All rights in this lecture, we are going to calculate the future value for a series of payments that
is an annuity, which means that the amount will be constant and it will be each year.
OK, so let us take a look.
In this case, we have discounted 10 percent and we are making a payment of one hundred thousand in
each year, one to five.
And when I say year one, it means that at the end of year one.
OK, so let's start first of all, we have to take the year one payment.
And now what we are trying to achieve is basically we are trying to calculate its value at the end of
year five, the future value and to calculate the value at five, we have to add the interest into this
value for your two, three, four and five, but not for year one, because I told you that this value
is at the end of year one, which means that the interest can only be added for your two, three, four
and five.
So basically, we have to add the compounding interest for four to four times.
So what I will do is that I will take this value.
I will multiply that with 100 percent plus 10 percent that is here and then now I will take the power
of that, which is basically four, because we have to take it four times.
So we take the power for now.
I'm just going to hardcoded for now just to save time.
And here is the value of this particular amount at the end of year five.
Now, I will just basically launched the sell of the interest rate.
And now what I'm going to do is that I'm just going to copy paste and I will correct the headings.
I will just correct this number here.
So at the end of your two minutes, we have to calculate the interest for your three, four and five.
That means the power should be three.
And similarly, the power here should be to similarly the power here should be run.
And similarly, the power here should be nothing.
Actually, I'm sorry.
The power here should be.
Nothing, there should not be any power actually at the end of year five simply means that we don't
have to calculate any interest on that if five means year five.
So actually, I will not be earning an interest on that.
I will delete here.
I will just give equal this one.
OK, so that will be the future value for all of these five payments combined together at year five.
So I'm going to sum all of them and here is the value of all these five years.
Alternatively, you can use this Excel function of free and calculate that in a shortcut.
So equals AFV and then rate is 10 percent and then a number of payments are five.
And then we have the PMT, which is basically the payment for each year.
That is one hundred thousand.
And then we don't have any Peevey.
So I will just ignore it.
I will ignore that for now that that is by default.
We will go with the end of the period and maybe I can just write to zero or we can skip it.
It, it means the same thing.
And I will press control enter and you can see that we have the same value that we have calculated manually
here.
So you can do manually or you can use this Excel formula to calculate the value and shortcut.
Okay, so let me show you the variation in this formula.
So what if we change this zero to one?
And that would mean that all the payments are at the beginning of the year.
So let's add one, which will mean beginning of the period and then press enter and here we have the
different value.
Know how this different value has been calculated?
Let me show you, first of all, the first thing years are not starting from one, two, three, four.
Basically, the payments are at the beginning of each year and the beginning of year one is basically
called zero.
So I should also be adding an apostrophe here.
And here it is.
So that beginning of your one is basically zero and the beginning of your two is basically one year
for discounting and compounding purposes.
Same goes for three.
We have two classes with two.
Four should be replaced with three and five should be replaced with four.
If this concept is not clear, you can definitely ask me questions as well.
Not amount remain the same.
But now this factor would be changed.
Now, since we have not properly related, we have hardcoded the values.
These values have not been changed, so I will have to fix them now.
And so the first thing, if a payment has been made and how many times the compounding will take place
years ago means today and the year one means 12 months from now.
So definitely the compounding will happen once and then after that second year, 30 or 40 and 50 or
so, first, second, third, fourth and fifth, five times.
So compounding will be taking place.
And similarly here, the compounding will be taking place four times because this is the beginning of
the year two, which is the ending of year one.
So end of year one means we have second to your third or fourth year and fifty or the power should be
four.
And likewise the power should be three here.
And likewise, the power should be to here and there should not be any.
Well, yes, we have good company here as well because you can see that the power was to here.
No, we have to take the compounding.
The reason is this is the year four and that is the beginning of the year five.
So we have to take the interest one time.
So what I'm going to do is that I'm just going to copy and paste it here and then take the power as
to one.
OK, so here we have the same value as X that has given us if the payments are made in a series of annual
payments and basically the payments are at the beginning of the year, I really hope that this formula
is now clear.
We have one more to go and then we will be done with the present values and future values.