# BM3.2 – Calculating Interest Using Simple Interest

Chapter 3, Lesson 2

In this lesson students will:

• understand the difference between simple and compound interest and give scenarios in which one might use each form
• calculate interest in dollars, rate of interest, principle amount, or length of time, given information about the other variables

## Introduction to Simple Interest

#### Simple Versus Compound Interest

Suppose we would like to borrow $\1500$ to purchase a stove for our house. When we borrow this money from the lender, they may charge us some kind of interest on repayment of the loan. In this example, we can think of interest as the amount of money added onto our amount owing during a repayment period. For example, let’s assume the lender applies a $5\%$ rate of interest. This means $\1500 \times 5\% = \75$ in interest would be added onto our bill during the next payment period. We call the initial borrowed amount of $\1500$ the principle amount. This, of course, is a simplistic version of interest that doesn’t take into account other important variables such as time. Let’s dive a bit deeper into the two main types of interest we will look at in our course.

There are two main types of interest used in the world of business: simple interest and compound interest. The focus of the next chapter will be on compound interest – a form of interest in which your interest is permitted to earn interest during future payment periods. The focus of this chapter will be on simple interest – a form of interest in which only the principle amount can earn interest. In general, we often use compound interest for lengthy loans or savings such as mortgages or retirement savings; whereas, simple interest might be used for shorter loans such as borrowing money from a retailer to purchase a household appliance. Simple interest is more advantageous to the borrower since it tends to keep overall interest payments lower when compared to compound interest.

#### Calculating Interest Earned Over One Year

As we can see from our calculation about the stove above, to determine how much interest $I$ in dollars we add to our amount owing, we multiply the principle amount $P$ in dollars by the rate of interest $r$.

\begin{aligned} I &= Pr \end{aligned}

This is a simplified version of simple interest that assumes the length of the loan (or savings) is one year. The video below will work through a few examples of calculating some yearly values.

#### Calculating Interest Earned Over Any Period of Time

In practice, we often require the time of the loan to be prorated for an amount of time more or less than one year. To do this, we introduce a time variable $t$ to our formula:

\begin{aligned} I &= Prt. \end{aligned}

The time variable must be inputted in years. For example, for a three year loan, we use $t=3$ yrs; however, for a three month loan, we use $t=\frac{3}{12}=0.25$ yrs. In general, we use the following denominators when applying prorated simple interest:

• months: denominator of $12$
• weeks: denominator of $52$
• days: denominator of $365$

Let’s work through a few more examples in which we must prorate our interest charges.