The Time Value of Money: What Is It and How Is It Calculated?

Let’s start with a hypothetical situation: Say someone offers you the chance to take $100 today, or $100 in a year. At first blush, it seems there’s no difference between the two. After all, the money would seem to be the same — $100 equals $100. Easy, right?

Wrong.

According to the time value of money (TVM) theory, the money you get today, or your present money, will be worth more than your future money because you can invest it, thereby increasing its value.

How does this work? Let’s dive in to explore further.

What Is The Time Value Of Money?

Let's begin by defining the time value of money, a core principle of personal finance that illustrates the importance of investing. This principal holds that the value of a dollar today is worth more than the value of a dollar in the future because the money you have today can be invested, which could enable it to grow into a larger amount in the future through the power of compounding interest.

When you accrue interest on your money, it increases in value. This increase leads to a higher base for future interest calculations because of compound interest, which is the interest calculated not only on the initial principal sum invested but also on the accumulated interest from previous periods. In other words, compound interest means the money you earn in interest is automatically reinvested and generates additional interest itself, causing your investment to grow at an exponentially higher rate over time compared to simple interest.

The concept of the time value of money and the compounding effect of interest are fundamental to understanding investment growth, making it crucial for effective financial planning and decision-making regarding savings, investments, loans, and other financial instruments that involve future cash flows.

For instance, let’s use the $100 example that we mentioned earlier. If you invest $100 and it earns an annual interest rate of 6%, it will become $106 at the end of a year. That may not seem like a life-changing amount of money, but it’s more than $100, no? Apply that principle to a higher amount of money and add compounding interest to the mix, and you can understand the concept — and appeal — of TVM.

Inflation’s Relationship With TVM

Another factor to consider when analyzing TVM is the effect of inflation, which is when the price of goods rises over time due to various economic factors (rising wages leads to more people buying more things, which in turn changes the dynamics of supply/demand, etc.). This increase in costs lowers the purchasing power of money and reduces the real rate of financial return.

In other words, it’s another reason that money today has more value than money in the future: A given sum of money today can buy more goods and services than that same amount in the future.

When calculating the future value of money, inflation must be considered because it reduces the real rate of return. High inflation rates decrease the time value of money more rapidly, making future dollars’ worth relatively less compared to present dollars because the cost of goods is higher.

The Time Value Of Money Formula

The time value of money isn’t just an abstract concept — there are ways to calculate the actual final figure. The formula that helps you tabulate this figure is:

FV = PV x [1 + (i / n)] ^(nxt)

Here’s what each item in the formula represents:

• FV: Future value, or the final amount of money remaining after the investment has grown
• PV: Present value, or the initial amount of money invested
• i: Interest rate, or the amount of interest being earned on the initial investment
• n: Number, or the number of compounding periods per year (12 for monthly compounding, 1 for annual compounding)
• t: Time, or the number of months (or years) the investment will remain before it is withdrawn

The Importance Of Understanding TVM

Once you grasp the critical nature of TVM, you can see how it can help you make smarter financial decisions. For instance:

• When you try to make your money work, one decision to make is whether to opt for long-term or short-term investments. While both options have some benefits, TVM holds that longer investments enable the compounding effect of interest to work, resulting in higher potential returns.
• When you want to purchase a car, you have several options: you can either lease one or buy one — and if you opt for the latter, you have to determine how much money to use as a down payment. According to TVM, leasing may be favorable if you prioritize lower short-term cash payments because you can invest the difference. But if plan to keep the car for an extended period and can afford the higher initial cash outflow, TVM would hold that you should purchase the car and make a lower down payment so you can invest the money that you’re not paying for the car while also using the car as a future asset.
• When you’re deciding how much money you need to retire, TVM holds that you should start as early as possible and contribute as much as possible. Because the earlier you start saving for retirement, the more time your money can grow through the compounding effect of interest (or investment returns).
• When deciding whether to rent or purchase a home, the concept of TVM would favor the idea of buying a home. Because while renting may be cheaper initially, you don’t build up any equity in the property — which means it has no future value. The future value of the home's equity, combined with its potential appreciation and potential tax benefits, would favor buying a home over renting it.

Future Value Of Money Vs. Present Value Of Money

Future Value Explained

Because variables like interest rates and market returns fluctuate, there’s no rock-solid way of determining how much your money will be worth in the future. The future value, however, can provide a reasonable estimate.

Here’s the formula to determine future value:

Future Value (FV) = Interest Rate (R) x Principal Amount (P) x Number of Years (T)

This formula can be used when you want to determine how much a certain amount of money — an investment, for instance — will be worth in the future.

Present Value Explained

The present value of money helps determine the current worth of a future sum of money. In other words, let’s say you have the opportunity to receive $10,000 in 5 years. The present value calculation would tell you how much that amount is worth today.

There is a formula that determines the present value of money:

PV = FV / (1 + r)^n

Where:

PV = Present Value

FV = Future Value

r = Interest Rate (or the required rate of return)

n = Number of time periods

The Bottom Line: Knowing the Value of Money over Time Helps Inform Your Financial Decisions

If you are trying to take charge of your financial future, it’s critical to have a deep understanding of how it works and its value — now, and in the future. One way to exert control over your finances is to download the Rocket Money^SM app, which can enable you to monitor your financial situation.