Introduction to Finance

Begin:
1 ÷ 1.08 × 1 ÷ 1.08 = $1,000 Future Value
End:
Present Value = $857.30
Year
0
1
2
(0.9259) × (0.9259)
Thus, for a one-year investment, the present value would be $925.90 ($1,000 × 1 ÷ 1.08, 
or 0.9259). A two-year investment would have a present value of only $857.30 ($1,000 × 
0.9259 × 0.9259).
The discounting concept can be expressed in equation form, as follows:
PV = FV
n
÷ (1 + 
r
)
n
or
PV = FV
n
[1 ÷ (1 + 
r
)
n
] (9.3)
where the individual terms are the same as those defi ned for the future value equation. Notice 
that the future value equation has simply been rewritten to solve for the present value. For the 
$1,000, 8 percent, two-year example, we have,
PV = $1,000[1 ÷ (1 + 0.08)
2
]
= $1,000(1 ÷ 1.1164)
= 
$1,000(0.8573)
= 
$857.30
= $857 (rounded)
If we extend the time period to ten years, the $1,000 future value would decrease to,
PV = $1,000[1 ÷ (1 + 0.08)
10
]
= $1,000(1 ÷ 2.1589)
= 
$1,000(0.4632)
= 
$463.20
= $463 (rounded)
Most fi nancial calculators are programmed to readily fi nd present values. As noted, fi nan-
cial calculators, typically, have a present value (PV) key, a future value (FV) key, a number 

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9.3 Discounting to Determine Present Values
227
of time periods (N) key, an interest rate (%i) key, and a compute (CPT) key. If you have a 
fi nancial calculator, you can verify the present value result for the ten-year example. First, 
clear the calculator. Then, enter 1000 (or –1000 for some calculators, to fi nd a positive PV) 
and press the FV key, enter 8 and press the %i key, and enter 10 and press the N key. Finally, 
press the CPT key followed by the PV key to calculate the present value of 463.19, which 
rounds to $463.