IGNOU : M.COM : MCO 7 : UNIT 2 : Q - 1. Explain "Time Value of Money". What is the role of interest rate in it ?

 

Ans. You must have heard that a rupee today is worth more than a rupee tomorrow. Did you imagine, why is it so? Let me tell you by an example. Anil's grandfather decided to gift him rupee one lakh (1,00,000) at the end of five years; and gave him a choice of having Rs. 75,000 today. Had you been in Anil's place what choice would you have made? Would you have accepted Rs. 1,00,000 after five years or Rs.75,000 today ? What do you say ? Apparently, Rs.75,000 today is much more attractive than Rs.1,00,000 after five years because present is certain than future. You could invest Rs.75,000 in the market and earn return on this amount. Rs.1,00,000 at the end of five years would have less purchasing power due to inflation, We hope you have got the message that a rupee today is worth more than a rupee tomorrow. But the matters money are not so simple. The time value of money concepts will unravel the mystery of such choices which all of us could face in our daily life. We may say a good understanding of time value of money constitute 90% of finance sense. Investment decisions involve cash flow occurring at different points of time. Therefore, recognition of time value of money is very important. In this unit, you will learn about compound interest aid discount concepts and how future value of a single mount and an annuity and present value of a single amount and an annuity is calculated

FUTURE VALUE OF A SINGLE CASH FLOW

First of all let us explain the meaning of future value. By future value (FV) we mean the amount of money an investment will grow to over some period of time at some given interest rate. In other words, future value is the cash value of an investment at sometime in future.

Future Value of a Single Amount for single period

If you deposit Rs. 1000 in a fixed account of your bank at 10% interest per year, how much you will get after one year ? You will get Rs. 1100. This is equal to your principal amount Rs. 1000 and Rs. 100 interest which you have earned on it in a year. Hence, Rs. 1100 is the future value of Rs. 1000 deposited (investment) for one year at 10 per cent. It means that Rs. 1000 today is worth Rs. 1100 in one year given that 10 per cent is the interest rate.

Thus, if you invest for one period at all interest rate of i, Your investment will grow to (1+i) per rupee invested. In the above example, I is 10 per cent.

 Future Value of a Single Amount fir more than One Period

Taking the various example, if you invest the same amount for two years what will you have after two years, assuming that interest rate remain the same '? You will earn Rs. 1100 + 10 + Rs. 100 interest during the second year so you will have total of Rs. 1210 (1100+ 110). This is the future value of 1000 for two years at 10 per cent.

You can notice here that this Rs. 1210 has four parts. First part is Ks. 1000 which is the principal amount, second part is Its. 100 as interest earned in first year and third part is another Rs. 100 earned as interest in second year. The fourth and last is Rs. 10 which is the interest earned in second year on interest paid in first year Rs. 100 x 10 = Rs. 10. So the total interest earned is Its 210. Hence, the future value is Rs. 1210 (1000+100+100+10).

The process of putting your money and any accumulated interest on an investment for more than a period, thereby reinvesting the interest is called compounding. Compounding the interest means earning interest on interest. We can call the result compound interest. The interest earned each period only on the original principal is called simple interest.