Now, there are two fundamental different ways to compute Interest and Interest Rate. There is that simple interest calculations and there is the compound interest calculations. Let's start talking first about that simple interest calculations. For the simple interest calculations, we do pay interest on the principle, which is the amount borrowed or loaned, and not on the interest accumulated. So every year, you have an interest coming. You don't input an interest on the interest accumulated every year. So let's take an example here. Let's assume we have an interest rate of 10%, let's say i = 10% And let's say the amount borrowed is around $1,000. So let's say the principal of the amount borrowed is equal $1,000. So let's do the calculation for the simple interest calculation, using a table here. So let's say we have, The following. I'm assuming this is the year. And this is, what I call the base. And this is to say, Interest, and let's say here. Or for simplicity let's take some space and put the line here, and call this F, from future value. And let's study a period of time of a three years. So, let's say this is 0 which is now and this is 1 and this is 2 and this is 3, 1, 2, 3. So, let's start with the calculations, so for now we have borrowed around $1,000. So, let's say, for currently we have $1,000 in hand. So we want to calculate the interest based on of an interest rate of 10% after the first year. So we want to calculate what is the first here would be of that interest plus the principal in hand. So the base, where we apply the interest rate 10 in the first year, towards the end of the first year, would be the same amount in hand, which is the $1,000. So the interest on the $1,000 will be $1,000 times let's write it here, Times the 10% which is 0.1 which is = $100. So that $100 is the interest in the first year. So what's the amount owed at the end of the first year, would be the $1,000 plus the $100, which will give you $1,100. So that's would be the value of the money at the end of the first year. Let's say F1 here. So year number 2 if we want to find, what is the interest on year number 2 the base to apply the interest would be also the principal you borrowed in the beginning, the $1,000. And it is not that F1. It's not that $1,100, which including the $100 in the first year. So with that being said, the interest on your money, all from the second year, towards the end of the second year, would be the interest rate times the base which is the same principle, because of simple interest calculations. So that will be $1,000 x 0.1 = $100. And that then, the future value at the end of year number two of your money, would be one that the $1,100, if one plus the $100 from year number 2, so you have $1,200 in hand. In year number 3, the base also for simple interest is going to be the same as the principle, then you have $1,000. And the interest of year number 3, I think you'll figure it out now, will be the 10%, which will be $100. And the $100, adding to the value at the end of year number 2. So the value at the end of year number 3 will be $100 plus the $1,200 will be the $1,300. So this is what we have as the simple interest rate calculations. As you noticed what we have here we do not have the interest paid on the interest accumulated. So the interest in second year and the third year we took the base as also the $1,000 here and we did not take into consideration the $100 was added in the previous year, for example, in year number 1. We take into consideration the interest on the interest, in that second method. So this is the first method, and let's move forward to highlight the equations on the first method. So that being said, from the simple interest calculations, and if we want to build this on the numbers that I just showed in the table, on the equations to come up and drive from the equation on the simple interest we have as you noticed, F1 which is future value of the amount you bought or loan at the end of the first year would be the P. Which is the present or the principle in this case plus that principle, which is the $1,000 we used times the i which is the interest rate, which is 10%. And we can rewrite this by using P getting it outside from the equation, and we have P(1 + i), which is the interest. And if we want to look at that in number of years because we took example of three years. So the more you go, you get the concept is going to be the principle times the interest in every single year. So that been said, we can say in number of years, the future value of that money, using the simple interest calculations, what would be P which the principle times 1 + n x i. In our previous example, we used $1,000. Let's say if we have $10,000, so the $10,000 for around three years also. Would be 10,000 times 1 + 3 times the 10% interest rate and on each here you are adding around $1,000 so that will be $13,000 at the end of the third year. So that being said from a simple interest calculations, this is the equation that you need to understand and to remember from simple interest point of view.
