What is meant by the Time Value of Money?

Money has time value. The idea behind time value of money is that a rupee now is worth more than rupee in the future.  The  relationship between value of a rupee today and value of a rupee in future is known as ‘Time Value of Money’.  A rupee received  now can earn interest in  future.  An amount invested today has more value than the same amount invested at a later  date  because it can utilize the  power of compounding. Compounding is the process by which interest is earned on interest. When a  principal amount is  invested, interest is earned on the principal during the first period or year. In the second period or year,  interest is earned on the original principal plus the interest earned in the first period. Over time, this reinvestment process can  help an amount to grow significantly.

Let us take an example:

Suppose you are given two options:
(B) Receive Rs.10,000 after three years.

Which of the options would you choose?

Rationally, you would choose to receive the Rs. 10,000 now instead of waiting for three years to get the same amount. So, the  time value of money demonstrates that, all things being equal, it is better to have money now rather than later.

Back to our example: by receiving Rs.10,000 today, you are poised to increase the future value of your money by investing and  gaining interest over a period of time. For option B, you don’t have time on your side, and the payment received in three years  would be your future value. To illustrate, we have provided a timeline:

If you are choosing option A, your future value will be Rs. 10,000 plus any interest acquired over the three years. The future  value for option B, on the other hand, would only be Rs. 10,000. This clearly illustrates that value of money received today is  worth more than the same amount received in future since the amount can be invested today and generate returns.
Let us take an another example:

If you choose option A and invest the total amount at a simple annual rate of 5%, the future value of your investment at the  end of the first year is Rs. 10,500, which is calculated by multiplying the principal amount of Rs. 10,000 by the interest rate of  5% and then adding the interest gained to the principal amount.

Thus, Future value of investment at end of first year:
= ((Rs. 10,000 X (5/100)) + Rs. 10,000
= (Rs.10,000 x 0.050) + Rs. 10,000
= Rs.10,500

You can also calculate the total amount of a one-year investment with asimple modification of the above equation: Original  equation: (Rs.10,000 x 0.050) + Rs.10,000 = Rs.10,500 Modified formula: Rs.10,000 x [(1 x 0.050) + 1] = Rs.10,500  Final  equation: Rs. 10,000 x (0.050 + 1) = Rs. 10,500 Which can also be written as:

S = P (r+ 1)
Where,
S = amount received at the end of period
P = principal amount
r = interest rate (per year)

This formula denotes the future value (S) of an amount invested (P) at a simple interest of (r) for a period of 1 year.

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