Time Value of Money

From the concept of compounding interest, lets discuss the time value of money. The time value of money is based on the fact that one will prefer to receive a certain amount of money today than the same amount in the future.

The example below will illustrate this point better.
Imagine you have won a cash prize! You are given 2 options to receive the money:A. To receive $1,000 now, orB. To receive $1,000 in three years.

Which option would you choose? Of course you would want the $1,000 now! Three years is a long time and why would you wait 3 years to get the money? You would say,”Give it to me NOW!” All things being equal, it is better to have money now rather than later.

A $100 bills does not have the same value as a $100 bill one year from now due to inflation. Although the face value of the bill is the same, you can do much more with the money if you have it now, and over time, you can earn more interest on your money.

Back to the example: by receiving $1,000 today, you can potentially increase the future value of your money (i.e. the value of your money in the future) by investing and gaining interest over a period of time. For option B, you actually lose out on the opportunity to earn interest.

How much would you have lost in choosing option B or how much would you have gained if you choose option A?In the earlier example where the compounding interest is shown step by step, the mathematical formula can be expressed as

FV = PV (1+ i)n
wherePV = the present value of the money
i = the interest rate
n =the number of compounding periods

Assuming the interest rate is 4.5% per annum, if you have taken $1,000 and invested it with compounded the interest over three years, the total amount you would have in 3 years
FV = 1,000 x ( 1 + 0.045)3= $1,141.16

In other words, your future value of $1,000 today is $1,141.16! Which means you would have lost $141.16 if you choosen option B or gain that amount if you have choosen option A.
Now you know why people say time is money.

The time value of money concept shows that there is a financial basis for saying that.