Wikipedia defines the Time Value of Money (TVM) as "the premise that an investor prefers a payment of a fixed amount of money today, rather than an equal amount in the future, all else being equal."This paper will look at how annuities affect TVM problems and investment outcomes. Specifically, the following areas will be explored:Ã¢ÂÂ¢Interest rates and compoundingÃ¢ÂÂ¢Present value (of a future payment received)Ã¢ÂÂ¢Future value (of an investment)Ã¢ÂÂ¢Opportunity costÃ¢ÂÂ¢Rule of 72Ã¢ÂÂ¢AnnuitiesInterest Rates and CompoundingIf I offered you $1000 now or $1000 in a year, which would you prefer? You would probably prefer the money now, while I would prefer to give you the money in a year. The reason for the difference in preference rests with the time value of money.

Currently the interest rate is 4.5% on an Orange Savings Account at ING Direct Bank (http://home.ingdirect.com/products/products.asp?s=OrangeSavingsAccount). This is the interest rate I can earn on that $1000 if I wait until next year to give it to you.

This means that I will have $1045 ($1000 x 1.045) if I wait. The $1045 is the future value of the initial $1000 investment after one year earning 4.5% interest annually. If I can talk you into waiting another year for your $1000, I can earn another 4.5% and end up with $1092 calculated by $1000 x (1 + .045)2. The $1092 represents my initial investment of $1000 after two years earning 4.5% interest. I would be earning interest on the original $1000 and the additional $45 earned in the first year. As Brealey, Myers, and Marcus (2004) state, "Earning interest on interest is called compounding or compound interest" (pp. 68-69).

Present ValueAlternatively, instead of banking the entire $1000, I can also bank just enough so that, at the end of one year, I will have earned enough...