Time value of money:
The time value of money is important when one is interested either in investing or borrowing the money. If a person invests his money today in bank savings, by next year he will definitely accumulate more money than his investment. This accumulation of money over a specified time period is called as time value of money.
Similarly if a person borrows some money today, by tomorrow he has to pay more money than the original loan. This is also explained by time value of money.
The time value of money is generally expressed by interest amount. The original investment or the borrowed amount (i.e. loan) is known as the principal .
The amount of interest indicates the increase between principal amount invested or borrowed and the final amount received or owed.
In case of an investment made in the past, the total amount of interest accumulated till now is given by;
Amount of interest = Total amount to be received – original investment (i.e. principal amount)
Similarly in case of a loan taken in past, the total amount of interest is given by;
Amount of interest = Present amount owed – original loan (i.e. principal amount)
In both the cases there is a net increase over the amount of money that was originally invested or borrowed.
When the interest amount is expressed as the percentage of the original amount per unit time, the resulting parameter is known as the rate of interest and is generally designated as ‘i' .
The time period over which the interest rate is expressed is known as the interest period . The interest rate is generally expressed per unit year. However in some cases the interest rate may also be expressed per unit month.
| Example: 1 |
A person deposited Rs.1,00,000 in a bank for one year and got Rs.1,10,000 at the end of one year. Find out the total amount of interest and the rate of interest per year on the deposited money.
Solution:
The total amount of interest gained over one year = Rs.1,10,000 - Rs.1,00,000 = Rs.10,000
The rate of interest ‘i' per year is given by;
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Similarly if a person borrowed Rs.1,50,000 for one year and returned back Rs.1,62,000 at the end of one year.
Then the amount of interest paid and the rate of interest are calculated as follows;
The total amount of interest paid = Rs.1,62,000 - Rs.1,50,000 = Rs.12,000
The rate of interest ‘i' per year is given by;
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Simple interest:
The interest is said to simple, when the interest is charged only on the principal amount for the interest period. No interest is charged on the interest amount accrued during the preceding interest periods. In case of simple interest, the total amount of interest accumulated for a given interest period is simply a product of the principal amount, the rate of interest and the number of interest periods. It is given by the following expression.
IT = P X n X i
Where
IT = total amount of interest
P = Principal amount
n = number of interest periods
i = rate of interest
Simple interest reflects the effect of time value of money only on the principal amount.