0:00

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

people get very confused when the periodicity of the interest payment

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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