Summary
The concept of time value of money (TVM) means that for the same amount of money, it is more beneficial to receive it now than to receive it in the future because you can invest the money and get a return. This concept can be further used to study the present value of future amounts and the future value of current amounts.
TVM can be expressed using a series of mathematical equations. When making TVM decisions, compound interest and inflation factors are often considered.
It’s interesting how much everyone values money concept. Some people seem to value money less than others, while others are willing to work harder to obtain it. While these concepts are fairly abstract, there is in fact a well-established framework when it comes to valuing money over the long term. If you're wondering whether it's more cost-effective to wait for a big raise at the end of the year or get a small raise right away, it's worth understanding the important principle of time value of money.
Time value of money (TVM) is an economic/financial concept that refers to the value of the same amount of money received now compared to what will be received in the future. more advantageous. This decision involves the concept of opportunity cost. If you choose to receive your funds at a later date, you will not be able to invest or use the funds for other worthwhile activities in the meantime.
A specific example is as follows: Not long ago, you loaned a friend $1,000, and now they contact you to pay back the money. If you pick it up today, they'll give you back the $1,000, but starting tomorrow they're going on a year-long trip around the world. If you don't pick it up today, they'll pay you back the $1,000 a year after your trip.
If you are really too lazy to go, you can wait a year. But what TVM means is that you'd better get the money you owe today. During the year, you can put this money into a high-interest savings account. You can even invest it wisely to earn profits. Inflation also means that the money will lose value over the next year, so you will get less real value.
Then we can think about how much money your friend will have to pay you back in a year to make it worth waiting for so long. ? First, the repayment must at least cover the income you may have earned during the one-year waiting period.
We can use a concise TVM formula to simply summarize the entire conversation above. But before that, we need to understand how the present value of funds and the future value of funds are calculated.
The present value of funds refers to the present value of future cash discounted at market price. In the previous example, present value is the actual value today of $1,000 that your friend will pay you back one year from now.
Future value is just the opposite. It refers to the future value of a sum of money today calculated at a given market interest rate. Therefore, the future value of $1,000 after one year will include the value of the interest during the year.
Final Fund Value (FV) is easy calculate. Returning to the previous example, we will consider an interest rate of 2% as the possible investment opportunity at hand. If you invest the $1,000 you receive today, the future value in one year will be:
FV = $1,000 * 1.02 = $1,020
If your friend calls it a trip The time period will be extended to two years, and the final value of the $1,000 fund will be:
FV = $1,000 * 1.02^2 = $1,040.40
Please note that in both cases, we take into account the compound interest effect. To sum up, we can summarize the final value calculation formula as:
FV = I * (1 + r)^n
I represents the initial investment, r represents the interest rate, and n represents the number of periods
Please note that we can also use I to In place of the present value of funds which we will cover later. The reason why we need to know the future value of money is because, on the one hand, it can help us plan and understand how much money invested today may be worth in the future. On the other hand, it also helps us to choose whether to receive a sum of money now or wait until later to receive a different amount of money, as mentioned in the previous example.
Present value of funds (PV ) is calculated similarly to the future value of funds. All we are doing is trying to estimate how much a sum of money in the future would be worth today. To do this, we need to reverse the calculation of terminal value.
Suppose your friend tells you that in one year, they will pay you back $1,030 instead of the original $1,000. However, you need to figure out whether the deal is a good one. We can do this by calculating PV (assuming the interest rate is also 2%).
PV = $1,030 / 1.02 = 1,009.80
This result shows that the present value of $1,030 is $9.80 higher than the $1,000 you can get from a friend today. Therefore, this deal is a better deal. In this case, it's worth waiting a year.
The calculation formula of PV can be summarized as:
PV = FV / (1 + r)^n
As you can see, PV can be calculated from FV and vice versa, and we can derive the TVM formula based on this.
Our The PV and FV formulas provide a good framework for discussing TVM. The concept of compound interest has been introduced in the previous article, and the following article will further expand on it and explore how inflation affects our calculation methods.
Compound interest has a snowball effect over time. What starts out as a small amount of money can, over time, increase in value far beyond what it would have been with simple interest alone. Our established model only accounts for annual compounding effects. However, you may compound interest more frequently, such as quarterly.
To take into account situations where compound interest occurs more frequently, we can fine-tune the model:
FV = PV * (1 + r/t)^n*t
PV represents the current value, r represents the interest rate, and t represents the number of annual compounding periods
We substitute the present value of $1,000, the compound interest rate of 2% and the annual compounding period of 1 into the above formula:
p>FV = $1,000 * (1 + 0.02/1)^ 1*1 = $1,020
Of course, this is the same as our previous calculation. However, if you have the opportunity to compound interest four times per year, the results will be higher:
FV = $1,000 * (1 + 0.02/4)^1*4 = $1020.15
An increase of 15 cents may not seem like much, but if the amount is larger and the term is longer, the difference between simple and compound interest The difference may be more significant.
As of now, we have not factored inflation into our calculations. What good is a 2% annual interest rate when the inflation rate is 3%? During times of high inflation, you're better off thinking about the inflation rate rather than market interest rates. When negotiating salary, you usually need to consider the inflation rate.
Measuring inflation, however, is a tricky business. First, there are different indices available for calculating price increases for goods and services. These indices are often not identical. Furthermore, unlike market interest rates, inflation rates are difficult to predict.
In short, there is nothing we can do about inflation. We can incorporate inflation discounting into our models, but as mentioned earlier, predicting future inflation rates is extremely difficult.
Cryptocurrency Space Contains multiple opportunities where you can choose between receiving one cryptocurrency fund now and another in the future. Locking and staking is an example. You may have to choose between two scenarios: keep your ether (ETH) now, or stake it and get it back in six months at 2% interest. In fact, you may find another staking opportunity with a higher return rate. Doing some simple TVM calculations can help you identify the best products.
More abstractly, you might be wondering when is the best time to buy Bitcoin (BTC). Although BTC is often called a deflationary currency, the reality is that its supply has been slowly growing until a certain point in time. By definition, this means that the current supply of BTC is inflated. So, should you buy $50 of BTC today, or should you wait until next month and buy $50 of BTC? TVM would recommend the former, but due to the violent fluctuations in BTC prices, the actual situation will be more complicated.
While TVM is formally defined in this article, you have most likely already used the concept intuitively. In our daily economic life, concepts such as interest rates, yields, and inflation rates are very common. The formal definition of TVM introduced in this article today will be of great benefit to large companies, investors and lenders. For them, differences of even a few tenths of a percent can have a huge impact on their profits and earnings. For cryptocurrency investors, TVM is also a concept worth keeping in mind when deciding which products to invest in and how to invest for the best returns.
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