Time is money: An introduction to financial calculators

Have you ever shopped around for a mortgage or auto loan? Have you invested in a certificate of deposit or Treasury bond, or looked at a chart of stock market returns? Or are you an older investor who’s been pitched a guaranteed lifetime income through an annuity?

Understanding the time value of money

Time is money.

You’ve no doubt heard that before, but what does it mean? Simply put, if you have money you’re not using, you can let someone else (such as a bank or the U.S. Treasury) use it for a certain amount of time, and they’ll pay you interest for the privilege. The more time, the more money. Conversely, if you need money to buy a car or home or finance an education, you’ll pay the bank for the privilege of using their money.

When you invest in the stock market, you’re essentially taking an ownership stake in various companies. That investment entitles you to a share of those companies’ earnings now and in the future. As earnings grow, so does the value of your investment.

Let’s start with some terms to understand up front:

• Present value vs. future value. If you have money and invest successfully, you’ll earn a return on it. Those earnings are added to your money pile, which means earnings grow increasingly faster the longer you’re invested. That’s the power of compounding. You can’t earn interest now on money that won’t hit your wallet for another 10 years (and which you may never receive), so future money is worth less, all things considered, than today’s money. In other words, you’d rather have $10,000 today than $10,000 in five years. If you have $10,000 today, and it grows at 6% per year, in five years you’ll have $13,382. (More on that later.)
• Real vs. nominal returns. Inflation erodes your money’s future value. Even inflation as low as 3% per year means money in your wallet now will be worth only about half as much in 20 years. So that nominal return of 6% in the example above would be—assuming annual inflation of 3%—a real (i.e., inflation-adjusted) return of 3%.
• Fixed-rate loans as inflation protection. When you buy a house using a 30-year fixed-rate mortgage, you’re borrowing money and making monthly payments with interest. On the surface, that runs counter to the power of compounding. But you get the house up front, which means you no longer have to pay rent to keep a roof over your head. Plus, you own the asset (the house) in today’s dollars, which essentially shields you from housing price inflation. It’s something to consider when weighing the pros and cons of buying or renting a home.

Time value of money calculator

Getting comfortable with the money math

Pretty much anytime you interact with money, you’ll encounter some version of this same basic money calculator. Some interactions might feel more complex, with more moving parts, but they’re really just different iterations of present value, future value, time, rate of return, and payments. For example:

• A retirement calculator, such as this one in Britannica Money, will ask for your current age, expected retirement age, current savings, how long you’d like your money to last, and a few other things. But it’s really just a more granular view of the basic formula.
• Are you a bond investor? Do you understand yield-to-maturity, why some bonds trade at a premium or discount to par value, and how those values are determined? Same calculator.
• A mortgage or other loan calculator is no different from a compounding calculator, except that with a loan, each payment draws down the balance you owe, rather than adds to the balance you earn. (Remember how the present value was entered as a negative number in the rate of return example?)
• An annuity—where you invest a pile up front (usually to an insurance company) and then receive a monthly payment for decades (or for the rest of your life)—can be quite complex, but really, that’s because of its flexibility. Annuity choices and calculations help the issuer pinpoint the expectations of time, present and future value, payments, and rates of return.
• An annuity is a mortgage—with you on the other side of the table. Think about it: When you take out a 30-year mortgage, the bank gives you a pile of money up front, and then earns a return on that investment for the next 30 years. How is that any different than when you buy an annuity?