TL;DR

The time value of money (in English, time value of money or TVM) is an economic/financial concept that states that it is preferable to receive an amount of money now than the same amount in the future. This is because you could invest the money and get returns. This concept can also be used to analyze the present value of a future amount and the future value of a present amount.

It is possible to mathematically represent the TVM through a set of equations. When making decisions based on TVM, it is also common to consider compound interest and inflation.

Introduction

The value each of us places on money is an interesting concept. It may seem that some people value it less than others. Others are willing to work harder for money. While these concepts are abstract, when it comes to assigning value to money over time, there is, in fact, a well-established framework. Have you ever wondered what the better option would be between getting a bigger raise at the end of the year or a smaller raise now? If so, it might be a great idea to learn about the concept of time value of money.

Introduction to the time value of money

The time value of money (TVM) is an economic/financial concept that states that it is preferable to receive an amount of money now than the same amount in the future. Within this decision-making concept is the idea of ​​opportunity cost. By choosing to receive the money later, you lose the opportunity to invest it now or use the money for some other valuable activity.

Let's see an example. Let's say a while ago you lent a friend $1,000 and now they've reached out to you to pay off the debt. He offers you the $1,000 on the condition that you must get the money today, as tomorrow he will begin a year-long trip around the world. If you can't pick it up, he promises to pay the $1,000 as soon as he returns from his trip, within 12 months.

You can even wait 12 months if you are too busy to collect the money. However, following the TVM concept, it would be better to look for it today. You can put the money in a savings account to earn interest/income during these 12 months. Another option would be to invest and generate profits. Furthermore, due to inflation, your money would be worth less after 12 months. In other words, you would effectively receive less than you lent.

An interesting question to consider is: how much would your friend have to pay after 12 months to make the wait worth it? Your friend would need to at least offset the potential earnings you could make over a 12-month period.

What is present value and future value?

We can summarize this entire conversation in a succinct formula known as the TVM Formula. But first, we need to do some other calculations: the present value of money and the future value of money.

The present value of money allows us to know the current value of a future amount, considering market rates. In our example, you might want to know the real value today of your friend's future $1,000 (after one year).

Future value is the opposite. It analyzes an amount of money today and calculates what its value will be in the future, at a certain market rate. Therefore, the future value of $1,000 in one year would include one year's worth of interest.

Calculating the future value of money

Calculating the future value (FV) of money is simple. Returning to our previous example, we will use the interest rate (2%) as a possible investment opportunity. After investing, the future value in one year of the $1,000 you receive today would be:

FV = $1.000 * 1,02 = $1.020

Now imagine that your friend decided to extend the period of the trip to two years. So the future value of your $1,000 would be:

FV = $1.000 * 1,02^2 = $1.040,40

Note that in both cases, we consider compound interest. We can generalize our future value formula:

FV = I * (1 + r)^n

I=initial investment, r=interest rate and n=number of periods

Note that we can also replace I with the present value of money, which we will cover later. And what is the benefit of knowing the future value? Well, it helps us plan and estimate the value of money invested today, in the future. Future value also helps in our previous example, where there is a decision to be made: whether to receive an amount now or in the future.

Calculating the present value of money

Calculating the present value of money (PV) is similar to calculating the future value. Basically, we are trying to estimate how much an amount of money in the future would be worth today. To do this, we invert the calculation used for the future value.

Imagine that your friend tells you that after a year he will give you $1,030 instead of $1,000. However, you need to check whether this is a good deal or not. We can do this by calculating the PV (considering the same interest rate of 2%).

PV = $1.030 / 1,02 = 1.009,80

In other words, your friend is offering a more advantageous deal. The present value is $9.80 more than you would receive from your friend today. In that case, it might be better to wait a year.

Let's look at the general formula for calculating PV:

PV = FV / (1 + r)^n

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

Effects of compound interest and inflation on the time value of money

Our PV and FV formulas provide a great framework for discussing TVM. We've already introduced the concept of compound interest, but let's expand on it further and see how inflation also affects our calculations.

Effect of compound interest

Compound interest has a snowball effect over the years. What starts as a small amount of money can become something much more significant than in cases where only simple interest applies. In our already established model, we analyze the interest composition for a period of one year. However, you can accrue interest more frequently. For example, every quarter.

To incorporate this, let's make some adjustments to our model.

FV = PV * (1 + r/t)^n*t

PV=present value, r=interest rate, t=number of interest accrual periods per year

Let's enter our compound interest rate of 2% per year. In other words, we will apply interest on the $1,000 once a year.

FV = $1.000 * (1 + 0,02/1)^1*1 = $1.020

In this case, the result will obviously be the same as we calculated previously. However, if you have the chance to accumulate your income four times a year, the result will be greater.

FV = $1.000 * (1 + 0,02/4)^1*4 = $1.020,15

An increase of 15 cents may not seem like much, but with larger sums and over longer periods, this difference can be significant.

Effect of inflation

To date, we have not considered inflation in our calculations. What good is an interest rate of 2% per year if inflation is 3%? In periods of high inflation, it may be better to consider the inflation rate in calculations rather than the market interest rate. This is a common measure in salary negotiations.

However, measuring inflation is much more complicated. There are different indices that calculate the increase in the price of goods and services. These indices generally provide different inflation values. Additionally, inflation is difficult to predict, unlike market interest rates.

In short, there is not much we can do about inflation. We can include an inflation discounting aspect in our model, but as mentioned, inflation can be extremely unpredictable when it comes to predicting the future.

How the time value of money applies to cryptocurrencies

There are several opportunities in the crypto sector. You have product options to choose between a crypto amount now or a different amount in the future. Locked staking is an example. You have the option of keeping your Ethereum (ETH) or locking and recovering the amount within six months, with an interest rate of 2%. In fact, you may even find another staking opportunity that offers a better return. Some simple TVM calculations can help you find the best investment product.

Thinking more abstractly, you might be wondering when you should buy Bitcoin (BTC). Although BTC is commonly called a deflationary currency, in fact its supply increases slowly to a certain extent. Technically, this means that Bitcoin currently has an inflationary supply. Should you buy $50 worth of BTC today or wait for your next paycheck and buy $50 next month? The TVM calculation would recommend the first option, but the real situation is more complex than that due to the fluctuating price of BTC.

Final considerations

Although we have formally defined what TVM is, you are probably already using the concept intuitively. Interest rates, yields and inflation are common economic aspects of our everyday lives. The formalized versions we cover today are very useful for large companies, investors and creditors. For them, even a fraction of a percentage can make a big difference in their profits and results. For us crypto investors looking to improve their returns, TVM is a concept worth knowing when deciding how and where to invest.

Further reading

• What is Money?

• How to Calculate Return on Investment (ROI)

• APY vs. APR: What's the Difference?