# Appendix B: The Time Value of Money: Future Amounts and Present Values

Time value of money is an important concept and is used for making several business decisions specially when evaluating an investment prospect. The concept of the time value of money assumes future amount always higher than present value, and value of a dollar today always higher than a dollar in a future date. In investment decision the most fundamental concept is the time value of money. Under this concept we consider the amount of money available today can be invested today for higher amount in the future. Hence, we can consider value of money available today is equivalent to the higher amount would be available in the future date. In other words, time value of money is the concept of equivalent value of different amount of money between two point of time. These amount of money at two different point of time are considered as present value (money available today) and future amount (higher amount in the future). Example: Mr. A invest today $1,000 safely in bank at the interest rate of 5% per annum for two years. After 2 years Mr. A will get higher accumulated amount of principal amount and interest on the investment. Thus, Mr. A will get future amount $1,102.5 after 2 years.

The concept, time value of money is based on the analogy that an amount of money available today is equal to a larger sum of money after a period of time. For example, an amount of Rupees 100 available today is equal to a sum of money more than Rs100 basing upon the discounting rates. The amount available today is known as present value of money and the amount available on a future date is known as future value of money. a. Future amount = Present value X Factor Future value of $50,000 invested today for 10 years at 6% interest, compounded annually = $50,000 X 1.791 = $89,550 b. Present value = Future amount / Factor Present value of $240,000 to be received after a period of 5 years from today at 10% annual interest = $240,000 / 1.611 = $148,976 c. Future amount of an annuity = Periodic payment X Factor Future value of $20,000 invested annually at the end of each of the next 10 years at 8% interest, compounded annually = $20,000 X 14.487 = $289,740 d. Future amount = Present value X Factor Future amount of an annuity = Periodic payment X Factor Future value of $80,000 invested today for 3 years at 12% interest, compounded annually = $80,000 X 1.405 = $112,400 Future value of $6,000 invested annually at the end of each of the next 3 years at 12% interest, compounded annually = $6,000 X 3.374 = $20,244

Reason for the lower value of present value of future amount than the future amount: • The interest factor is the main reason for the difference between the lower values of the present value of the future amount as compared to future value. The time value of money is based on the fact that a dollar received today is worthiest than a dollar to be received in future. • The reason behind this is the dollar received today can be saved or invested and will be worth more than a dollar a year from today. Hence, the dollar to be received one year from today is currently worth less than a dollar today.