It is defined as the time-dependent value of money stemming both from changes in purchasing capacity of money (inflation or deflation) and from the real earning potential of alternative investments over time. Since money has the capacity to earn interest, its value increases with time. Hence it is the relationship between interest and time.

Money has a time value. The economic value of an amount depends on when it is received. Money has earning power over time.A rupee today is more valuable than a year hence. It is based on concept “the time value of money”. The recognition of the time value of money and risk is extremely vital in financial decision making.

The time value of money is the idea that money available at the present time is worth more than the same amount in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received.

Future sum = Principal + Interest

The time value of money establishes that there is a preference of having money at present than a future point of time. It means that a person will have to pay in future more, for a rupee received today.

The cost of money is measured by an interest rate, a percentage that is periodically applied and added to an amount of money over a specified length of time. Although the money left in the savings account earns interest so that the balance over time is greater than the sum of the deposits but whenever we go for any investment, we will have to consider the following three factors:

1. Liquidity: It is the reward for not being able to use your money while you are holding the stock or mortgage or promise.

2. Risk premium: It is the reward for any chance that you would not get your money back or that it will have declined in value while invested.

3. Inflation factor: It is compensation for the decrease in purchasing power between the time you invest it and time it is returned to you.

Hence interest may be defined as the cost of having money available for use.

For example:

Suppose your father gave you Rs. 100 on your tenth birthday. You deposited this amount in a bank at 10% rate of interest for one year. How much future sum would you receive after one year? You would receive Rs. 110

Future sum = Principal + Interest = $100 + 0.10 \times 100$ = Rs. 110

$FV_n = PV (1 + r)^n$

Where,

$FV_n$ = Future value of the initial flow n year hence

PV = Initial cash flow

r = Annual rate of Interest

n = Number of years