Time and money are interrelated.
When we think of investing money in an asset such as buying shares from stock market, creating a fixed
deposit or purchasing a property, etc., we spend some money today with the hope of getting more money
tomorrow.
Some investments are more secure or less risky, such as government bonds or fixed deposits, where
we usually know the exact return which we will get after a certain point of nine.
On the other hand, there are certain investments where we do not know the exact return that is these
investments are risky, such as buying shares from stock market, but we still put money in those because
of the possibility of higher returns.
But regardless of the kind of investment, the assumption is that future value of the investment will
be more than what you invest today.
In this lecture, we will learn how to calculate future value of our investment if we know certain parameters
related to the investment.
The first concept that we will discuss is of interest rate.
When we deposit money into a bank.
The bank usually adds money to your deposit on the basis of some pre decided percentage.
This percentage by which your deposit will increase at the end of one time period is called interest
rate.
For example, if I stole a hundred dollars in a bank.
And at the end of one time period, I get one under six dollars back.
This means that the interest rate is one under six minus hundred by a hundred, which comes out to be
six percent part time period.
Now, the time period could be your month, quarter, etc..
When we have the deposit stored for more than one time period, two situations may arise.
For example, if you stored two hundred dollars in the bank, which was offering three percent per annum
interest rate.
Now, after the end of Forestier.
You will get two hundred plus six dollars in the interest.
That is the calculated interest will be six dollars, which is three percent of two hundred dollars.
Now, in the second year, the bank has two options, either to give you interest only on the two hundred
dollars which you initially stored in the bank.
If the bank does so, three percent of 200 will again come out to be six dollars and the total interest
that you will earn will be twelve dollars.
Or the other option is that at the end of year one, the total balance in your account will be two hundred
six dollars.
Which is two 200 initial investment done by you and six dollar interest earned by you on this investment.
So on two hundred six dollars, the bank will pay you three percent interest, which will come out to
be six point one dollars.
So the total interest earned by you will be twelve point one eight dollars.
The first type of system where you get interest only on the initial deposit on all the time period.
This is called applying simple interest.
And the other type of system where we get interest on the previously owned interest, also, this is
called compounding of interest.
Now, let us look at these two types mathematically to understand them more deeply.
So if we store principal amount B, that is B, deposit B amount.
If we are applying simple interest.
At the end of time, it is equal to one the simple interest that we will not be will be paying to the
rate of interest.
Here we are denoting a rate of interest with the smaller.
Similarly, on the next time period.
Since it is simple interest and the interest will be calculated on the principal amount, only the new
interest will again be being told.
Same goes for the third time period.
And so on.
Finally, the total amount that you will have in your account at the end of time, be will be the principal
B plus the total interest, which is B into R and B.
So this is the formula of future value if you are getting simple interest on your investment, be.
If you put big dollars today and you are earning interest at rate R and you put it four times better
to the final amount, the future value of that investment would be B plus being do our T.
If you're doing compound interest.
At the end of time, one, the interest will be again being Duaa, which is the same as in Berlin just.
But on the second time period, the initial balance will be B plus being the word on which you will
under interest at a rate R, so it will be B plus peer into what?
In the third time period, your interest will be on the complete value P plus PR plus B plus PR in the
war.
On this, you will earn the interest and if you solve this.
You will get this value being too far into one plus R-squared.
And so on, and if you look at the these values carefully, this becomes a geometric progression.
If you continue like this and add all these values, the final value that you will get is built into
one plus are raised to the poverty.
So if you compare earlier, it was B plus B into our industry now is being two.
One plus are raised to the power the.
This is calculated using the formula for some of geometric progression, which is a very common mathematical
series, if you want to know more about it, just sort some of geometric progressions.
So this is the final value.
So this is a formula for future value, if we are doing compound interest, it will be B plus being
the address to the poverty.
Now, let us look at.
Some examples in Excel to understand it more clearly.