# BM3.5 – Calculating the Simple Interest Rate

Chapter 3, Lesson 5

In this lesson students will:

• determine the rate of simple interest given information about the future value, principle amount and term of the investment

## Rate of Simple Interest

#### Using the Future Value Formula

In our last couple lessons, we used the future value formula $FV = P(1+rt)$ to find the future value or principle value of money. In this lesson, we will suppose that we happen to know both the principle and future value of our money. If we know how long the term of the investment is, we can determine the rate of simple interest by rearranging our formula:

\begin{aligned} FV &= P(1+rt)\\ \frac{FV}{P} &= 1 + rt \\ \frac{FV}{P} - 1 &= rt\\ rt &= \frac{FV}{P} - \frac{P}{P}\\ rt &= \frac{FV-P}{P}\\ r &= \frac{FV-P}{Pt} \end{aligned}

#### Using the Interest Formula

While the formula above certainly works, if we realize that $FV - P$ is actually the amount of interest $I$ that we earn in dollars, we can simplify this formula a bit.

\begin{aligned} r &= \frac{FV - P}{Pt} \\ r&= \frac{I}{Pt} \end{aligned}

Of course, this is exactly the formula that we would obtain if we had started with the interest formula $I$ and isolated the rate $r$.

\begin{aligned} I &= Prt \\ Prt &= I \\ r &= \frac{I}{Pt} \end{aligned}

Let’s work through a few examples using the simplified formula.