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*.

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.

#### 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:

If we were interested in figuring out the total amount of money we had after a period of time, we could add the interest to our principle amount to obtain the *future value* of our initial investment.

However, we know that , 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.

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