Simple interest

Banks attract their clients to open accounts, e.g., savings accounts, to deposit their money. These deposited amounts will in turn be invested into products that would derive profit. To reward their clients who might have placed their money elsewhere, banks to pay them interest. In other words, banks are borrowers who pay interest to their clients (lenders) as compensation for using these monies. In the context of bank interest, banks pay interest rates as a reward for saving money.

We begin with a very simple mathematical model for deriving interest \(I\) when a client placed a deposit of a principal
\(\$ P\) in the bank over a period of time of \(T\) years. In this model, the bank pays the client a simple interest based on an interest rate of \(R \%\) calculated per annum. Invoking the Big Idea of Proportionality, since for each year the amount of interest to be paid out is \(\$ \left( \frac{R}{100} \times P \right)\), it follows that the simple interest \(I\) paid out in dollars is given by the formula:

\[I = \frac{R}{100} \times P \times T = \frac{PRT}{100}\]

Thus, the \(A\) total amount in dollars that can be withdrawn at the end of the \(T\) years is

\[A = P + I = P + \frac{PRT}{100} = P \left( 1 + \frac{RT}{100} \right)\]

Simple interest model
Principal = \(\$P\)
Interest rate = \(R\%\) per annum
Time = \(T\) years
Simple interest = \(\$I\)
\[I = \frac{PRT}{100}\]
Amount = \(\$A\)
\[A = P \left( 1 + \frac{RT}{100} \right).\]