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Understanding the 3 Time Value of Money
O L Learning Objectives
Explain the mechanics of compounding.1
Use a financial calculator et’s just do what we always do—hijack to determine the time value of2 money. some nuclear weapons and hold the world “Lransom.” These are the words of Dr. Evil, played by Mike Myers in the movie Austin Powers, Understand the power of time in compounding. International Man of Mystery. Frozen, along with his cat, 3 Mr. Bigglesworth, in 1967 after escaping from the Electric Psychedelic Pussycat Swinger’s Club in London, Dr. Explain the importance of the interest rate in determining how Evil is thawed out in 1997 and immediately resumes his an investment4 grows. evil ways. Dr. Evil continues with his plan: “Gentlemen, it has come to
Calculate the present value of my attention that a breakaway Russian Republic Ripblackastan money to be received5 in the future. is about to transfer a nuclear warhead to the United Nations in a few days. Here’s the plan. We get the warhead, and we hold the world ransom for . . . one million dollars!” Define an annuity and calculate its compound or future value. Silence, followed by, “Umm, umm, umm” from Dr. Evil’s 6 Number 2 man, played by Robert Wagner: “Don’t you think we should ask for more than a million dollars? A million dollars is not exactly a lot of money these days.” “OK, then we hold the world ransom for $100 billion.” KEOWMC03_0132213893.QXD 15/2/06 9:35 PM Page 59
A million dollars in 1967 certainly bought more than a million dollars in 1997 did. But consider this, if Dr. Evil had taken a million dollars in 1967 and put it in the stock market, it would have accumulated to over $30.7 million when he was thawed out in 1997. However, that $30 million wouldn’t have the same purchasing power it did 30 years earlier. In fact, given the rate of inflation over that period, it would only purchase about one-fifth of what it would have in 1967. Three decades is a long time. The year Dr. Evil was frozen one of the top-rated TV shows was Bewitched, and The Monkees took top honors at that year’s Emmy Awards for best comedy show. The Green Bay Packers won Super Bowl I. Thirty years later Dr. Evil woke up to those same sitcoms airing on “Nick at Night” and the Green Bay Packers winning Super Bowl XXXI. But times had changed—now the world was full of personal computers, compact disks, MP3s, and cable TV. Now look to the future: For most of you, it will be well over 30 years before you retire. If you want to work out how much you will need for your golden years, how the heck do you look at today’s dollars and come up with a dollar figure? As we saw
in Principle 2: The Time Value of Money, a dollar received Principle today is worth more than a dollar received in the future. For 2 one thing, a dollar received and invested today starts earning interest sooner than a dollar received and invested some time in the future. Remember, the time value of money Time Value of Money The concept that a dollar received means that we can’t compare amounts of money from two today is worth more than a dollar received in the future and, different periods without adjusting for this difference in value. therefore, comparisons between Clearly, if you want a firm grasp on personal finance, it’s sums in different time periods cannot be made without important to understand the time value of money. adjustments to their values.
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Just how powerful is the time value of money? Think about this: if you were to invest $1,000 at 8 percent interest for 400 years, you would end up with $23 quadrillion—approximately $5 million per person on Earth. Of course, your invest- ments won’t span 400 years—it’s doubtful that you’ll be cryogenically frozen like Dr. Evil and Austin Powers—but your investments will rely on the time value of money. If you manage properly, time can be the ace up your sleeve—the one that lets you pocket more than you would have imagined possible. In personal finance, the time value of money is just as widespread as it is powerful. We’re always comparing money from different periods—for example, buying a bond today and receiving interest payments in the future, borrowing money to buy a house today and paying it back over the next 30 years, or determining exactly how much to save annually to achieve a certain goal. In fact, there’s very little in personal finance that doesn’t have some thread of the time value of money woven through it.
Explain the 1mechanics of Compound Interest and Future Values LOcompounding. How does the time value of money turn small sums of money into extremely large Compound Interest sums of money? Through compound interest. Compound interest is basically inter- The effect of earning interest on est paid on interest. If you take the interest you earn on an investment and reinvest interest, resulting from the it, you then start earning interest on the principal and the reinvested interest. In this reinvestment of interest paid on an investment’s principal. way, the amount of interest you earn grows, or compounds. Principal The face value of the deposit or debt instrument. How Compound Interest Works Anyone who has ever had a savings account has received compound interest. For example, suppose you place $100 in a savings account that pays 6 percent interest annually. How will your savings grow? At the end of the first year you’ll have earned 6 percent or $6 on your initial deposit of $100, giving you a total of $106 in your Future Value (FV) savings account. That $106 is the future value (FV) of your investment, that is, the The value of an investment at value of your investment at some future point in time. The mathematical formula some future point in time. illustrating the payment of interest is
future value present value or beginning amount interest earned FV1 PV PV(i) PV(1 i) (3.1)
where FV1 the future value of the investment at the end of 1 year i the annual interest rate; the interest earned is based on the balance at the beginning of the year and is paid at the end of the year. In this case i 6% Present Value (PV) or, expressed in decimal form, 0.06. The current value, that is, the value in today’s dollars of a future sum PV the present value, or the current value; that is, the value in today’s of money. dollars of a sum of money
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In our example