So hopefully, you've had the time to kind of stare at what their bond is trying to

say and so on and so forth. Let's, we did the time line and formula. Just remember,

match the interest rate with the periodicity. Always make your interval of

thinking to compounding into it. And it will be pretty obvious when you're looking

at the bond or whatever the idea and so on, what it is. Match the compounding

integral interest rate. Let's do some calculations. And here, I'm going to go

over to my friend, the Excel. And there's some number from the past which we'll

ignore for the time. So, I'm going to stick in cell C. If you can see me,

hopefully you're fine. What I'm going to do is I'm going to do PV. Why? Because

I'm trying to do a PV here for bond, and what was the interest rate on similar

bond? Remember, it was six% but we are doing everything on my annual, 0.03. How

many number of periods? Twenty. What is the PMT? 30. And what is the future value?

You can do everything. What do you notice? I purposely picked this example first

construction. What do you notice? The price of the bond is equal to the face

value. Yes. Do you notice that? So, let's go here and I'll show you the intuition

for it. The price of the phase bond is the face value. That means today, you are the

phase exactly equal to the face value. Even though that face value is coming

twenty period from now. And the reason for it is, what is, what do you see the

relationship between coupon which is like a percentage and the interest rate? They

are both what? The same. 30 over a 1000 is 0.03. And what is my interest rate? 0.03.

So, what's happening? Very intuitively. The coupon is the numerator. It's coming

to you. But time is hurting you at the same rate so they cancel each other. And

what do you left with? $1,000. So, this is a neat thing that they'll say in the real

world that the bond is trading at face value, right? At Par. Par, P, A, R is face

value. Let's assume now that the interest rate in the real world is actually four%

per month, per year which is what per month? Two%. What does happen to the

price? It's gone up, it's created in face value. It's called trading at the premium.

Premium doesn't mean you're paying a higher price than you should. Premium

simply is relative , right. Discount is relative to . Okay, 1163. Quick question.

Why did this happened? Forget about the exact price and this is what I want you to

have in your gut-feeling for Finance not just numbers. You know the answer has to

be created in thousand and why is that? Notice the coupon is still 30, and it

cannot change once you've issued the bond because what's the coupon, who the term is

the coupon, the person is showing it and we are assuming the government is not

going to default in the thirtieth lays, right? But what can change is the market

rate that we using. So, the market rate is now two% and the coupon is three%. So,

what it's going to do? It's going to make the value of the bond go over a thousand,

simply because the value of getting it at the higher rate coupon than the discount rate.

Now, suppose the price is such that the rate of return that you are

getting in the similar instrument out there in the market is actually 8% and half of

eight is what, four%. What will happen to the price? It will go below a thousand ,

and it is called selling it to discount. Zero coupons always sell at a discount.

Zero coupon bonds always sell at the discount because there's no coupon

compensating for it whereas, coupon being bonds can and do sell it to discount but

what has to be true? Let's look at the parameters. The face value is a $1,000.

I'm not changing that. The coupon is 30, I'm not changing that. The n is twenty,

I'm not changing that, I'm standing to today, what did I changed? The interest

rate. Now, I'm hurting the bond's price at the higher rate than the coupon flowing in.

So, what happened because it's less than face value? So, this tells you something

about the pricing of bond which is this. Interest rates go up, price goes down.

But for a coupon paying bonds, government bonds, there's this neat relationship where, the interest rate and

the coupon rate are the same, the price of the bond has to be the face value. And

then, if the interest rate is higher, it's lower and the interest is

lower than the coupon rate, price is higher. So, let's try to take this

learning and graph it. So, you've done the calculations and I would really encourage

you to go back and do those calculations again, right? So, but I'll write out what you should find.

So, if coupon rate is greater than r, price will be greater than face value.

If coupon rate is less than r at a specific time, the price will be less

than the face value. If the coupon rate is equal to r, price will be equal to face

value. So, this is what you should find and just mess around with this because it

will help you. So, what I would like to show you know is a graph. And this graph

is important. Price, r, zero. It looks like this. So, the price of a bond falls

when interest rate goes up, alright? That's what it's showing and that makes

sense. So, if the interest rate is six% or three% per, what, six months. And the

coupon rate of this bond was what? Three%, what will the price be?A thousand. It just

did this, okay? One thing I really want to emphasize about this, coupon rate is not a

market thing, it's fixed by the government, don't ask me why, alright?

Because that's like getting into detail. Its something determined by their ability

to pay periodically versus face value, right? So, this curve is telling you the

relationship between bond prices and interest rate. And let me just give you

one little bottom line thing. Price goes down if r goes up. Second, short term