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Notes on Present Value (PV), Future Value (FV), Compounding and Discounting
Assume an opportunity cost of capital, r, of 4% p.a.
Future Value:
What is $100 worth at a future date (time t)?
Present Value
Time t = 0
Future Value
t = 1 Year
Future Value
t = 2 Years
Future Value
t = 3 years
Future Value
t = 4 years
$100
100(1 + .04) =
104
PV(1 + r)
104(1 + .04) =
108.16
PV(1 + r)
2
108.16(1 + .04) =
112.49
PV(1 + r)
3
112.49(1 + .04) =
116.99
PV(1 + r)
4
Future Value Factor
(FV/PV)
(1 + r)
1.04
(1 + r)
2
1.086
(1 + r)
3
1.1249
(1 + r)
4
1.1699
Notice that we are compounding interest, i.e. the interest earned each year is reinvested in succeeding years.
Generally:
FV = PV (1 + r)
t
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*Sign up* Present Value:
What is $100 payable at time t worth today?
One way to look at this question is to let the answer be
x
, i.e.
x
is the present value of the $100 to be paid at a future
date.
From what we did above, we know that
x
(1 + r)
t
= 100, where
x
is the Present Value and $100 is the Future Value.
x

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