And the parameters are as follows,

they're issued at a discount and first of all,

we will find what this discount is.

So, the face value for 100 bonds will be 100,000.

Now, of the maturity period will be 10 years,

that is what we sort of postulate.

And then, the coupon rate is

four percent while the market rate is six percent.

So, we can see that C is less than R so this corresponds to a discount.

Now, we know how to calculate how much money we will collect in this process.

So we know all of the cash flows.

The first one will be coupons of the four percent a year here.

So each six months,

they're are going to be $2,000.

So, this is 20 cash flows of $2000 and then the final cash flow of $100,000.

Well, 102 with the last coupon,

and that should all be discounted at three percent,

because this is the annual rate and semi-annual will be three percent.

So if we did that,

then we can say that the issue price,

so, this is present value, will be $85,122.

Well, you can check it with the use of

your advanced knowledge of corporate finance and PV calculations.

And therefore, the amount of discount,

this is the difference between the face value and the issue value, which is $14,878.

So, this amount should be amortized.

How can we do that?

Well, we'll study two methods.

The first will be a straight line amortization method,

the most simplistic but not the most accurate.

And the other one,

will be much more accurate but a little bit more cumbersome.

Alright, so let's keep this in mind and proceed.

First of all, with Case 1,

straight line amortization.

So, in this case,

the amortization charge A,

the same as for D,

when we use depreciation in our analysis of tangible assets.

That would be the overall amount of discount 14,878,

and then we divide by 20.

20 is the number of periods because again,

this is a semi-annual bond.

So ten years corresponds to 26-month periods and that is $744.

I am rounding things up.

So what do we have here?

So each six months,

we will have interest expense.

Let me put it here, interest expense,

and interest expense here will be the overall amount that consists of two parts.

So first of all, that will be 2,744.

So, 2000 is just the coupon payment.

Now here, we have cash because

this is the amount we pay out in the form of our coupon.

But then, we also introduce another account that is discount on bonds payable.

So, here we have 744 and this account,

then our new carrying value will be,

remember it was 85,122.

Now, add this and the new carrying value will be equal to 85,866.

So, the difference is this amortization of the bond discount.

So, this is simple method but the story is what is

the actual interest that we have over the first period?

So, we take this amount and divide that by 85,122.

So, we can say that the first interest,

this is about 2.35 percent.

Let's say 10th interest expense will be about 2.18 percent.

So, we can see that the interest expense,

it changes over time.

The discount doesn't.

So, that shows to you that this is an easy method.

But sort of, I'm not saying misleading but not a very

clear method because the actual effective interest rates,

they are always different here and most often,

people use another way.

That is called, here on we put a case 2.

Effective interest method.

Now, what is this method?

We say that the interest expense

is calculated at the market rate.