# BM4.6 – Discounting Money Using Compound Interest

Chapter 4, Lesson 6

In this lesson students will:

• recall the time value of money concept
• discount money using the compound interest formula

## Discounting Money

#### Time Value of Money

Recall that we discussed the time value of money principle in Lesson 3.4. In this principle, we assume that money has earning potential over time. This means if we would like to compare two monetary amounts, we must ensure we are comparing them at the same time periods.

Suppose we have two payments: a payment of $\500$ one year in the future, and a payment of $\1000$ six years in the future. 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 being paid out at two different time periods. To determine the solution to this problem, we use the discounting technique discussed in the lesson linked above.

#### Calculating the Principle Amount

Let’s determine the discounting formula for compound interest. Recall that discounting is a way to remove the accrued interest, and will allow us to compare monetary amounts at the present day. You may also think of it as calculating the principle amount of money. We can rearrange our compound interest formula to solve for $P$ and this will allow us to calculate the principle amount of money.

\begin{aligned} FV &= P \left( 1 + \frac{r}{f} \right)^{t \times f}\\ P \left( 1 + \frac{r}{f} \right)^{t \times f} &= FV\\ P &= \frac{FV}{\left( 1 + \frac{r}{f} \right)^{t \times f}} \end{aligned}

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