What I want to do in this content. Today, we discuss a little bit about Compound interest introduction and . Hence discussion a way to find out. how a value is increasing Fast and approximate? We will see how that approximation very good Just as a review. Let’s say, I run one type of bank and tell you that I am Offer a 10% interest multiply annually. This usually does not happen in real banks often multiplied continuously. I will just keep it a simple example Double annually. These make the calculations slightly simpler. All this means is to say that you are Today, I deposited $ 100 into that bank account. If you keep the money in the account and wait one year. You will have your $ 100 Plus 10% on your $ 100 deposit 10% of 100 would be an extra 10 dollars. After a year, you will have $ 110. You can just say I added 10% to 100.
Compound interest introduction
After two years, or a year after the first year, After two years, you’ll get 10%. Not only 100, you get 10%. On 110 10% on 110 you will get On extra 11, 10% on 110 equals 11 You will have 110 That was, you can imagine, entering your deposit Second year, then you get an extra 10% on your deposit Not 10% on your initial deposit. For this reason we say complications. You get interest on interest from previous years. 110 plus $ 11. Every year it increases The amount we get – if we don’t withdraw anything – Now we have $ 121. I can keep doing this.
How Much Money We Can Earn?
General way To find out how much you have after n years It’s hit, I’ll use a little algebra here Let’s say this is my primary deposit, or principal, As you want to show it. After n years, After one year, you will only be beating … To get to this number here, multiply it by 1.1 In fact, let me do it this way. I don’t want to make it too brief Just to understand the calculations here, to get this number Here, we just multiplied that number 100 times 1 plus 10%, or 1.1 This number here will be, 110 times 1.1 again he’s here 100 times 1.1 which was the number there Now we will hit it by 1.1 again Remember, where did 1.1 come from? 100% + 10% This is what we get for our 100% of our basic deposit In addition to another 10% So we multiply by 1.1 Here we do this twice.
We multiply it by 1.1 twice. Three years later, how much money do we have? After 3 years he will be We have 100 times 1.1 cubed. After n years We became a little short. We would have 100 times 1.1 up to the power. You can imagine that they are not easy accounts. This case when we deal with 10%, If we are dealing with 7%, The situation will be different here We have 7% interest, multiplied annually. After a year, we will have 100 hits Instead of 1.1, it would be 100% plus 7%, Or 1.07. Let’s move on to 3 years. After 3 years, I can put Year 2 in the middle, 100 times 1.07 raised by the power of 3 Or 1.07 times itself 3 times. After n years It will be 1.07, with the power up. I think you understood here that though the idea is logically simple, to calculate the double dividend is really complex.
Let’s say, I asked you. How long will it take to double your money? If only you would use these accounts You would say: to double my money. I will start with 100 dollars. I will hit This, suppose that Interest is 10%, or 1.1 The power of x is equal to. Well, I’m going to double my money for that I will have 200 dollars. Now I will solve x, I’m going to do some algorithms here. You can divide both sides by 100. You will get 1.1 x equal to 2. Only divided both sides by 100. You will take logarithms for both sides. For the 1.1 basis, you get x. I show you. This is intentionally complicated. I know this is confusing. There are several content on, How to fix this. You get x equal to logarithm of 2 for base 1. 1 Most of us cannot do these calculations in our heads.
Although a simple idea, how long does that, It would take me to double my money. Solve it to get the exact answer, It is not easy. This can be used Simple calculator, you can continue increasing. The number of years to reach a close number. There are no direct steps to do so. It is with 10%, if we were to do it with 9.3%, It will become more difficult.