Maria's parents hope to have a comfortable retirement. They recognize that careful planning can put them on the right track toward achieving that retirement, and they are lucky to have a daughter who can help them formulate that plan. Maria, her parents, and most people recognize that the value of money depends not only on the amount received, but also on when it's received. The tricky part is accurately quantifying the relationship between time and value, which is where Maria's skill becomes handy.

As you study finance, you will gain the mathematical skills necessary to estimate how value is affected by time. For example, the Washington State lottery advertises its grand prize as $1,000,000. On closer scrutiny, the prize is paid as 20 annual installments of $50,000 each. Very few lottery customers are fooled into believing that the value of the prize is really the same as receiving the full million dollars up-front in a single payment. That is because most people have an intuitive sense of the time value of money - a dollar received today is worth more than a dollar received in the future. How much less is a function of at least two important variables. First, how far into the future will the money be received? The more time until the receipt, the less the money is presently worth. Second, how certain can one be that the money will actually be received in the amount and at the time that it is expected? That is, the riskier or more uncertain the future cash flow is, the lower its present value. These fundamental ideas underlie time-value mathematics, also known as discounted cash flow analysis.

An understanding of the following terms is crucial to the successful completion of the exercises that follow.

• Compounding - The process of determining the future value of a payment or series of payments.
   
• Discounting - The process of determining the present value of a payment or series of payments.
   
• Present Value - The process of discounting future cash flows back to the present.
   
• Future Value - The process of compounding or bringing cash flows forward to some future period of time.
   
• Annuity - An annuity makes fixed payments over equal periods of time.
   
• Ordinary Annuity - Makes payments at the end of each payment period.
   
• Annuity Due - Makes payments at the beginning of each payment period.

 
 
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