Although the name of “financial calculations” seems to be reserved for operations carried out by experts in the field, the truth is that their results will surely be useful for everyone in choosing the financial products or services that best suit their needs.
Thus, in practice, it will be advisable to find out how much a certain investment will be worth at maturity, if the money we have invested will be worth the same in a few years, what is the APR (Annual percentage rate) of a product to which its advertising refers, etc. To answer these questions there are financial calculations: The laws of capitalization, discount laws, calculation of profitability, etc.
We often see in the written press and hear both on radio and television talk about a series of concepts, figures and abbreviations of a financial nature that seem completely unintelligible to us. We might even think that the mathematical procedures and calculations that have led to these results are reserved exclusively for people with a special gift.
The mathematical calculations that produce these results are called Mathematics of Financial Operations or Financial Mathematics, although in a simpler way we can call them Financial Calculations. Financial Calculations are not a proper branch of Mathematics, although they make intensive use of different mathematical tools.
This use of mathematics should not scare us at all, since, as we will see below, they are mostly crushing common sense calculations, and they use very basic mathematical knowledge. Obviously, as one deepens into financial calculations, the mathematical apparatus becomes more complicated, falling outside the pretensions of this guide.
We all know from experience that the prices of the goods and services we buy tend to increase over time. We also know that, because of rising prices, the purchasing power of our money is decreasing. With the same amount of money, for example 100 c.u., we can buy fewer things today than a year ago.
From the simple observation above, it is easy to understand that, when we talk about money (capital), any amount that we consider must be associated with a certain time point (expiration), since the same amount of money will have a different value depending on the moment when it is received. Thus, when we talk about financial capital (money) we will refer to a pair of numbers formed by a capital and its maturity (C, t).
The reasoning is easy when there is inflation, that is, there is a continuous increase in prices over time. However, what would happen in a hypothetical situation of complete price stability, that is, assuming that prices did not change?
Even in that utopian situation, in which, with 100 c.u., we could buy the same goods today or in a year, however, it would not be indifferent for us to receive 100 c.u. today or in a year. It would be preferable to receive the 100 c.u. today, since we could make the 100 c.u. profitable and within a year recover that sum plus the return that we could have received.
In this context, some questions automatically arise: “Those 100 c.u. now, how much money do they amount one year from now?”, or “What did those 100 c.u. now equal 10 years ago?”
For a financial capital, that is, a specific pair of numbers (100 c.u., June 20 of year N), to be equivalent to another one within a year, the capital will be greater than 100 c.u., for example (106 c.u., 20 June of year N + 1). Likewise, for such capital to be equivalent to another two years ago, the money will be less than 100 c.u., as it could be (85 c.u., June 20 of year N-2).
Of course, we would ask ourselves “why 106 c.u. and 85 c.u.? Couldn’t it be 105 c.u. and 84 c.u.?” To determine these figures, the so-called Financial Laws are used, which establish the amounts that are considered equivalent when changing the maturity.
There are many financial laws, although they can really be classified into two groups:
- Capitalization Laws: They are the laws that allow us to move a capital “forward” in time, that is, to change its maturity to a later date. Example: “To take out a term deposit”, that is, we take the money to a financial institution and get it back a few days, months or years later, with interest.
- Discount Laws: They are the laws that allow us to move a capital “backwards” in time, that is, to change its maturity to a previous date. Example: “To cash a bill in advance”, that is, we have a bill that reflects that we are going to be paid money on a certain date. If we want to cash it before such maturity, we take the bill to the financial institution that advances the money to us, with a discount depending on the time that the payment is advanced.
