PV Example I: Saving for the Future

An application. Remember very very similar to real world problems, but here we are thinking present value applications not future value. So, in this application you are starting college. How much money do you need in the bank today, so you can spend $3,000 bucks every year for the next four years? This is probably something if you are being, your tuition is being paid by a parent or you have worked you need to worry about having this money in place, right? And this is over and above the tuition. So what you're doing is you're figuring out you want to be able to spend some money every year. $3000 on things that you need other than tuition and boarding.

And suppose the interest rate in the bank is 5%, so the question asking you is how much money do you need in the bank today so that you could spend 3,000 every year? As always, the beauty of online is, you can just pause right now and do the problem yourself. You don't need to listen to me. In fact I would encourage you to do that. But I'm making short clips, and then the problems are easy. I'm just doing, going ahead and doing them. And more complicated problems, we will have longer videos but I also will try hard to stop. But at the same time, remember the beauty of this class is not necessarily the videos, but the assignments.

And they have been created very carefully, so that they match the real world, and help you learn. So let's draw a timeline here, and I encourage you to use Excel. So timeline.

0, how many years? One 4, and you can spend 3,000 every year for the next four years, so put 3,000.

So let's think, do we have all the ingredients here? We are not going here.

It's saying how much do we need in the bank now?

And now equates to PV. So we need to figure out PV, what are the ingredients of PV? Remember, in PV function. You will say, =PV. Do this with me on the Excel. I think that's a good thing. I'm doing Excel, but without going to it. Okay. So PV. The first number's rate. So look in the problem, what is the rate? Remember, not, don't rate 5%, right. .05 What's the other number Excel is looking for? How many years? And you found that they were, you're thinking, four.

Right? Who determines this four? You do, right? You almost determine everything, and by the way, you have very little control of the factors in any ways. [LAUGH] And so you just take what you get.

So what's amazing about most problems in life is you're far more in control than you think you are. Right? And things that you can't control don't worry about them. Four, right? And the next good news is the natural next button in Excel is PMT. Unlike when we were doing our FV thing. So PMT's how much? 3,000. So let's pause before that and see, what kind of number should we get? If there was no time value of money, you would get what? You put in 3,000 bucks four times, you get 12,000. Now just think about it. Before you press return do you want a number to show up that makes sense? Answer is yes.

Will it be greater than or less than 12,000? The answer is because you are discounting and because of compounding and because time value of money is not zero, you'll get a number less than 12,000. And I think it turns out to be 12,637, so I'll write it out here.

You see the design I can do? Who said I can't write well? I guess I did. 637.64.

Now again, if these numbers are positive, this will show up negative. If these numbers are negative, this will show up positive. So you are in control of that. I'm just doing, how do you get to the numbers? Now if you're spending these in the future, You need them, right? So you need to put away $10,637 in the bank today, and it'll finance it. When we go to real world problems, what I'm going to do is, I'm gonna spend a lot. Real world problem meaning more complicated. This is real world too. I will actually make you double check all of your answers. To make sure that you know you're getting it.

And the way you double check is you make sure that you're actually, when you spend 3,000 four times, how much will you have in the bank at the end? If you start out with 10,637? If you think about it, you'll have zero. And you can show it period by period.