11.1: The Constant e and Continuous Compound Interest. Review (Mat 115). Just like π , e is an irrational number which can not be represented exactly by any finite decimal fraction. However, it can be approximated by for a sufficiently large x. e.
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for a sufficiently large x
Use your calculator, e = 2.718 281 828 459 …
DEFINITION OF THE NUMBER e
with n = 1 (interest is compounded annually
– once per year)
semiannually(2), quarterly(4), monthly(12),
weekly(52), daily(365), hourly(8760)…
A = Pert
A: future value
r: interest rate
t: number of years
Your Grandma puts $1,000 in a bank for you, at 5% interest. Calculate the amount after 20 years.
A = 1000 (1 + 0.0520) = $2,000.00
A = 1000 (1 + .05)20 =$2,653.30
A = 1000 e(.05)(20) = $2,718.28
What amount (to the nearest cent) will an account have
after 5 years if $100 is invested at an annual nominal rate
of 8% compounded annually? Semiannually? continuously?
A = Pert = 100e(.08*5)