# BM3.4 – Discounting Money Using Simple Interest

Chapter 3, Lesson 4

In this lesson students will:

• understand the time value of money concept
• discount money using the simple interest formula

## Discounting Money

#### Time Value of Money

Suppose we want to compare amounts of money that are given at different reference points in the future. For example, let’s consider $\960$ three months in the future, and $\1000$ one year in the future. Assuming a fixed simple interest rate of $5\%$, which of these two values is worth the most today?

One might be tempted to state that the $\1000$ is worth more; however, we cannot compare these two values at the moment since they are at two different time periods (one is a year from now, the other is three months from now). In order to compare two monetary values, we must ensure that they are compared at the same reference point in time, taking into account any interest rates. This is known as the time value of money – we always assume that money has earning potential over time.

#### Calculating the Principle Amount

To help us answer the question posed above, we could remove the simple interest that was earned over time to compare both of these values at the present day. The action of removing interest from an amount of money is sometimes called discounting. You may also think of it as calculating the principle amount of money. We can rearrange our simple interest formula to solve for $P$ and this will allow us to easily calculate the principle amount of money. This is often helpful when comparing monetary values when we have to take into account the time value of money.

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

Let’s apply this formula to our problem from above to see which monetary value is worth the most today.