Pop quiz: Why is a dollar today worth more than a dollar tomorrow? If you answered, “It isn’t,” then you’re lucky this quiz isn’t graded. Maybe you answered, “Why do I care?” If so, I’d first direct you to my previous post on investing for retirement.

Simply put, a dollar today can earn one more day of interest than a dollar tomorrow. Let me explain:

As young savers and investors, we should be concerned with growing our wealth over time. However, this doesn’t just mean stashing $100 per paycheck in a piggy bank for a year. It means leaving your money somewhere where it can work for you.

Other people and institutions—banks, companies, governments, and more—can make use of your $100. They can use your savings while you don’t need it. That money has a time value. Those institutions are the borrowers and you are the lender. The “rent” these institutions pay for your money is called interest.

Now allow me to give you the long answer.

## Time is Money

The time value of money is simply the idea that money available at the present time is worth more than the same amount in the future due to its potential earning capacity. Knowledge of this concept is invaluable for assessing the fair price of any investment. It makes comparisons between prospective investments less murky and allows one to develop further understanding of financial instruments, markets and risk. A simple mathematical example will illustrate these points:

Suppose you have $100 left over after this month’s expenses. You’d like to find a safe investment that can grow your $100 in one year’s time. Your bank offers you a one-year certificate of deposit (CD) that provides a 5 percent annual interest rate (0.05 when not quoted as a percentage). You decide to put your $100 in the CD. How much will you receive one year from today? If you answered $105, you are correct! Mathematically, this is simply:

$100 * (1.05) = $105

Here, the 1.05 is the gross interest rate, which comes from adding your annual interest rate of 0.05 and 1. In this market, where 5 percent is the prevailing rate of interest, $105 is said to be the future value of $100 over a one-year period. Generalized, the formula for the future value is:

Future Value = Present Value * (1 + r)

Here, r is the interest rate (0.05 in our example). Present value is the value of your *present* sum of money ($100). Imagine instead that you’ve been offered a CD with a 5 percent interest rate. Assume that the prevailing interest rate for safe investments remains at 5 percent. The question becomes: How much should you be willing to pay for this product? If you answered $100, bingo! Finding the present value of a future payoff simply reverses the process of finding the future value. In this case, it is:

Generalized, the formula for present value is:

When finding the present value, r is often called the discount rate instead of the interest rate. There are a few important things to note about these formulas. First, they only work over one period of time. However, as long as the interest rate matches the period of time (e.g., using an annual interest rate for a payoff exactly one year away), they will work. Here is a more general formula that allows multiple time periods to be used:

Future Value _{N} = Present Value * (1 + r)^{N}

N is the number of periods. Using this formula, you can answer questions like, “If you invested your $100 in a five-year CD that pays 5 percent annually, how much would you have in five years?” Hint: N = 5. A caveat with this multi-period formula is that it assumes a compound interest rate. Essentially, that means that your interest will itself earn interest. In our example, not only will your $100 earn 5 percent of interest yearly, but that interest will earn 5 percent in future periods as well.

## Lessons for Investing

By now, the answer to my first question, “Why is a dollar today worth more than a dollar tomorrow?” should be clear. Although one day’s worth of interest will not amount to much, imagine if you invested $100 today at a safe 5 percent annual interest rate. It would more than quadruple to $432.19 in thirty years. That is well worth the time.

Many lessons can be gleaned from the time value of money. Most importantly, time value explains why you should save in an interest-bearing account, rather than hoard cash, and it is the first step toward understanding how different levels of risk affect the prices of assets—a topic for a future post!

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