Summary
Time value of money (TVM) is a concept that states that it is better to have an amount of money now than to have the same amount in the future, this is because you can invest the money, giving you a return. This concept can be extended to consider the present value of a future amount and the future value of a present amount.
The time value of money can be represented mathematically by a selection of equations. Multipliers can also be added, and inflation is commonly taken into account when making decisions regarding the time value of money.
the introduction
How much each of us values money is an interesting concept. It may seem that some people value it less than others. Others are willing to work harder to get it, too. While these concepts are very abstract, when it comes to valuing money over time, there is actually a well-established framework. If you're wondering whether to wait for a larger raise at the end of the year or get a smaller raise now, the time value of money is a great principle to know.
We give you the time value of money
Time value of money (TVM) is an economic/financial concept that states that it is better to have an amount of money now than to have an equal amount in the future. Within this decision lies the idea of opportunity cost. When you choose to get the money later, you miss the opportunity to invest it now or use the money for some other valuable activity.
Let's look at an example. You loaned your friend $1,000 a while ago, and now he's contacted you to return it. Today he offers you $1,000 if you want to pass by him to collect the money, as he will travel the next day to go on a trip around the world for a year. However, when he returns after 12 months, he will give you $1,000.
If you're feeling lazy, you can wait 12 months. But the time value of money means that you're better off getting the money today, since within those 12 months, you can put that money into a high-interest savings account, and you can even invest it wisely and make some profits. Inflation may also mean that your money will be worth less in the future than it was worth 12 months ago, so you will actually receive less in real terms.
An interesting question to consider is what will your friend be paying you in 12 months to make it worth the wait? For one thing, your friend will need to at least offset the potential profits you could make in the 12-month waiting period.
What is present value and future value?
We can neatly summarize this entire discussion in a succinct formula known as the time value of money formula. But before we move on to that, we need to talk about some other math first: the present value of money and the future value of money.
The present value of money lets you know the present value of a future cash sum, discounted by the market price. For our example, you might want to know how much $1,000 your friend in one year is worth in real life today.
Future value is the opposite. It looks at an amount of money today and calculates its value in the future at a specific market price. So, the future value of $1,000 in one year will include one year's interest value.
Calculating the future value of money
It is easy to calculate the future value (FV) of money. Let's go back to the previous model, and use the interest rate (2%) as the potential investment opportunity at hand. The future value of the $1,000 you would have today when invested in one year would be:
Future value = $1,000 * 1.02 = $1,020
Imagine that your friend now says that his journey will take two years. The future value of $1,000 would then be:
Future value = $1,000 * 1.02^2 = $1,040.40
Note that in both cases, we assume doubled interest. We can generalize the future value formula as follows:
Future value (FV) = I * (1 + r)^n
I = initial investment, r = interest rate, and n = number of time periods
Note that we can also replace I with the present value of money which we will cover later. Why would we want to know future value? This helps us plan and know the value of money invested today in the future. It also helps us in our previous example, where a decision needs to be made to take one amount of money now or another amount later.
Calculate the present value of money
Calculating the present value of money (PV) is similar to calculating future value. All we are doing is trying to estimate the future value of today. To do this, we reverse the future value calculation.
Imagine that your friend told you that after a year, he will give you $1,030 instead of the original $1,000. However, you need to know whether this is a good deal or not. We can do this by calculating the present value (PV) (assuming the same 2% interest rate).
Present value = $1,030 / 1.02 = 1,009.80
Here, your friend is actually offering you a good deal. The present value is $9.80 more than you would get from your friend today. In this case, it would be better to wait a year.
Let's look at the general formula for calculating present value:
Current value (PV) = FV / (1 + r)^n
As you can see, the future value (FV) can be rearranged to get the present value (PV) and vice versa, giving us the formula for the time value of money.
The effects of doubling and inflation on the time value of money
The present value (PV) formula and future value (FV) formula provide a great framework for discussing the time value of money. We've already introduced the concept of doubling, but we'll expand on it further and see how inflation can also affect our calculations.
Multiplier effect
Doubling has an increasing effect over the years. What starts as a small amount of money can become much larger than just a small amount of money. In our established model, we considered doubling once a year. However, your money may double more regularly than this, for example, every quarter.
To create this, we can modify our model a bit.
Future value (FV) = PV * (1 + r/t)^n*t
PV = present value, r = interest rate, and t = number of doubling periods per year
Let's substitute the compound interest rate of 2% per year given once a year on the $1,000.
Future value = $1,000 * (1 + 0.02/1)^1*1 = $1,020
This is of course the same as what we calculated previously. However, if you have the opportunity to quadruple your profits in a year, the result will be even greater.
Future value = $1,000 * (1 + 0.02/4)^1*4 = $1,020.15
An increase of 15 cents may not seem like much, but with larger amounts and over longer periods of time, the difference can become significant.
Inflation effect
Until now, we have not taken inflation into account in our calculations. What is the benefit of an interest rate of 2% per annum when inflation reaches 3%? In periods of high inflation, you may be better off setting the inflation rate rather than the market interest rate. Wage negotiations are a common example of this.
However, measuring inflation is much more difficult. First, there are different indicators to choose from to calculate the increase in prices of goods and services. These indicators usually provide different numbers. Inflation is also somewhat difficult to predict, unlike market interest rates.
In short, there is little we can do about inflation. We can incorporate an inflation discounting aspect into our model, but as we mentioned, inflation can be highly unpredictable when we talk about the future.
How does the time value of money apply to digital currencies?
There are many opportunities in cryptocurrency trading where you can choose between a cryptocurrency amount now and a different amount in the future. Reserved storage is one example of this. You may have to choose between holding one Ethereum (ETH) now or holding it and getting it back in six months at a 2% interest rate. In fact, you may find another storage opportunity that offers a better return. Some simple time value of money calculations can help you find the best product.
More abstractly, you may be wondering when you should buy Bitcoin (BTC). Although BTC is commonly called a deflationary currency, its stock slowly increases up to a certain point. This, by definition, means that it currently has an inflationary buffer. Should you then buy BTC for $50 today or wait for your next paycheck and buy it for $50 next month? The time value of money recommends the first suggestion, but the actual situation is more complicated due to the volatility of the BTC price.
Concluding thoughts
Although we have formally defined the time value of money, you are probably already using this concept intuitively. Concepts such as interest rates, returns, and inflation are common in our daily economic life. The official versions we have worked on today are largely used by large companies, investors and lenders. For them, even a fraction of a percentage can make a huge difference in their bottom line. For us, as cryptocurrency investors, this is still a concept worth taking into consideration when deciding how and where to invest your money to get the best returns.
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