[MUSIC] Welcome back, we had an application one I call it mega and particularly useful to understand finance because it has all the components. It has time value of money, it has moving forward, moving backwards, and then you'll see very cool stuff now. So what are the patterns we have observed in what we call the amortization table. Which by the way, a bank can print out and should print out for you, if you so desire. If If not, you can ask for it, right? So it basically shows you how loan works. So quickly, let's capture the main elements, how many components of a payment so our payment was about $23,739. And the answer is two, right? One is what interest which you pay on the beginning of the period balance not then, right? Pay interest for the usage of time and money. And the second is whatever remains goes and pays off part of the principal. Which component decreases over time. If you're paying off part of the principal the component that is decreasing given that your payment is fixed has to be interest, right? So interest drops, and which one increases, the repayment increases such that the last repayment is exactly equal to the beginning of the period. Because if that's not the case, you're still keeping on paying some interest and so on, so forth. So what I'm going to do next is ask you some simple questions to show you the power of finance. So how would you figure out for example, the outstanding balance after the second payment? So let me just ask the following question. So here's the pen. I'm asking you this. You have one, 5, the payment you're making every year is 23,739.64. I'm asking you the following question at time 2. After you've made the second payment, how much do you still owe? As I said, these are snippets I'm doing with you in complex problems and I'm keep going because you become a genius in finance. Now, you could do it the long way, which we just did. You could start at time zero and work your way forward. But this is the awesomeness of finance, finance, one of the main elements of finances it looks forward it doesn't look back. It makes life very simple by recognizing the value of anything is the present value of the future value of anything today is the present value of the future. So, watch matrix time travel to time 2 and ask yourself, how much do you owe? That's the question given you made two payments. Think for a second the answers pretty straightforward, but very complex if you don't know finance and it has to be the present value of what you owe the bank. So, how do you do PV interest is 0.06. The payment is 23739.64, but you want to know n now how many n are left 3. When you do this, you will get the answer of 63,456.34, isn't that cool? Right, so the one thing I've told you now is a very deep lesson of finance or of thinking of value. Value comes from the future and looking forward and then remember you got a discount because of time value of money. But when we look forward from is dictated by the problem you're trying to solve. Trick question, if you were standing at time 0 and asked you what is the present value? What would change here? This 3 would become 5. But what answer should you get and this is one of the most profound realizations of people when they figure it out. You don't need to do this, you should know the answer it has to be 100,000. So one of the things we realize down the road is that finance itself cannot add value in present value, in present terms. Because it's just an exchange of money value creation, where you make more than what you put in comes from real ideas, right? It comes from producing something like an iPhone, which is very popular and people seem to value a lot rather than just exchanging money, okay? So let's do one more question and then what I'll do is I'll keep taking breaks within this first mega problem because as I said, it's pretty complex. I may do it in other mega problems still. But I will do one more question before we take a break. How would you figure out the interest component of the third payment? So now I'm asking a very simple question. So you made a third payment, how would you figure out the interest component. Now if you remember your basics that, the interest you pay in any period is a function of two things. The dollar amount, the interest rate, and the amount you owe at the beginning of the period. Do we know the amount we owe at the beginning of the third period which is also time period two after you made. Yes, we just calculated it. It was 63, 456.34, right? So I'm asking you what is the third payments interest component we know the third payment was what also 23,739.64. I'm asking what is the interest component of this? Very simple multiply it by 0.06 and I think the answer works out to be 3,807.38. You see how simple this is? So you can basically do anything you want, even if there are a gazillion periods to pay off the loan. So if you took a 30 year mortgage, right mortgage is a loan against the house and you paid monthly payment. How many periods do you have? 360 you'd got nuts figuring out the amortization table. We are going to take a break and kind of go in that direction to show you the real power of the first mega problem.