What is the time value of money?

Overview

The value we each place on money is a compelling topic. Some people seem to value money less, while others are willing to work harder for it. Although these ideas are abstract, there's a well-established framework for evaluating the value of money over time. Have you ever considered whether it's better to receive a larger raise at the end of the year or a smaller one right now? If so, it's a great time to learn about the time value of money.

Introduction to the Time Value of Money

The time value of money (TVM) is a core principle in economics and finance. It states that receiving a sum of money now is preferable to receiving the same amount in the future. This concept hinges on opportunity cost: if you choose to receive the money later, you forfeit the chance to invest or use it for other valuable purposes today.

Consider a practical example. Suppose you loaned $1,000 to a friend a while ago, and now your friend is ready to repay you. They offer to give you the $1,000 today, but only if you collect it immediately, since they're leaving for a yearlong trip around the world tomorrow. If you can't collect it today, they promise to repay you the $1,000 when they return, in 12 months.

You might decide to wait 12 months if you're too busy now. However, according to TVM, you should collect the money today. You could deposit it in a savings account to earn interest or invest it for potential profits over those 12 months. Inflation would also reduce the purchasing power of your money after a year, meaning you'd effectively get back less than you lent.

This raises an important question: how much should your friend pay you after 12 months to make waiting worthwhile? At a minimum, your friend needs to compensate you for the potential earnings you could have made during those 12 months.

What Are Present Value and Future Value?

We can distill this discussion into the concise TVM formula. But first, we need to calculate two key metrics: the present value and the future value of money.

Present value tells you what a future sum is worth today, using current market rates. In our example, you might want to know the true value today of the $1,000 your friend will pay you in a year.

Future value works in reverse. It calculates what a sum of money today will be worth in the future, given a particular market rate. So, the future value of $1,000 after one year would include a year’s worth of accrued interest.

Calculating the Future Value of Money

Calculating the future value (FV) of money is straightforward. Returning to our example, assume a 2% interest rate as a potential investment opportunity. If you invest the $1,000 today, its future value after one year would be:

FV = $1,000 × 1.02 = $1,020

If your friend extends the trip to two years, the future value of your $1,000 becomes:

FV = $1,000 × 1.02² = $1,040.40

In both cases, we use compound interest. The general future value formula is:

FV = I × (1 + r)ⁿ

Where I is the initial investment, r is the interest rate, and n is the number of periods.

You can also substitute I with the present value, as we'll cover later. Knowing the future value helps you plan and estimate how much your investments today will be worth in the future. Future value is especially useful when you need to choose between receiving money now or later.

Calculating the Present Value of Money

Calculating present value (PV) is similar to calculating future value. Here, you estimate what a future sum is worth today by reversing the future value calculation.

Suppose your friend offers to repay you $1,030 after one year instead of $1,000. You need to determine if this is a good deal. Using the same 2% interest rate, you calculate PV as follows:

PV = $1,030 / 1.02 = $1,009.80

This means your friend is offering a better deal—the present value is $9.80 more than what you’d get if paid immediately. In this case, waiting a year could be worthwhile.

The general present value formula is:

PV = FV / (1 + r)ⁿ

As you can see, you can rearrange the FV and PV formulas to derive the TVM formula.

Effects of Compound Interest and Inflation on the Time Value of Money

The PV and FV formulas provide a solid foundation for discussing TVM. We’ve introduced compound interest, but let’s expand on it and see how inflation impacts these calculations.

Impact of Compound Interest

Compound interest creates a snowball effect over time. A small sum can grow significantly larger than with simple interest. In our model, we considered annual compounding, but you can compound more frequently, such as quarterly.

To account for this, adjust the formula as follows:

FV = PV × (1 + r/t)^n×t

Where PV is the present value, r is the interest rate, and t is the number of compounding periods per year.

Let’s use the 2% annual compound interest rate and apply it to $1,000, compounded once a year:

FV = $1,000 × (1 + 0.02/1)^1×1 = $1,020

This matches our earlier calculation. However, if you compound returns four times per year, the result increases:

FV = $1,000 × (1 + 0.02/4)^1×4 = $1,020.15

While a 15-cent difference may seem small, with larger sums over longer periods, it becomes significant.

Impact of Inflation

So far, we haven’t factored inflation into our calculations. What’s the benefit of a 2% annual interest rate if inflation is 3%? During high inflation, it’s often better to use the inflation rate in your calculations instead of the market interest rate. This approach is common in salary negotiations.

However, measuring inflation is complicated. Various indexes track price increases for goods and services, and they often yield different inflation rates. Unlike market interest rates, inflation is also hard to predict.

Ultimately, there’s little you can do about inflation. You can include a discount factor in your model, but as mentioned, inflation can be extremely unpredictable in long-term forecasts.

How the Time Value of Money Applies to Cryptocurrencies

The crypto space offers many opportunities. You can choose between receiving a crypto amount now or a different value in the future. Locked staking is one example: you can keep your Ethereum (ETH) or lock it away and redeem it in six months at a 2% interest rate. You might even find another staking opportunity with a higher yield. Simple TVM calculations help you identify the best investment options.

On a more abstract level, you might wonder when to buy Bitcoin (BTC). Although BTC is often called deflationary, its supply actually rises slowly, so technically it’s inflationary. Should you buy $50 worth of BTC now or wait for your next paycheck and buy $50 next month? TVM calculations recommend buying now, but price volatility makes the real scenario more complex.

Final Thoughts

While we’ve defined TVM formally, you’re likely already using the concept intuitively. Interest rates, returns, and inflation are part of everyday financial life. The formal approaches outlined here are crucial for large companies, investors, and creditors. For them, even a fraction of a percent can greatly impact profits and outcomes. For crypto investors seeking better returns, understanding TVM is essential when deciding how and where to invest.

FAQ

Is the time value of money an important concept? Why does it matter?

Absolutely. Money is worth more today than in the future due to inflation and investment opportunities. This knowledge helps you make better financial decisions and maximize crypto gains.

What is the difference between present value and future value of money?

Present value is what a future payment is worth today. Future value is what today’s amount will be worth in the future, taking into account interest rates and elapsed time.

How does the time value of money affect my investment and savings decisions?

The time value of money affects your decisions by factoring in inflation and interest rates. Money today is more valuable than tomorrow, so investing early maximizes returns. Interest rates help you choose between saving and investing in crypto, balancing future gains with present costs.

How do you calculate present and future value using interest rates and inflation?

For future value, use FV = PV × (1 + i)ⁿ, where i is the interest rate. For present value, invert the formula: PV = FV ÷ (1 + i)ⁿ. To adjust for inflation, subtract the inflation rate from the nominal rate to get the real rate of return.

Why is money today worth more than the same amount in the future?

Money today can be invested to generate returns, and inflation erodes future purchasing power. A dollar now offers immediate earning potential that future money cannot match.