PV Example II: Taking a Loan

Now for probably one of my favorite problems in finance, which is very, very powerful. We'll do it in a simple way first, and then we'll shred it to bits and try to understand how finance is so awesome. This little problem reflects so much, that we can squeeze out so much value out of it. But in the beginning, I just want you to understand how things work. So read the problem. It says, again kind of a PV problem, you plan to attend and in-state college.

And for those of you who are not in the US, and most of you are probably not in the US, instead, it means when you are studying at a university like Michigan, you have a lower tuition because we are a public university, if you are from Michigan, and there are a set of rules that apply for you to qualify. Like you were born here, you're a resident, then your tuition is less, but still it's a lot. And higher education is really worried about how

the tuition we charge cannot keep going up. Even in-state tuition is pretty high. So here, a student coming to Michigan is saying okay, my parents will have to take a loan of $100,000 at 6%. I'm choosing an interest rate pretty much randomly, but I'm changing them over time. Hopefully, the interest rate is lower. So, you're taking a loan, and you're taking a loan today. You will make yearly payments, and you will have five years to pay back the loan, starting pretty much in year one.

Now, this could change and we'll do more complicated stuff, where you take a loan today, and you could have two years of no payments, and then start paying later, but we are taking the simple loan. So let's write out the timeline of this. Again, this time we are red, and we'll have fun with it. 0, 5. So we have figured out m=5.

1, 2. So this is a PV problem, but unlike the previous problem, we are given the PV.

So the PV is $100,000, right.

And we are going to now try to figure out the PMT. So we are trying to figure out, what are the yearly? And if you notice, if you looked at the problem, first please start doing it on your own. You can pause, but I'll keep going because we can't take too many, many breaks, right. So this problem is, we now get a feel of it. We should be able to do it. Do it with Excel, or do it on your own and come back and see what it's like, right. The thing I wanted to emphasize is the thing in bold. I say yearly payments. This is simplifying things. Why? Because typically, payments will be monthly.

But we'll come back to that in a second, in a more complicated problem. Okay so for now, let's stick with five years, now. Okay it's actually not very complicated if you're using Excel to make it monthly. Five years, so the question is, what is that question mark? And the question mark is the PMT.

Before we start, let's again do the simple exercise.

Suppose you bought a $100,000 and the interest rate is 6%. How much will you pay every year if interest rate is 0.

First of all, the 100,000 will be positive for you today, but negative for the bank. I'm just repeating what Excel is going to do. You put a positive, you get a negative. You put a negative, you get a positive. So for the bank, it's a negative. For you, I'm laughing because I'm like what the heck is going on, $100,000, you get positive. But then you have to put a bunch of negatives five times. If there was no interest at all, how much would you pay every year? $20,000, so think of the interest as the use for money. So I'll let you do that, but this time let's start with PMT.

As soon as you do that in Excel, and I hope you have Excel open next to you. You can actually use the formulas too. And for those who are geeks like I used to be use the formula to double check what Excel is used for, once you know what you're doing. Put rate .06, and is how much? Five years. And I believe, and if I say something wrong like this it's a silly wrong because you can always check, I think the next number is PV. And the final number you can enter is in f3. So, the PV turns out to be.

Don't enter commas where they're not applicable in the Excel formula. Because otherwise it will get confused, it'll think if you put a comma here, it'll think its PV is only 100. So, just write out the 100,000, if I by mistake put a comma say is a bozo, which I am, and move on. So, PMT, the answer will be what? 23,739.64 23,739.64. It is $3,739 more per year than if the interest rate was 0. Does that make sense? Sure. Here it's hurting you. Why? Because you are paying, so if you put this is a positive, this will come out as a negative. So, if this was a positive, this will be a negative.

Which in this sense, makes sense from your perspective. >From the bank's perspective this was a negative outflow, then get a positive of these. Again, isn't this cool? It's so simple, so powerful. Let me again repeat one thing, though. How much control you or your parents have over the decision making? You decide, based on whatever your needs are, that you need 100,000 over 5 years, collectively with their parents, and then you take a loan. After that, you choose how many years you want to take to pay it back. Typically you will have a choice over that a little bit. And then, the interest rate, everybody thinks that it is under your control. It's not. That's why markets are so beautiful.

Nobody In this marketplace really and usually control 6%, it's determined collectively by all of us. Do this problem and you'll see how easy Excel makes life for you, you can make n 500 too, and it'll get an answer.