Money today is worth more than tomorrow: find out why

Summary In finance, there is a fundamental principle: a sum of money in hand today will always have a greater value than the same amount received in the future. This concept of the time value of money allows us to calculate both what our money will be worth in the future and what a sum we will receive later represents today. Through mathematical equations and considering factors such as interest compounding and inflation, we can make smarter investment decisions.

Why does your money lose value over time?

Imagine that someone owes you money. You have two options: receive it today or wait a year. Even though it's the same nominal amount, most people should choose to receive it now. The reason? Because if you have it today, you can place it in some investment that generates returns during that year. When you wait, you lose that opportunity for profit, which is known in economics as the opportunity cost.

Let's consider a concrete case: your friend owes you 1,000 dollars. He offers to give them to you today if you go pick them up, but if you wait 12 months, he will deliver them to you without you having to move. If the idea of going right now doesn't appeal to you, you might think that waiting a year is the same. However, the concept of the time value of money tells us otherwise. In those 12 months, you could deposit that 1,000 dollars in an interest-bearing account or invest them wisely to earn additional returns. Moreover, inflation would cause your money to have less purchasing power, recovering less real value in 12 months.

The two sides of the coin: present value and future value

To better understand this concept of the value of money over time, we need to distinguish two complementary calculations.

The future value answers this question: if I invest money today, how much will I have in the future? We take a current amount and project what that amount will be in the future considering a rate of return.

The present value does the opposite: if someone promises me money in the future, what is the equivalent value of that today? It is useful for assessing whether a future offer is really worth it.

Following our previous example with $1,000, you could calculate how much those $1,000 will be worth in a year if you invest them. Or, if your friend offers to give you $1,030 after a year, you need to know what that represents in today's money.

Formulas to calculate both scenarios

The calculation of the future value is straightforward. If we assume an available interest rate of 2% per year:

For one year: VF = $1,000 × 1.02 = $1,020

If your friend says that his absence will be for two years:

For two years: FV = $1,000 × 1.02² = $1,040.40

The general formula that expresses this is:

VF = I × (1 + r)ⁿ

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

Now, if your friend offers you $1,030 in a year, you need to know if it's a good deal. We calculate the present value by subtracting the effect of time:

VP = $1,030 ÷ 1.02 = $1,009.80

This result means that receiving $1,030 in a year is equivalent to having approximately $1,009.80 today. Your friend is offering you $9.80 more than what you would currently have, so waiting would be worth it.

The general formula for present value is:

VP = VF ÷ (1 + r)ⁿ

Note that both formulas are related and can be rearranged one to obtain the other.

The composition: how your money grows exponentially

The concept of the time value of money becomes more relevant when we consider the composition of interest. Over the years, what starts as a modest amount of money can turn into something significantly larger, simply because interest generates more interest.

In our basic model, compounding occurs annually. However, most financial institutions apply compounding more frequently: quarterly, monthly, or even daily.

To include more frequent compositions, the formula is adjusted as follows:

VF = VP × (1 + r/t)^(n×t)

Where t represents how many times interest is compounded in a year.

Taking our $1,000 with annual compounding at 2%:

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

But if the interest is compounded quarterly (4 times a year):

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

The difference of 15 cents may seem insignificant, but with larger amounts and longer periods, the effect is considerably magnified.

Inflation: the silent enemy of purchasing power

So far, our calculations have not taken inflation into account. What good is it to earn 2% annual interest if prices rise by 3% in the same period? In contexts of high inflation, it is more accurate to subtract the inflation rate rather than just using the market interest rate.

The problem lies in the fact that inflation is difficult to measure and even more difficult to predict. There are multiple indices that calculate price increases, and they do not always coincide. Furthermore, inflation fluctuates according to time and region.

In practical terms, while we can include an inflation adjustment in our models, we have little control over it. The important thing is to recognize that the concept of the time value of money must consider that future money has not only earned interest but also lost purchasing power.

Applications of the concept in the crypto world

The cryptocurrency sector offers multiple scenarios where the concept of the time value of money is directly applicable.

Crypto Asset Staking: If you hold Ether (ETH), you face decisions similar to our example. Do you keep your ETH accessible now, or do you lock it in a staking contract that pays you 2% interest for six months? Present value and future value calculations help you compare different staking opportunities and choose the most profitable one.

Timing of Purchases: The case of Bitcoin (BTC) is interesting. Although it is described as deflationary, its supply gradually increases until it reaches the limit of 21 million. This means that it currently has supply inflation. If you have $50 to invest, should you buy BTC today or wait for your next monthly salary? The concept of the time value of money would suggest doing it immediately. However, the volatility of BTC's price complicates the analysis, introducing additional variables that go beyond the simple calculation of rates.

Return Assessment: When evaluating different yield protocols or lending platforms in cryptocurrency, you need to compare annual rates and periods. The concept of the time value of money provides you with the framework to determine which option maximizes your capital over time.

Conclusion

Although we formalize the concept of the time value of money through equations and case studies, you may have already applied it intuitively in your financial life. Interest rates, returns, and inflation are factors we constantly face in our economic decisions.

For large companies, professional investors, and lenders, these precise calculations of the time value of money concept are critical: even small percentages significantly influence final outcomes. For those investing in cryptocurrencies, this concept remains fundamental when deciding how to allocate capital to maximize returns. Understanding that money today is worth more than money tomorrow is the first step towards more rational and profitable investment decisions.