Application IV: Making Complex Simple

Welcome back, this is make a problem or make an application number four. And the reason I want to do this one is to show you how you can do things smarter. And, I hope you enjoy this one. It looks simple, but can get very complicated if you start worrying about how to do it. You can do it in a very simple way or a very complicated way. And by the way all the problems I'm using now, should help you with solving the assignments, because the assignments can get tricky, and if you work through these it will really help you do the assignments. Okay. So let's get started, please stare at the screen.

You've invested $75,000 in a trust fund at 7.5% for your child's education. Your child will draw $12,000 per year from this fund for four years starting at the end of year seven. What will be the amount that will be left over in this fund at end of year ten, after the child has withdrawn the fourth time? This sounds similar to the first problem, I'm taking away a little bit of the complexity to show you a way of going quickly in solving problems, right? So the complexity I've removed is that tuition is not changing with inflation, but what I've thrown in is I'm asking you a question where, your trust fund will have some money left after ten years.

Rather than taking a loan and paying it all off, right? Let's see, whether you have money left, or not. So let's draw the timeline as always. So at how many points in time. You start off with zero and then ten more.

What do we know? And let's place that on the board. We know you have $75,000 at this point, plus. However, we know starting in year seven in some senses we did a more complex problem first, right? Because of the complexity of inflation. You start with drawing 12k.

Yeah. So the question is this. How much is left at the end of 10 years? Now you can do a very simple way of thinking about it. And the simple way is ignore all time value on money and make me feel very sad about it. But remember, the interest money is 7.5%, so ignoring it is much more drastic than if it was close to 0% which is basically no time value of money. So the simplistic way of saying this would be I have 75 and then let's subtract 12,000 four times which is about 48, yeah, 12 times four is 48. So you're left with what? 75 minus 48,000 is $27,000.

That's the very simplistic naive way, but let's do it smarter way. Many people start doing it one step at a time, so they'll take this to year seven, then take this to year eight, and start subtracting. We did something like that to show you the confirmation of the result, right? Let's do it in a way that's pretty simple. Break up the problem into two pieces. And the two pieces is don't mix the value of the trust fund with the payments being made annually, starting in year seven, right? Even if they will be made starting in year one, it will be complex. Do what? Separate the negatives from the positive. Let's break it up into two pieces.

The positive piece, which I'll call positive is 75K carried forward how many years? Ten years, can you do this? Answer is yes, it's a future value problem.

What is the interest rate? 0.075. What is n? 10. What is PMT? Zero. What is PV? 75,000. And how much does this work out to be? If my numbers are right, press enter. You get 154,577.37. This is the amount of money you will have. Now clearly, more than double and the reason is quite simple, actually there are two reasons. One is the interest rate is high, the second is that ten is not a small number, ten years is a fairly long time for the money to work, right? Now this one, then do the negative, what is the negative?

Negative is draw the timeline. Negative first one is 12 k. Second one is time period 12 k, 12 k, negative 12 k.

Okay? So what are you seeing over here is If you mix the two it might become very very complex. Right you can do that for fun. Like I did it earlier to see how you can confirm your results. And we'll do a little bit of that here. But this is pretty straight forward. Do the future value of what? [SOUND] It's not a one time, it's a annuity. So, what is the interest rate? 0.075, and remember I'm gonna press in a positive number, but I know it's negative that I'm paying right? So 0.075, what is n? N is four. Remember I'm doing future value because I want to be in time 10. N is four. PMT is how much?

Here you can press the negative 12,000 but I'm not going to add that set value about it. And why did I close the parenthesis? Because there's nothing else. Right. There's nothing else. You can make it more interesting but I won't right now. And it turns out to be $53,675.06. So you now know the two pieces. One piece is 154577.37.The other piece is negative and now I make it negative because I am not paying. So what is the net fund balance? In richer year ten. It turns out to be take 154,577.37 subtract 53,675.06 and I think the answer will work out to be $100,000. 902. I'm a bozo, I keep laughing at myself. And 30 cents.

So how much will you have? You'll have $100,000, almost $101,000, even after you've paid off 12K four times. And this shows you the power of compounding. Because you have a reasonable amount of money. Stick with me for a minute, and we'll be done for today. Do this for me. Now let's confirm that this is indeed true. So do this for me, and I'll be thrilled. Let's start and do it the more complicated way. Let's start with $75,000 and carry it forward to reach here, year seven. Can you do that? Let's call that x7.

Then from that, what will we subtract?

12K. You're left with, net x7. Don't you like that? Net x7. Then what will you do in year eight? You will carry this forward, at 7.5%. To get y7, which is

the amount in your bank or your trust fund after you have paid off the first 12k and you are left with whatever remains. Then subtract what? Another 12k. [SOUND] Keep going, and in year 10, what should we have here? Approximately 101K. And I'm saying approximately, because it's slightly less than that. Please do this, and the force will be with you. We have done a lot of Problems and I have done them purposely. Even with my bad handwriting and now going to Excel on purpose so that you understand the logic of timelines. But remember, go to Excel especially if what's true

You know that your cash flows are changing over time. You know you have to use functions different than PMT, PV, and so on, for which there are simple formulas. So when will that happen? When the cash flows are changing in nature. So for example, the growth induction, if this were happening now. Try this out. Assuming that the 12K is increasing over time. It's 12K today and it'll increase at say, 3% a year. You'll go back to the first application and you can redo it all. May the force be with you. Next time, next module, what we'll do is a real world application of this, and it would be called bonds. But don't worry about the name.

Bonds basically is a very sophisticated name for loans. And there are all kinds of loans, loans taken by governments, loans taken by corporations. We have largely focused on loans taken by individuals here. But next time we'll get excited and do more interesting loans taken by different entities. See you.