# BM3.3 – Future Value of Money Using Simple Interest Chapter 3, Lesson 3

In this lesson students will:

• use a time diagram to organize questions involving multiple payment streams
• calculate the future value of money using the simple interest formula

## Future Value of Money

#### Time Diagrams

Often when working with loans or savings, there are multiple times at which a person will make payments or deposit money. When this occurs, it is often helpful to organize the payments along a payment stream line making note of the dates and times of the payments. This payment stream line is known as a time diagram. When calculating a future value we will use an arrow to the right in a time diagram.

A time diagram will not only help you organize your thoughts, it can also indicate whether or not we will be applying a formula to calculate a future value of the payment, or discount the payment (more on discounting in Lesson 3.4). We can indicate future value by drawing an arrow to the right, and a discount by drawing an arrow to the left. Other important information that might help with calculations can be placed on these arrows as well. When calculating a principle value we will use an arrow to the left in a time diagram.

#### Future Value Formula for Simple Interest

Recall that we can calculate the simple interest, in dollars, that money will earn by applying the following formula: \begin{aligned} I &= Prt. \end{aligned}

If we were interested in figuring out the total amount of money we had after a period of time, we could add the interest $I$ to our principle amount $P$ to obtain the future value $FV$ of our initial investment. \begin{aligned} FV &= P + I \end{aligned}

However, we know that $I = Prt$, so making this substitution and cleaning our formula up a bit, we obtain a new formula that can be used to quickly calculate the future value of money that earns simple interest. \begin{aligned} FV &= P + I \\ &= P + Prt \\ &= P(1 + rt) \end{aligned}

The following video will work through two examples where we utilize the future value formula for a simple interest problem.