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# Time Value Of Money (Tvm) Paper

1344 words - 6 pages

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:•Interest rates and compounding•Present value (of a future payment received)•Future value (of an investment)•Opportunity cost•Rule of 72•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 ...view middle of the document...

5% interest to end up with \$1000 in a year, we will use the following formula:PV = FV / (1 + r)nWhere PV = present value, FV = future value, r = return (interest), n = number of periods.PV = 1000 / (1 + .045)1 = 1000 / 1.045 = \$956.94So, in order to have exactly \$1000 available in one year, I need to deposit \$956.94 in the ING Direct Bank at 4.5% interest.Again, if I can talk you into waiting two years for the \$1000, I would need to deposit less into the bank to have exactly enough to pay you:PV = 1000 / (1 + .045)2 = 1000 / 1.092025 = \$915.73So if you are generous in your payment demands and let me slide for two years, I need to deposit \$915.73 in the ING Direct Bank at 4.5% interest to have your \$1000 available on time.Future ValueI finally pay you the \$1000 and you decide to buy a Certificate of Deposit with your windfall. You go to the bank and see they are offering CDs with interest rates ranging from 4.90% to 5.10%. The bank offers CDs in the following term and interest rate combinations:CD TermAnnual Percentage Rate (APR)12 months5.10%24 months5.05%36 months5.00%48 months4.95%60 months4.90%The question before you is, "How much money can I make with these different interest rates and terms?" To calculate the future value of an investment we use the following formula:FV = PV x (1 + r)nWhere FV = future value, PV = present value, r = return (interest), n = number of periods.The value of each term/APR combination is shown in the following table:CD TermAnnual Percentage Rate (APR)FormulaFuture Value of \$100012 months5.10%1000 x (1 + .0510)1\$1051.0024 months5.05%1000 x (1 + .0505)2\$1103.5536 months5.00%1000 x (1 + .0500)3\$1157.6348 months4.95%1000 x (1 + .0495)4\$1213.1960 months4.90%1000 x (1 + .0490)5\$1270.22This is another example of compounding of interest. Every year past the first, you are earning interest on the interest. No wonder Albert Einstein is purported to have referred to compound interest as the greatest force on earth.Opportunity CostIf we go back to the \$1000 that I can pay you this year or wait until next year to pay, we will see that you should get your money now. Remember that ING Direct Bank is paying 4.5% interest, so why should I earn that interest and not you? As we have seen, if I keep the money and pay you next year, I can earn \$45 in interest. If you took the money now, you could have earned that \$45 - or even \$51...

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