Future Value and Compounding
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A future value (FV) is the amount of money an investment today (present value, or PV) will grow to over some period of time (t) at some given interest rate (r).
Investing for a Single Period The fundamental future value equation for one time period is: FV = PV(1 + r). $10,000 invested for one year at 10% will grow to _____. CONCEPT CHECK
Investing for More than One Period
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The fundamental future value equation for multiple time periods is: FV = PV(1 + r)t, where t represents the number of time periods. $10,000 invested for ten years at 10% will grow to _____. CONCEPT CHECK
Present Value and Discounting
The Single-Period Case
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The fundamental present value equation for one time period is: PV = FV[1/(1 + r)]. The value today of $10,000 to be received in one year, given a 10% discount rate, is (a) $10,000, (b) $9,090.91, or (c) $8,264.10? CONCEPT CHECK
Present Values for Multiple Periods The fundamental present value equation for multiple time periods is: PV = FV[1/(1 + r)t]. The value today of $10,000 to be received in ten years, given a 10% discount rate, is (a) $10,000, (b) $7,196.92, or (c) $3,855.43? CONCEPT CHECK
More on Present and Future Values
Present versus Future Value Note that the PV factor is the reciprocal of the FV factor, and the FV factor is the reciprocal of the PV factor.
Determining the Discount Rate
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The basic PV equation contains four variables: present value (PV), future value (FV), discount rate (r), and the number of time periods (t). Given any three of these, we can always solve for the fourth. For $9,523.81 you can buy a U.S. Treasury bill that will pay the holder $10,000 in one year. What is the rate of return (r) on this investment? CONCEPT CHECK
Finding the Number of Periods
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Finding the number of periods is simply solving the basic PV or FV equation for t. Assume you invest $25,000 today at 12% compounded annually. How many years would it be before your investment grows to $1 million? (a) 100, (b) 77.44, (c) 56.09, (d) 32.55 CONCEPT CHECK
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