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# Present Value – Multiple Periods

Present Value - Multiple Periods
4.9
Okay, let's now change the one thing that was very simple and retain one thing that was simple, but we don't want to change two things at the same time. Especially because we're trying to just crack open the legos. So the one thing we'll keep is we give you payment once in the future. But unlike the previous problem where you got 1,100 one year from now and figured out its present value, what I'm going to do is read what the problem is. I'm going to give you $1,210 and most of you are probably smiling because you already can figure out what the heck I'm doing. 41.1 Suppose you will inherit$1,210 two years from now and the interest rate in the marketplace is 10%. What is the value of this to you today? It's a present value problem. So let's first draw the timeline. Sorry, I'm getting a little carried away, 0, 2. You're standing here figuring out the PV. By the way, as I said, probably I'll say this over and over again, if you know how to draw a timeline and you can put money at the right spots or value, figuring out value and doing stuff is very easy. Future value, present value. It's all about time, see metrics, and you'll understand finance.
85.5
You know what I mean, Star Wars, all futuristic stuff is very easy, once you know that stuff then it becomes very easy. So you now have $1,210 here. You know why I picked 1,210, but let's do it. So what is the value today of it? The good news is you'll know how to do the present value of. So time travel, and image you're sitting here at time one. Can you tell me what is the present value of$1,210? I hope so. So let's do it. We'll take $1,210 and divide it by 1 + r. 128.6 Which in our case is what? 1.1. That'll bring you to which point? It'll bring you to this point. But you're not done yet. I'm not asking you what is the value of 1,210 two years from now, in period 1. I mean, there you could do that and what would you substitute for our 10%? I'm asking you a little bit more difficult question, which is what is the present value today? So what do you do to this? You have to then do another PV of this. Remember the way I did future value, I did it per period. It's very cool, very cool stuff. So what will you do to this? You'll divided again. 169.6 You know this 2 as you mixed that, you divided the circle number again by 1 + r. Let's put this in parentheses. So what will you get? You'll get FV, which is over (1 + r) what? Not 2 times, but squared. So this is very intuitive, right. It's kind of mirror imaging. What is PV? It's the inverse of FV, kind of the opposite of FV. But what's happening now? If you start noticing on it, what will the value be if you put (1 + r) squared? Turns out it'll turn out to be$1,000. Okay, please do this. What I'm going to do next is go to excel with more complex problems.
218
But I wanted you to understand the concept and the formula, and now we'll do more examples where I'll show you the power of compounding in reverse, and it'll hurt. You get excited what your future value will be [LAUGH], but your future values will be discounted now going back.

Do you have any questions? What was your key takeaway?