This one’s going to be all ELI5. Tried to keep out the gory math details for this. Goal is to provide intuition on this topic and help provide a basis for future discussions.

There are a couple of fundamental concepts with regards to money that are useful to understand. One of the most important is the time value of money. This sounds a lot more intimidating that it actually is. The definition is that a sum of money now is worth more than the same amount in the future. Let’s make it concrete and look at a couple scenarios.

### Example #1

You have the following two options in this case —

• Option #1: You take \$100 now with a (almost) risk-free 2.5% interest rate investment.
• Option #2: You take \$100 one year from now.

If you can place your money in an investment like a 1-year US Treasury bond for an interest rate of 2.5%, you take Option #1. You’d invest your money in this bond, and at the end of the year receive \$102.5 (\$100 + 2.5% * \$100). If you took Option #2, at this same time you’d only get \$100. You end up making \$2.50 more with Option #1.

We’re capitalizing on the earning potential of money. Money that rests as cash, isn’t living up to its full earning potential, so generally we invest that money to make use of its potential.

The two follow up ideas are present value (PV) and future value (FV). The present value of money is the current value of a future sum of money based on a discount rate. In contrast, the future value of money is the future value of a current sum of money based on a growth rate.

In the example above where we were looking at time value of money, we were actually calculating the future value of money. In Option #1, the present value of \$100 has a future value of \$102.50 at the end of a year based on an interest, or growth rate, of 2.5%.

### Example #2

Now, let’s take our example above and spice it up. Here’s case #2 —

• Option #1: You take \$100 now with a 2.5% interest rate investment.
• Option #2: You take \$105 one year from now.

Now the question really is – how do we compare the two options? Which one’s better? There are a couple ways to do it.

#### Method #1

Compare the future value of Option #1 with Option #2. From the earlier case we know the FV of Option #1 is \$102.5. This is less than Option #2, so we’d rather go with Option #2.

#### Method #2

Instead of comparing the future values, we can also compare the present values. PV for Option #1 is \$100. What’s the PV for Option #2? In other words, how do you determine what the value of \$105 in a year is right now?

Similar to the interest rate which projects forward in time, we also have the discount rate which projects backwards in time.The discount rate helps us translate some future value of money to the present value. We can determine the PV with some very straightforward math. We can start by using the formula from Option #1 actually.

```P = Principal (initial investment amount)
i = Interest Rate
V = Value after one year

Simple interest formula for one year investment.

V = P + P * i
V = P (1 + i)
P = V / (1+i)

In our example, V is \$105 and I is 2.5% for the 1-year Treasury bond.
Let’s swap out V and i with these values.

P = \$105 / (1 + 2.5/100)
P = \$105 / (1.025)
P = \$102.44```

That’s it! Not too much math. The present value of \$105 at the end of one year is equal to \$102.44 at present. Now, we can ask ourselves is it better to have \$100 or \$102.44 now? Hopefully you answered the latter. Even with this method, we arrive at Option #2 being the best case. It’s important to note that this factors in present value for one year. Things get a little more interesting when looking at multiple discount rates, varying cash flows and discount rates. Let’s table that for later.

A couple important concepts to extract from this. In the equation, the bolded value of 1.025 is the discount factor. It’s a factor that lets us figure out the PV from the FV. The discount rate is the % value of 2.5%.

It’s important to realize the present value calculation depends heavily the discount rate. This number is an estimate – there’s no way to be completely certain what this will be in a year and even less so ten years from now. However, this method is useful in providing a way to compare and evaluate investments.

Hopefully you gained some intuition from the example, but you might be asking what’s the use of this? If you know of potential cash flows in the future, like the \$105 you’d receive in a year, you can effectively compare them with your current investment options. If the present value of these future cash flows is higher than the initial amount you have, then it’s a good option.