In finance, the "time value of money" concept states that any amount of money is worth more today than in the future. Because you can earn interest on the money, it follows that a fixed sum of money will be worth more in the future since at the end of the period, you will have the principal plus the interest earned on any investment, such as a deposit in a savings account. The value of a fixed sum today is its present value, and the value at a certain point in the future is its future value.
Money and Time
Suppose you have the option of receiving $1,000 today or a year from now. You would most likely opt to receive the money today; as Investopedia points out, "All things being equal, it is better to have money now rather than later." In this example, the choice to take the money today is relatively straightforward because the two sums (future and present) are the same. But this is not always the case--for instance, if you had the option of receiving $1,000 today or $1,100 a year from now, you may not accept the money as readily as before.
If you have $1,000 today and invest the entire sum at an annual interest rate of 5 percent for a year, you will have $1,050 at the end of the year. The amount is calculated by multiplying the principal (1,000) by the interest rate (5) and then adding the interest amount (50) back to the principal. This example demonstrates that, given the prevailing interest rate, $1,000 today is worth $1,050 a year from now, or conversely, $1,050 a year from now is worth $1,000 today.
In the previous example, at the end of the one-year period if you invested the money for another year, you would have $1,102.50. This amount is calculated by multiplying the principal amount (1,050) with the interest rate and adding the interest earned to the principal. So, $1000 today is worth $1,102.50 two years from now given the interest rate. Similarly, you can calculate future values for any sum and for any number of periods by simply incorporating the new principal amount in the calculations.
Future Value Factor
In determining the future value of money, you do not have to calculate the value at the end of each period. If you know the number of periods, you can convert any sum of money to its value at a certain point in the future. For example, suppose you have $500 today and want to determine its value five years from now given an annual rate of 4 percent. You can calculate the value by multiplying the principal (500) to one plus the interest rate (1+0.04), raised to the power of the number of periods (5). In the example, the value of $500 five years from now is approximately $608.
In determining the present value of an amount you will receive in the future, you will have to look at the amount as the future value of an investment you made today. For instance, to calculate the present value of $1,000 that you will receive two years from now, pretend that the $1,000 is the total future value (principal plus interest) of some amount that you invested. This method determines the present value by calculating how much money you would need to invest, at an annual rate of 5 percent, to receive $1,000 two years from now. The present value is calculated by dividing the future value (1,000) by one plus the interest rate (1+ 0.04) raised to the power of the number of periods (2). In the example, the value of $1,000 two years from now is approximately $925.
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