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Unformatted text preview: Continuous
compounding involves compounding over every microsecond—the smallest time
period imaginable. In this case, m in Equation 4.18 would approach infinity.
Through the use of calculus, we know that as m approaches infinity, the equation
FVn (continuous compounding) PV (ei n) (4.19) where e is the exponential function10, which has a value of 2.7183. The future
value interest factor for continuous compounding is therefore
FVIFi,n (continuous compounding)
EXAMPLE ei n (4.20) To find the value at the end of 2 years (n 2) of Fred Moreno’s $100 deposit
(PV $100) in an account paying 8% annual interest (i 0.08) compounded
continuously, we can substitute into Equation 4.19:
FV2 (continuous compounding) $100
$100 e0.08 2
1.1735 $117.35 Calculator Use To find this value using the calculator, you need first to find the
value of e0.16 by punching in 0.16 and then pressing 2nd and then ex to get 1.1735. 10. Most calculators have the exponential function, typically noted by ex, built into them. The use of this key is especially helpful in calculating futu...
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