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Application II: Saving for College (Cont.)

Application II: Saving for College (Cont.)
Welcome back. We are doing Mega Problem Application Two and what I'm going to do now is something cool. Because I want to, like in application one, get as much value out of this problem. Because it'll kinda enable you to run on your own and empower you. And finance is for everyone is this course, I keep reminding myself. It's important that I give you some tools to work with problems, right? So what I'm going to do is I'm gonna confirm that my calculations are right. How do you do that? And that's one of the beautiful things about finance, is that you can play things out in real time, and see if all of it makes sense. So what does that mean?
I'm going to start with the amount that we decided Amillia needed in the bank today, in her fund. And it was 34,000, at time zero, it was 34,213.09, yeah? We needed that money in the bank and I'm going to play it out in real time. And then later, I'll do an application which will make you do things smarter and quicker, but right now I want to go stepwise. So here's the timeline and I'm interested in years five, six, seven, eight. She will, of course, graduate in year nine, okay, if things go as planned. So the first thing I'm going to do is I'm going to tell you the value or work with the value of the fund.
Then from this I will subtract tuition every year. And the fund, please remember, increases at 5% and this increases at 2.5%. We have calculated these numbers already, the tuition that is, and it's a negative number. So what I'm going to do is I'm going to take fund to each year after figuring out the net value, net fund. And at the end, if you've saved enough and things work out, you would have come up with zero at the end. So I'm going to put a zero right here. That's what I want to get, right? Because you would have paid off everything. You wouldn't be left with either positive or negative, right? So let's start off.
The first issue is what is the value of the fund in year five. Very simple, how would you do it? It's a future value problem, very simple. Where the interest rate is what? 5% and number of years is five. And the PV is 34,213. So I'm going to write out that number. It's 43,665.53. This is the amount of money in my fund. However, at the end of five years, I'll have to make a withdrawal from this fund for tuition. And the withdrawal amount will be 11,314.08. We have already calculated it, but you can redo it. What is this number? How would I get it?
It'll be 10,000, today's value of the tuition, carried forward for five years, but now at 2.5%. What am I left with? I am left with 32,351.45. This is the first step, but we have got to keep going and that's what makes it interesting. So the question is, in year six, what's the value of the fund after having paid one tuition? And the answer is it's got to be greater than 32, but at which rate? 5%. It's a future value problem, where N equals one. 33,969.02 but now I have to subtract the second tuition in year six and that second tuition has to be greater than 11,314. Why? Because of inflation of 2.5%.
So it turns out 11,596.93 and you're left with 22,372.09. Because there's a lot of numbers I'm kind of going a little slow. So that I don't make a silly mistake. It is making sense, right, because the tuition is pretty hefty. So you go from 33 to about 22. How do I get this top number now? Again, take 22,000 forward, but at which rate? 5%. So this is 23,409. Sorry, 490. 23,490.69.
And I want to now subtract attrition that's increased again, one more time, for one year. And that is 11,886.86. And what am I left with? I'm left with 11,603.84
I should carry this forward, but the number I should get here is the same as the tuition. And it seems like I'm on the right track, right? But I carry this forward at 5%. And get 12,184.03 and that's exactly the tuition. 12,184.03. Isn't this cool? So what I have done is I have worked on two mega problems. Which I promise you will not only empower you to do these in your own time, which I would recommend very strongly. But it will empower you to do the problems in the assignments, which in turn will help you run with things even beyond the assignments. I purposely make some of the questions on the assignments tough. So that you have to think.
But in this course, I'm doing a lot of stuff applied and more so to problems that you'll encounter in different aspects of your life. Obviously, I can't cover every aspect. But hopefully, the flavor of the problems is such and the mixes between them across problems are such that it'll cover most issues.
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