Simple and compound interest

There are some terms related to the economy that can be misleading, or that are not well understood. There are even many that can be confused, especially when several terms refer to the same thing, only with different nuances, which are what differentiate them. Such is the case of simple and compound interest, do you know which is which?

If the difference between simple and compound interest is not clear to you, or you want to know exactly what each of these terms refers to, then we will help you understand it perfectly.

What is simple interest

Understanding simple interest is pretty straightforward. Imagine that a person asks you for a loan and you decide to give it to them with an interest, whatever it is. When that person returns the money, they do so with interest, that is, instead of receiving what you have loaned, you receive something more for the use of the money.

That we could say is simple interest.

In other words, Simple interest is the amount of money that a person, entity or company pays you for having used your money for a fixed period (in a borrowed way).

What is the composed interest

As for compound interest, we continue with another example so that you understand. Imagine that you lend money to a person, at interest x. When maturity comes, that person can return that money that you have lent him, and also the interest, but what if instead of keeping that money what you do is lend it again, both the initial capital and the interest earned? When the period ended, you would receive that new principal and interest, plus some new interest.

That is, compound interest is that amount that is becoming larger because the interest on that payment is added to that capital in such a way that you invest more, but also receiving higher interests.

Difference between interests

Now that it is a little clearer to you what is simple interest and compound interest, it is time to make things clearer and, for this, nothing like putting on the screen the differences that are between the two.

In this sense, we have:

• Simple interest is non-capitalizable interest, In other words, it has no impact on the money you invest in the beginning. On the other hand, with the compound the thing changes because that interest is added to the capital, making the initial investment greater in the end.
• Simple interest will always be calculated on the initial capital, without there being a change in it or an increase. Quite the opposite of what happens with the compound, which will be calculated based on the final capital and will increase and increase the initial money.

How they are calculated

Now that you are clear about simple and compound interest, and the differences between each of them, the next phase is to understand how each of them can be calculated. And this, in the first case, is simple; but we cannot say the same in the second case, where the formula is a bit more complicated.

Calculate simple interest

There is no doubt that the formula for calculating simple interest is much easier than compound interest. You will come across this:

I = C * R * T

In other words:

Interest = Principal * Interest rate * Time

Taking an example, imagine that what you want is to find the interest of a capital of 100 euros, an interest rate of 1% and 1 year of time.

I = 100 * 0,01 * 1

Now, this formula that we have given you is the one that has been applied for years. Does that mean that there are other formulas depending on whether we want to know the simple interest for days or months? Yes, there are, but all of them are just as easy.

If you want to calculate the simple interest for months, you will need to divide the time by those 12 months, in such a way that the formula will look like this:

Interest = Principal * Interest rate * Time (in months) / 12

And what if you want to calculate it by days? If you prefer to take out the interest by days, then the time base that is used should be divided by the days of the month. However, it has a peculiarity, and that is that, in economics, they do not treat all the months separately (that is, they do not count the months of 28 days or those of 31). What they do is equalize all to 30 days. Hence, instead of 365 days (or 366 if the year is a leap year), 360 days are put.

Thus, the formula would be as follows:

Interest = Principal * Interest Rate * Time (in days) / 360

This formula is very easy to apply but has a downside. And it is not going to take into account the accumulated interests, those that are obtained between periods. For this reason, many times the value it gives us is not the real one, and at the accounting level it can end up causing problems. That is why compound interest and the formula to calculate it emerged (which we will discuss below).

Calculate compound interest

We advise you in advance that the compound capital formula is not easy. In fact, it may impress you first. But once you see how it should be done, it sure has no secrets for you.

The compound interest formula is:

I = Cf {(1 + R) ^ n - 1}

In this case, we are talking about:

• Cf: it would be the final capital, or what is the same, Final Value (VF) in case you find it in other formulas.
• Ci: would be the initial capital (you can also find it in other formulas such as Present Value (VA).
• r: is the interest rate (it can also be represented by an i).
• t: is the time (or you may find it with an n).

Basically, what this formula does is multiply the initial capital you start with by one and also by interest. Then raise everything by the number of periods.