Getting Started - The Time Value Of Money
The concept of compounding dovetails into another concept you need to understand: the time value of money. This refers to the fact that a dollar today is worth more than the promise of a dollar in the future. Some reasons for this include the common human desire for immediate gratification and the increased risk of non-payment when the expectation of cash is deferred over a period of time.
Even if the person who owes you money is scrupulously honest, there is always a chance that he could run into problems and be unable to pay you back. Besides, if the money is in your pocket, you can do whatever you want with it, making it inherently more valuable dollar-for-dollar than money that is out on account. This is why lenders charge interest on money borrowed, and why investors expect some kind of financial return on their investments.
Present Value is the mathematical concept that compares the value of a dollar today versus the value of that same dollar in the future. You know from the preceding example that the present value of $115,762.50 at 5% interest over three years is $100,000. But how do you arrive at that number?
- Take 1 + the interest rate and raise it to the power of the number of years. In this example that would be 1.157625 (1.053).
- Instead of multiplying the present value by the factor to find the future value, you divide future value by that factor to find the present value. The final result is $100,000 ($115,762.50 ÷ 1.157625).
The formula states this more succinctly:
Basic Statistical Concepts
Present Value (PV) = FV ÷ (1+r)n
See Understanding The Time Value Of Money for more on this topic.