is lent
interest should be directly proportional to some rate which is based upon the borrower's perceived ability to repay and based upon current market conditions.

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Often, when dealing with monetary value over time one can more easily illustrate the setting using a time line

\begin{matrix} Money Amounts & P & \to & A \\ Time & 0 & \to & t \end{matrix}

$\begin{equation*} \begin{matrix} \text{Money Amounts} & P & \rightarrow & A \\ \hline \\ \text{Time} & 0 & \rightarrow & t \end{matrix} \end{equation*}$

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Definition 2.1.1. Simple Interest.

Simple interest is a cost of funds directly proportional to the principal P, to a constant rate $i\text{,}$ and to the length of the loan $t\text{.}$

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Theorem 2.1.2. Simple Interest Formula.

Using the definition of simple interest 2.1.1 and the idea of direct proportionality between interest earned $I$ and $P\text{,}$ $i\text{,}$ and $t$ (respectively) yields