## More on the Time Value of Money

Read this section that discusses the time value of money. "Why is the time value of money important?". The answer to this question lies in the concepts presented in this section. In finance, a dollar is more valuable today than it is one year or ten years from now. To explain why this is the case, we will give formulas and examples to demonstrate how money is used. As part of this discussion, we will also address why a dollar is worth more today than in the future. Pay particular attention to the definitions and problems presented related to interest rate, future value, and present value.

### Defining the Time Value of Money

The Time Value of Money is the concept that money is worth more today that it is in the future.

#### LEARNING OBJECTIVE

• Identify the variables that are used to calculate the time value of money

#### KEY TAKEAWAYS

##### Key Points
• Being given $100 today is better than being given$100 in the future because you don't have to wait for your money.
• Money today has a value (present value, or $PV$) and money in the future has a value (future value, or $FV$).
• The amount that the value of the money changes after one year is called the interest rate ($i$). For example, if money today is worth 10% more in one year, the interest rate is 10%.

##### Key Terms
• Present Value ($PV$): The value of the money today.
• Interest Rate ($i$ or $r$): The cost of not having money for one period, or the amount paid on an investment per year.
• Future Value ($FV$): The value of the money in the future.

One of the most fundamental concepts in finance is the Time Value of Money. It states that money today is worth more than money in the future.

Imagine you are lucky enough to have someone come up to you and say "I want to give you $500. You can either have$500 right now, or I can give you $500 in a year. What would you prefer?" Presumably, you would ask to have the$500 right now. If you took the money now, you could use it to buy a TV. If you chose to take the money in one year, you could still use it to buy the same TV, but there is a cost. The TV might not be for sale, inflation may mean that the TV now costs $600, or simply, you would have to wait a year to do so and should be paid for having to wait. Since there's no cost to taking the money now, you might as well take it. There is some value, however, that you could be paid in one year that would be worth the same to you as$500 today. Say it's $550 - you are completely indifferent between taking$500 today and $550 next year because even if you had to wait a year to get your money, you think$50 is worth waiting.

In finance, there are special names for each of these numbers to help ensure that everyone is talking about the same thing. The $500 you get today is called the Present Value ($PV$). This is what the money is worth right now. The$550 is called the Future Value ($FV$). This is what $500 today is worth after the time period ($t$)- one year in this example. In this example money with a $PV$ of$500 has a FV of \$550. The rate that you must be paid per year in order to not have the money is called an Interest Rate ($i$ or $r$).

All four of the variables ($PV$, $FV$, $r$, and $t$) are tied together in the equation in . Don't worry if this seems confusing; the concept will be explored in more depth later.

$F V=P V \cdot(1+r t)$

Simple Interest Formula: Simple interest is when interest is only paid on the amount you originally invested (the principal). You don’t earn interest on interest you previously earned.

Source: Boundless