However, this is not the case with the $10000 received 3 years from now. Its value will be $10000 only since no interest will be earned as illustrated in the figure below:

In short, we can say that "a dollar today is worth more than a dollar one year from now" because the time value of money decreases over time. Why it decreases is the actual question. Interest rate, as we saw above is one apparent reason why money is related to time. Investing the money today would enable you to earn interest, causing it to grow to a larger amount over time. Let us now examine some of the other reasons and their impact on the time value of money.

Present value refers to a value that is equal to a value or values in future that have been discounted at relevant interest rate. For example, if you are expected to receive $10000 three years from now, the value of this 10000 today would be $9497 if the interest rate is 5% (PV= FV/ (1 + i )N) ) but if you were to receive $10000 five years from now, the present value would only be $7836.This $9497 at the beginning of the period is equal to $10000 at the end of the three years , showing that the value of money is related to time and therefore, causing the present value of an amount in the future to be less and less, the more you have to wait for it. When you had to wait for 3 years, the present value of $10000 was $9497 but when you had to wait for 5 years, the value of the same $10000 fell to $7836. This process of finding present values from future values is called discounting. The opposite is applicable for compounding. Compounding causes the future value to be larger and larger than the value today, the longer you have to wait for it because the value of money is related to time as illustrated by the numerical above.

2. Opportunity Cost:

The time value of money also includes the concept of opportunity cost or the cost of foregoing the next best alternative. For example, if you decide to get $10000 in three years rather than now, you are foregoing the enjoyment, interest and other benefits you could have acquired by taking it now. How much you will have to forego depends on the interest rate. The higher the interest rate, the greater the interest that you will have to forego and hence, higher your opportunity cost.

3. Annuities:

Annuities are a series of payments at regular intervals for a specified number of periods. If for example, you expect to receive the amount $10000 in 4 equal installments of $2500 each for the next 4 years, the present value of this stream of cash flows would amount to $8865 if the interest rate is 5% (PV = PMT [(1 - (1 / (1 + i)n)) / i]) while the future value would amount to $10775 (FV = PMT [((1 + i)n - 1) / i]). However, if the same $10000 was to be paid in 5 equal installments of $2000 each in the next 5 years, the present value would be $8659 and the future value would be $11051.Clearly, the same rules are applicable here and affect the time value of money in the same way. The longer it takes for you to receive your sum of $10000, the lower will be the present value of the annuity and the higher will be the future value. When you had to wa
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