# Time Value of Money

### Time Value of Money

One of the fundamental ideas in economics is that a Rupee tomorrow is worth less than a Rupee today. This is because of two reasons.

(i) The future is uncertain

(ii) The interest rate – inflation

Todays Rs.100= 00 can be invested at 8% interest so that one year after today Rs100 will become Rs.108= 00. Another way of saying the same thing is that Rs.100 one year hence is not equal to Rs.100 = 00 of today, but less than that. But how much money today is equal to Rs.100 one year hence. To find it out we shall have to find out the relevant rate of interest which one would earn if one decides to invest the money.

Suppose the rate of interest is 8%. Then we shall have to discount Rs.100 at 8% in order to ascertain how much money today will become Rs.100 one year after. The formula is

P.V. = Rs100 / 1 + i

Where P.V. = Present Value & I = Rate of interest.

 P.V. =  100 = 100 = Rs. 92.59 1 + .08 1 + .08

As a cross check Rs. 92.59 x 1.08 = Rs.100 = 00

i.e. Rs. 92.59 deposited at 8% today will become Rs. 100 = 00 after one year.

The same reasoning applies to longer periods. A sum of Rs. 100 = 00 two years from now is worth

 P.V. =  100 =  100 = 100 = Rs. 85.73 (1 + i)2 (1 +08)2 1.1664