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FV Example II: Power of Saving Regularly

FV Example II: Power of Saving Regularly
Let's do the power of saving regularly, the same simple idea. On the deck which you should be able to see now on the camera, you'll see a problem which says how much will you have in your bank account 50 years from now if you save $1,000 every year at either 5% or 15%? You'll remember I did this in the past in one period, one cash flow problem. And here, the previous problem that we just did was you wanting to go to college and saving $1,000. This is a more long-term problem where you're trying to save, say, for retirement. And you're starting as soon as you start working.
So think you're about 25, and you're saving and wanting to know how much you'll have when you're 75. First of all, saving is a good thing, of course, if you have cash flows. And what that does is this also shows you the power. So this is what's going on, let's quickly take a second to see what's going on. I'm going to draw the time line with you, zero, one, how many years? Fifty years.
Now what are you doing? You're saving $1,000. How many times? 50 times. And the question you are asking is, M is 50, PMT.
I promised you my handwriting was terrible, this 1,000. But I'm giving you r of either 5% or 15%. So I'm really showing you the power of two things. One is time and the other is the interest rate combined. And time is more powerful here because you're making investments over and over again. Before we start this, and I'm going to go to Excel to do this with you, though it's not too complicated, you know what to look for, the FE function. Before we go there, let me ask you a simple question. Think about how much would you have if there was no time value of money.
Life would be very simple in terms of calculating, because you take 50 and multiply it by 1,000. So you'll have 50,000, right? But life becomes very interesting, and I'm going to go over to Excel, And do it with you, one shot. So if you go to Excel, let's go to cell A1, and I'm going to stick there and try to do the problem with you. So you press equal sign, you press FE, and then you press what? 0.5 then I press the 50, and I then press how much, thousand. If you notice, I don't need to press anything in pv or free dot coms then I hit it. Return, how much do you get? We should get about $209,348.
I think we do get that. So, that was the first part, now the cool thing is if you look at it, how much did yo have if you didn't have any time value of money? You had five $1,000 50 times, $50,000. You already have at 5%, 4 times that. And the difference between 50 and $209,000, about $159,000, is because of compounding. Compounding, interest with compounding, obviously. So I'm going to now change this a little bit right here. The other thing was, take a guess how much will it be at 15%. Many people will think, look, you know, 5%, 15% should be about 3 times. What are they ignoring?
They're ignoring the fact, that actually there is compounding, which is highly non-linear. So I've changed the 0.05 to 0.15 right there. I hit enter and I am just double checking with my numbers so that, because this is online and we don't want to keep typing small mistakes even though I'll make them, I do the numbers a little bit ahead of time. Turns out it's $7 million. And plus $217,716, so actually, it's about $7 million more than what we found at 5%. So, I mean, think about it. Isn't that cool? First.
Second, it shows you that life can get very, very complicated when we do non-linear stuff, and as I said earlier, many people are surprised, including me, to see, how powerful compounding can be. It looks very cool moving forward. But it can be devastating, when you go do PVs. And, incredibly valuable things in the future, could look, of very little value today if you use high interest rates, which may or may not be justified. That's a whole debate. In very long term investments, right, for future generations.
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