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Time and money are interrelated.

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When we think of investing money in an asset such as buying shares from stock market, creating a fixed

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deposit or purchasing a property, etc., we spend some money today with the hope of getting more money

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tomorrow.

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Some investments are more secure or less risky, such as government bonds or fixed deposits, where

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we usually know the exact return which we will get after a certain point of nine.

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On the other hand, there are certain investments where we do not know the exact return that is these

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investments are risky, such as buying shares from stock market, but we still put money in those because

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of the possibility of higher returns.

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But regardless of the kind of investment, the assumption is that future value of the investment will

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be more than what you invest today.

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In this lecture, we will learn how to calculate future value of our investment if we know certain parameters

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related to the investment.

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The first concept that we will discuss is of interest rate.

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When we deposit money into a bank.

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The bank usually adds money to your deposit on the basis of some pre decided percentage.

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This percentage by which your deposit will increase at the end of one time period is called interest

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rate.

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For example, if I stole a hundred dollars in a bank.

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And at the end of one time period, I get one under six dollars back.

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This means that the interest rate is one under six minus hundred by a hundred, which comes out to be

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six percent part time period.

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Now, the time period could be your month, quarter, etc..

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When we have the deposit stored for more than one time period, two situations may arise.

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For example, if you stored two hundred dollars in the bank, which was offering three percent per annum

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interest rate.

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Now, after the end of Forestier.

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You will get two hundred plus six dollars in the interest.

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That is the calculated interest will be six dollars, which is three percent of two hundred dollars.

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Now, in the second year, the bank has two options, either to give you interest only on the two hundred

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dollars which you initially stored in the bank.

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If the bank does so, three percent of 200 will again come out to be six dollars and the total interest

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that you will earn will be twelve dollars.

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Or the other option is that at the end of year one, the total balance in your account will be two hundred

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six dollars.

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Which is two 200 initial investment done by you and six dollar interest earned by you on this investment.

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So on two hundred six dollars, the bank will pay you three percent interest, which will come out to

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be six point one dollars.

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So the total interest earned by you will be twelve point one eight dollars.

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The first type of system where you get interest only on the initial deposit on all the time period.

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This is called applying simple interest.

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And the other type of system where we get interest on the previously owned interest, also, this is

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called compounding of interest.

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Now, let us look at these two types mathematically to understand them more deeply.

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So if we store principal amount B, that is B, deposit B amount.

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If we are applying simple interest.

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At the end of time, it is equal to one the simple interest that we will not be will be paying to the

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rate of interest.

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Here we are denoting a rate of interest with the smaller.

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Similarly, on the next time period.

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Since it is simple interest and the interest will be calculated on the principal amount, only the new

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interest will again be being told.

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Same goes for the third time period.

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And so on.

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Finally, the total amount that you will have in your account at the end of time, be will be the principal

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B plus the total interest, which is B into R and B.

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So this is the formula of future value if you are getting simple interest on your investment, be.

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If you put big dollars today and you are earning interest at rate R and you put it four times better

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to the final amount, the future value of that investment would be B plus being do our T.

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If you're doing compound interest.

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At the end of time, one, the interest will be again being Duaa, which is the same as in Berlin just.

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But on the second time period, the initial balance will be B plus being the word on which you will

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under interest at a rate R, so it will be B plus peer into what?

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In the third time period, your interest will be on the complete value P plus PR plus B plus PR in the

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war.

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On this, you will earn the interest and if you solve this.

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You will get this value being too far into one plus R-squared.

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And so on, and if you look at the these values carefully, this becomes a geometric progression.

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If you continue like this and add all these values, the final value that you will get is built into

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one plus are raised to the poverty.

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So if you compare earlier, it was B plus B into our industry now is being two.

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One plus are raised to the power the.

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This is calculated using the formula for some of geometric progression, which is a very common mathematical

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series, if you want to know more about it, just sort some of geometric progressions.

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So this is the final value.

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So this is a formula for future value, if we are doing compound interest, it will be B plus being

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the address to the poverty.

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Now, let us look at.

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Some examples in Excel to understand it more clearly.