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Application III: Financial Planning

Application III: Financial Planning
Mega example or application number three, and I call it financial planning. I will draw your attention to the problem and take a few minutes to write it down. I'll read it out for you. Abebi, who has just celebrated her 25th birthday, plans to retire on her 55th birthday. So what should you be doing right away? Drawing a timeline. She has just set up a retirement fund to pay her an annual income starting on her retirement date. When does she retire? Age 55. And to continue paying for 20 more years, now sometimes the wording of a problem becomes complex by just writing it. So let me ask you, how many retirement incomes does she want annually?
She wants the first on her 55th birthday and 20 more, so 21. Remember, n is important in all our calculation. Abebi's goal is to receive $50,000 for each of these 20 years. So the good news is that you know exactly what planning you've done. And how much you'll need every year, based on looking forward, figuring out how much money you want. This is again your decision, based on your needs, right? Abebi has committed to set aside equal investments at the end of each year for the next 29 years, starting on her 26th birthday. And I'm laying this all out for you in a way that makes it easy for you to use standard formulas.
But when you get into Excel and feel very comfortable, you can just rock and roll over time. But right now, I'm making sure you understand. The annual interest rate is 5%. And the question says, how much does she need to save every year, okay?
This problem is a little bit complex, because it's similar to the previous one. But in my book, with a different kind of perspective. The perspective of the previous one was tuition for college. This is the perspective for retirement. And I said I'll try very hard to bring you into the course, based on what you wanna do and what is appealing to you. So this is kind of a different mindset of person than the person going to college. Okay, so let's draw the timeline first. And that'll help us break up the problem. So the timeline is this.
And I'm going to interpret the problem, which maybe will make it simpler for you, okay? So your timeline is this, 0, which in this case happens to be what? Age 25. So I'm writing the age of the person so that it becomes easy, but time 0 means today. So that's the 1. What's the next age that's important? 55. Why is it important? Because that's the decision point at which things will, that's a point in the future which is a life event, they call it. Where you suddenly become from the saver to spender because you're retiring. You're of course spending too while you're up to age 55, but you know things. So starting at the retirement, what does it say?
That she has just set up a retirement fund to pay her annual income on her retirement day. And to continue paying for 20 years. So the first payment is 50,000 50,000.
How many times? n is 21. Well, this n is for what? Retirement income. Remember there are two n's. One is for how do you solve the problem of what you need in the future? The other n is how many times will you save, okay? So this is fine, and you know you need this 21 times, and you need it in the future. So 75 will go on, I mean, 25 will go on til 75, okay? We know now what the problem looks like, but what don't we know? We don't know the saving every year needed which is also PMT problem, all right?
I could make it complex like last time, by making the saving grow every year. But I'm not going to do it, because this is already pretty complex. So given this timeline, can you now break it up into bite size pieces? Let's do that. And let's try to solve the problem, okay? So the first solving the problem issue is what is the PV of return? So think about it. The interest rate turns out to be, is, I'm just looking at 0.05. How many years will you need retirement income? 21. What will be the retirement income you need annually, is it a PMT or a FV? It's a PMT of 50,000.
This is very straightforward, but remember, the key here is to remember, the first payment is year 55, second one is year 56. Remember, you are going forward in time. So when you do this PV, in which year will this PV be? It'll be in year 54. I almost feel like apologizing but that's the convention. The convention is the first payment's one year from now, and you will slip up on this, everybody does. So this PV turns out to be, if I calculate it, it will turn out to be 641,057.64. So, what do I know? I know in year 54 I need to have $641,057.64 to do what? To be able to finance $50,000 how many times? 51 times.
That's based on me, Abebi's projection. Now what's the next step? Figure out PMT. Think about it for a minute, can you, answer is yes. But you have to recognize the nature of the beast so when are you starting to save? And when are you ending to save? You're starting to save pretty much in the year 26, you're starting at year 25.
26 will be your first payment, and the last one will be in year 54. So you have 29 payments. 26,27,28,29,30,31,32,33 and so on and so forth, right? So this n turns out to be 29. And you've clarified that and I did it with you on the timeline. Now in the real world, this will become much easier. Because when you're doing your own problem, you'll know your timeline, whatever that is, and so on. So this is a key number.
We are assuming r is 5%, okay? Now what do I need to do? I know n, I know r, do I need to solve a PV problem? An FV problem? PMT problem? What combination do I need? Well, I know my number that I need at the year 54. So I have to be thinking future value. I cannot be thinking PV. I could do PV by bringing this back to year 25, but that is an unnecessary step. Why? Because I know how to solve for PMT with future value too. So, I do PMT 0.05, what is n?
I've done it, so these two numbers I know. And then finally, I know that the first function is 0, because it's PV, so you put a 0 there. And then put what? 641057.64.
So what do I get? I get all the numbers in, and if I press Enter, you should get an answer of,
Required saving is 10,286.10. So if you save $10,286, you will save how many times? 29 times. How much will you have after 54, at age 54? 641,000, which is a lot of money, right? So if you were saving $10,000, approximately, and there was no interest, the amount would be what after 29 years? Little less than 300,000. How did I get that? I multiplied 10,000 by 30. I had 300,000. Now you get a lot more money, you get 641,000. Because the interest rate is 5%, reasonably high, but what's important is you're working. The money is working for you and you're repeatedly putting money. 29, over 29 years. So this solves the problem.
Let's take a break before we do the next mega problem. And then we'll be done with the application phase, for the first component of this course, which I call the basics of time value of money, applied to more and more complex situations.
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