Imagine a scenario where someone is gifting you $10,000. You can have the money now, or you can have the money in five years. Which would you choose?
Most people would take the money now, and not just because a tropical vacation now is a heck of a lot more enticing than a tropical vacation in five years. Money received now can be invested during those five years, earning a rate of return. That money could be used to pay off debt, saving in interest costs.
Therefore, a dollar now is worth more than a dollar in the future. And for this reason, timing does matter when it comes to assessing the value of a dollar. Said another way, money has a time value.
There is no single time value of money formula, because there are multiple applications for its use. Here is a look into a few of those uses, and why it’s so important for savers and investors.
What Is the Time Value of Money?
The time value of money is the relationship between a dollar at one point in time and the value of that same dollar at another point in time. For example, $50 today likely won’t have the same value as $50 a year from now, just as $1 million now is not the same as $1 million 20 years ago.
Several forces are at play here. First, there is the potential for both interest to be earned (on an investment) and income to be paid (on debt). Inflation, the rising of prices over time, is also a consideration. As goods get more expensive, each dollar can accomplish less.
The time value of money is a framework for comparing lump sums of money and/or periodic payments across different time frames. Dollars can be future, present, or past.
When extrapolating a value of some dollar figure in the future, a future value calculation is used. When recalibrating the value of money to a current dollar figure, it’s called a present value calculation. There are as many applications as there are real-life scenarios where dollars at different points in time require thoughtful comparison.
The time value of money equation always has two sides: a borrower and a lender, a payer and a payee, or even a gift giver and a receiver. Time value of money can consider either side of the equation, whether those dollars are flowing in (as money received) or flowing out (money paid).
No matter which direction the money is moving, time value accounting considers that the dollars may be subject to interest payments, and that interest may or may not be compounding.
If you were to open a textbook to find a simple problem regarding the time value of money, it might look like this: You have two options. Either you make a $400 payment today, or pay $100 each year for the next five years, resulting in a total payment of $500.
As you might sense, it is not totally logical to compare only the two sums of money. Time must also be considered. Such a problem may ask a student to calculate the present value of the five periodic payments using some provided interest rate. By accounting for time, it is possible to make a more accurate comparison of the two sums.
The time value of money may seem like a purely academic concept, but has plenty of real-world applications. (And not just in a hypothetical gift of $10,000 paid to you by some long-lost aunt.) The time value of money is used in personal finance, real estate, and investing decisions.
Real-Life Applications of the Time Value of Money
To solve a time value of money problem, you can use a financial calculator or spreadsheet. If the formula is complicated—if, say, compound interest is involved—you might be able to find published tables with the information. This could be easier than performing the calculation.
Here are a few examples of the real-world use of time value of money formulas. Consider investors who buy a property. They will have tenants and will collect rental payments. Because future payments are not worth as much as current payments, time value of money provides the formula that investors can use to determine the value of those future payments.
Here’s another: Use the time value of money to discount the value of some future property or sum of money into today’s dollars. For example, an investor may think a property in a high-growth neighborhood will be worth a certain amount in five years. A time value formula allows the investor to discount the value to determine the current, approximate value of the home—aka the present value.
The time value of money for “sinking funds” is an application that just about any saver will find useful. Say that you are saving up for something in the future, like a kitchen remodel. Perhaps you’re hoping to save $20,000. How much money do you need to save in each of the next five years, if you are earning interest? The sinking fund factor is a time value of money formula that will come in handy.
One last helpful (and dare we say, exciting) example of a time value of money calculation: What is the value of some future dollar if that dollar is invested today, earning a compounding rate of return? For example, imagine your hypothetical $10,000 gift, invested and earning a 7% rate of compounding returns. What will the value of this gift be after 30 years? Forty? Fifty?
Although it’s easy to find an online compound returns calculator , there is a time value of money formula for this.
Time Value of Money and Compound Returns
For the individual investor, there is perhaps no way in which the time value of money is more important than with earning compound returns.
To earn compound returns is to earn a rate of return on both the initial principal invested and all previous profits. As profits grow, so does the potential to earn more and more—and all that this exponential growth requires is that you stay invested.
The key to harnessing the raw power of compound returns is to spend as much time invested as possible. Each year of positive returns is fuel for greater future returns. This can be hard for investors to wrap their heads around because the most powerful results can take decades to reveal themselves. To understand compound returns, it helps to start with a comparison to simple returns.
With simple returns, a rate of return is produced on the principal investment in each period. An example is a bond that pays a 5% rate of return on $1,000 each year for five years. Each year, the bondholder receives a $50 payment ($1,000 x 5%). The amount is not reinvested, and the $1,000 principal is returned at the end of the five years. The investor makes a total profit of $250 (5 x $50).
Compare that to a 5% compounding rate of return. Envision a $1,000 investment in a stock. Each year, the investment grows by 5%. After the first year, the stock is worth $1,050. In year two, that 5% rate of growth applies to both the initial $1,000 investment and the $50 profit from the first year, resulting in a profit of $52.50. The investor is earning a rate of return on a bigger sum of money with each passing year (assuming only positive growth)—without adding money.
At the end of the five years, the investor’s initial $1,000 investment has grown to approximately $1,276. This is a total profit of $276, compared to simple interest’s $250. While this might not seem like much, this gap will continue to grow as compound return growth increases.
Factors Affecting Compound Returns
There are four variables at play when calculating compound returns: the rate of return, the principal invested, the duration, and the frequency of compounding. (Does compounding happen monthly? Annually?)
Check out a compound returns calculator for a better understanding of how these variables interplay. What you’ll find is that all factors can have a powerful impact on the outcome.
Investors should also consider inflation. Inflation, or rising prices over time, also has a compounding effect. There is certainly a time value of money formula for inflation, though in this context it might be easier to simply subtract the expected rate of inflation from the expected rate of investing returns.
You do not have to invest in an individual stock to harness the power of compound returns. The effect works with any investment where the profits are reinvested, whether automatically or manually.
A look at a dollar at one point in time and the same dollar at another point in time: That’s the time value of money, a concept with lots of real-world applications. For individual investors, probably the most important application of the time value of money relates to compound returns.
There are lots of options for getting invested and achieving compound returns, ranging from the involved to the hands-off.
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