# BM3.6 – Calculating the Term of the Investment

Chapter 3, Lesson 6

In this lesson students will:

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

## Term of Investment

#### Using the Future Value Formula

Often when working with loans and investments, we are interested in the length of time it will take to reach a certain goal. The length of time required to obtain a certain future value of money is sometimes called the term of the investment. Similar to what we did in our last lesson, we can begin with our future value formula and solve for the time variable $t$.

\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}\\ t &= \frac{FV-P}{Pr} \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} t &= \frac{FV - P}{Pr} \\ t&= \frac{I}{Pr} \end{aligned}

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

\begin{aligned} I &= Prt \\ Prt &= I \\ t &= \frac{I}{Pr} \end{aligned}

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