Let's say you lent your friend $1,000 six months ago. Would you rather they repaid you today or in another six months? The logical choice would be today because then you could put that money in a high-yield savings account or even the stock market and watch it grow to a larger sum over the next six months. This scenario illustrates the time value of money.
What Is the Time Value of Money?
The time value of money is the idea that money received in the present is more valuable than the same sum in the future because of its potential to be invested and/or earn interest. This principle is central to western finance.
Money is worth more in the present than in the future because there's an opportunity cost that comes with not putting it to work. In addition to missing out on interest, gains, and dividends by not geting to use your money right away, there's also inflation, which gradually erodes its value and purchasing power.
In other words, $1,000 a year from now is worth less in real terms than $1,000 now because goods and services will cost more a year from now than they do currently (assuming inflation is positive over that period, which it usually is).
For the reasons listed above, if you're going to part with your money for any period of time, you probably expect a larger sum returned to you than you started with. This is why loans cost money.
Whether you're lending your money or investing it, the goal is to make a gain to compensate you for going without your money for awhile.
Suppose your friend offers to repay you $1,000 today or $1,050 next year. You must consider whether you'd earn more than $50 over the next year by investing your money elsewhere before choosing to delay receiving the payment.
Other factors include your time preference (whether you need the money right now or can wait awhile to get it back) and whether you trust your friend to actually repay you—another reason money is worth more in the present than: It may never materialize in the future. As the saying goes, "a bird in the hand is worth two in the bush."
Why Does Money Have a Time Value?
The time value of money matters because people and businesses use money—often on a daily basis—to purchase goods and services and invest in securities. American financial systems are driven by the idea that lenders and investors earn interest paid by borrowers in an effort to maximize the time value of their money.
Your job within this system is to limit the cost of money to you and to increase the returns on your investments. This way, you can maximize the value—in real terms—of your money both now and in the future. This concept isn't new; it dates back to ancient times.
How to Calculate the Time Value of Money
So, how do we measure the time value of money? The formula takes the present value of money, then multiplies it by compound interest for each of the payment periods and factors in the time period over which the payments are made.
Time Value of Money Formula
Formula: FV = PV * [ 1 + (i / n) ] ^ (n * t)
- FV: Future value (how much money you'll have in the future)
- PV: Present value (how much money you have now)
- i: Interest rate
- n: Number of compunding periods per year
- t: Number of years
For instance, if you start with a present value of $2,000 and invest it at a 10% interest rate (compounded once annually) for three years, you
FV = $2,000 * (1 + (10% / 1) ^ (1 * 3)
FV = $2,000 * (1.1) ^ (3)
FV = $2,000 * 1.331
FV = $2,662
How Do Interest Rates Affect the Time Value of Money?
Interest is essentially the price an entity pays for borrowing money. In other words, interest payments compensates a lender for the time they spend apart from their money. Interest rates are expressed as a percentage of a principal amount charged at specific intervals (often annually).
Usually, the longer someone lends their money to another party, the higher the interest rate they charge for it. For instance, a 15-year, fixed-rate mortgage usually commands a lower rate than a 30-year mortgage of the same type.
Likewise, an interest-bearing investment like a bank certificate of deposit usually pays a lower interest rate the shorter the term. If you commit to leaving your money in the account longer, you're often rewarded with a higher interest rate.
Interest rates are either simple or compound and either fixed or variable. Let's dig into the differences.
Simple vs. Compound Interest
Simple interest is only ever charged on the principal amount borrowed. For example, if Party A lent $1,000 dollars to Party B at a 10% annual simple interest rate, they would receive $100 (10% of the $1,000) for each year Party B had the use of that money.
Compound interest, on the other hand, is paid on both the principal amount and any accrued interest. For example, using the scenario above, Party A would still receive $100 (10% of $1,000) after the first year, but after the second year, they would receive $110 (10% of $1,100), and after the third year, they would receive $121 (10% of $1,210), and so on.
Fixed Interest Rates vs. Variable Interest Rates
Fixed interest rates don't change over time. If you have money invested in a certificate of deposit (CD), chances are it pays you a fixed interest rate. The opposite of that is a variable rate, which is an interest rate that changes depending on how much benchmark rates rise or fall in the open market. A loan with a variable rate recalculates the interest paid or charged periodically.
Loans with variable interest rates (like certain mortgages) can be dangerous because borrowers can start off paying a low interest rate, but if interest rates go up in general, they may have to start paying a higher interest rate, which increases the total amount they'll eventually have to pay.
Opportunity Cost and the Time Value of Money
When thinking about the time value of money, its important to also consider opportunity cost. Any time you do something with your money, you forgo the benefits of making an alternative choice.
For example, if you put $1,000 in a CD with a fixed interest rate of 2% per year, you may be foregoing an opportunity to earn a 10% return by instead putting that money into an ETF or mutual fund that invests in the stock market.
Alternatively, if you have $1,000 in credit card debt, and your credit card charges you a 13% interest rate, you'd save more money by paying that balance off than you would make investing $1,000 in a CD, even if that CD had an interest rate of 10%.
