Time Value of Money

# Time Value of Money - o If interest rate is 7%, a deposit...

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THE TIME VALUE OF MONEY Why Investment Borrowing Declines as the Interest Rate Rises Future Value o The amount the sum will be worth at a given future date, when allowed to earn interest at the current rate. o EX: Deposit \$100 in the bank at 5% interest. o What is the future value (FV) of this amount? In N years, FV = PV(1 + r ) N FV = \$100(1 + 0.05) N o In three years, FV = \$100(1 + 0.05) 3 = \$115.76 o In two years, FV = \$100(1 + 0.05) 2 = \$110.25 o In one year, FV = \$100(1 + 0.05) = \$105.00 Compounding o The interest earned on the sum earns additional interest! o So even small differences in interest rates could lead to big differences in FV over time. o EX: Buy \$1000 worth of Microsoft stock, hold for 30 years. o If rate of return = 0.08, FV = \$10,063 o If rate of return = 0.10, FV = \$17,450 The Rule of 70 o If a variable grows at a rate of x percent per year, that variable will double in about 70/ x years. o If interest rate is 5%, a deposit will double in about 14 years.

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Unformatted text preview: o If interest rate is 7%, a deposit will double in about 10 years. Present Value o The \$\$ amount needed today to yield a future sum at the current interest rates. o EX: Let r = 0.06. Should General Motors spend \$100 million to build a factory that will yield \$200 million in ten years? o Find the present value of \$200 million in 10 years: o PV = FV/(1 + r ) N o PV = (\$200 million)/(1.06) 10 = \$112 million o Since PV > cost of factory, GM should build it. Present Value o What if r = 0.09? o Should General Motors spend \$100 million to build a factory that will yield \$200 million in ten years? o Find present value of \$200 million in 10 years: o PV = FV/(1 + r ) N o PV = (\$200 million)/(1.09) 10 = \$84 million o Since PV < cost of factory, GM should not build it. o Present value helps explain why investment falls when the interest rate rises....
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## This note was uploaded on 02/17/2011 for the course ECON 011 taught by Professor Yezer during the Fall '07 term at GWU.

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Time Value of Money - o If interest rate is 7%, a deposit...

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