0:00

So what I'm going to do is I'm going to introduce the concept of compounding.

Â Therefore I do another problem and then what I would like you to do is, do a

Â problem with compounding. So simple interest rate we've talked about, simple

Â interest is very simple which is if I give a $100,000 to the bank and pays ten

Â percent every year, you get $10,000 every year but that's not how the world is.

Â Let's do compound interest. Suppose you take the same problem, right? You plan to

Â attend the business school and you will be forced to take out a $100,000 loan at ten

Â percent but now the loan characteristic changes. What are your monthly payments

Â given that you'll have to payback the loan in five years? Remember what I have

Â changed. Have I changed the amount you're borrowing? No. Have I changed the interest

Â rate, you're borrowing it yearly? Actually, yes but we'll see that in a

Â second. The interest rate is written as ten%. The thing that I've changed on you

Â is another real world's twist which I think is important. I've changed the

Â annual payments to monthly payments and the number of years are the same. So,

Â quick question, what is your monthly payment and what is the real annual

Â interest rate? So these are the two thing we will do and I will show you how to do

Â this and I will expect you to understand and do it on your own but I'll, I'll go to

Â the steps, okay. So what has changed? R is ten percent annual and, but my payments is

Â monthly so five years implies, how many months? 60 months. If the interest rate is

Â t10 percent annual and by the way the good news is, that's how interest rates are

Â quoted. What is the interest rate per month? It's .1 / twelve. And the reason is

Â there are twelve months. Why is five years 60 months? Because there are twelve months

Â in a year, okay. And what is Pv? 100,000. And what are we trying to figure out? Pmt.

Â But we are not doing five of them, we are doing how many of them? 60. So a lot of

Â people get very confused when the periodicity of the interest payment

Â changes so you could have monthly interest, you could have annual interest,

Â you could have daily int erest, you could have quarterly interest. The way I think

Â about this problem is to remember you are in control. So the best way to deal with

Â this problem is to change the timeline, so do this. Start at zero, put 100,000. Then

Â how many periods? One through 60. Why? Because I'm doing the problem monthly.

Â What is the interest rate per period? Apples to apples remember take .1 /

Â twelve. Does it make sense? I'm being internally consistent. Why is this a good

Â way to solve the problem? Because the problem is now fixed to what I know

Â already so what will happen? Let's go on a spreadsheet and do this problem and then

Â see so, okay. The good news is I have this problem solved for an annual basis. So

Â what do I do? I just divide .1 by twelve. What have I done? I've converted the

Â interest rate to monthly. Then what do I do? Whatever I've divided the interest

Â rate by, I have to multiply the number of years by the same amount and it's 60,

Â right? What is $100,000? Hasn't changed. My interest rate, my payment amount is

Â 2124. So I'm paying about $2125 per month to repay the loan so you see what I've

Â done. I've just simply taken the fact that I know that I can mess with the timeline.

Â So I made m 60, I made R .1 / twelve, and my Pv, the amount of loan, was 100,000 and

Â I came up with I believe 2125. Let me just double check that the numbers are

Â right.Yes, it is. So, so the question now is, this is the question number one, how

Â many of these will I pay? Obviously 60. I will encourage you to do one exercise.

Â What is the present value of paying 2125 at that interest rate 60 times? Answer has

Â to be this, the amount of [inaudible] right? Let me ask you, how much will you

Â owe fter thirty months. Right? How much will you owe after thirteen months? Very

Â simple, make PMT 2125 which you just calculated, right? R is what? .1 / twelve,

Â right? M is how much? Remember where we are standing now? You're standing at point

Â 30 looking forward to 60. M is 30. Do the Pv of this, you have the amount of money

Â you owe the bank. It's so simple, right? You don't even have to d o that whole

Â table. The reason I went through this problem in detail, with and without

Â compounding and with the, the annual and monthly is simply to emphasis to you is

Â that it is extremely important for you to recognize that finance is very logical and

Â you take yourself to the problem and not let the problem scare you, okay. What is

Â the actually interest rate? How much is my annual are actually? Okay. So this is a

Â good question to ask, right? So here's for you to pause and think. The stated R is

Â ten percent but the actual R can't be ten%. It has to be more and the reason is

Â again pause compounding, right? So let's just quickly do that and then I encourage

Â you right after that to take another break as I said, today is a little bit intense

Â and I want to emphasize. We have done the time and the formula very simple so what

Â I'm going to do, is I'm going to just use this formula and explain. If I put $one at

Â what interest rate? R is annual ten%. This is always annual. What is K? K is, is the

Â number of periods that are within that year so K is twelve here. Why? Because

Â it's monthly. So how many periods? Twelve month period, twelve^12 What is this? This

Â number is the future value of $one after twelve intervals so what is the interest

Â rate being charged? Is that -one? And I would encourage you to do this calculation

Â and the answer is, you should know, this number is greater than ten%. Why? Because

Â you are paying ten percent annually but actually that's not true. You're not

Â paying ten percent annually, you're paying ten percent divided by twelve monthly and

Â with compounding, raised to power twelve, this works out to actually be about

Â 10.47%. Now you may think that .5 percent is not a big deal, it is especially if

Â you're borrowing a lot of money, it's a big deal. So the difference between this

Â and this, these two, this is stated and this is actually the real interest that

Â you are being charged. So I hope you take a break now. What we have done is we have

Â taken a loan problem. We have dissected it because it's, it's just reflects

Â everything awesome about finance, And then what we have done is w e have gone back

Â and said to ourselves, what if we took the loan and we make it a monthly loan? No

Â problem. If you know finance and you are thinking clearly, you're logical, you

Â won't mess with anything except your timeline. So you're month matches the

Â period and if there are five years, there are 60 months. The interest rate changes

Â accordingly and changes accordingly and then your payment is calculated based on

Â the same kind of information you give. Okay. So I would at this point again take

Â a break. We have little bit left, one problem left and little bit of concept for

Â today and then we will call it quits. It's a, it's a long day today but I definitely

Â encourage you to just kind of a little bit of break.

Â