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Dr. Raja Latif.Finite Mathematics.Pg:1
Math131
(
043Smr2005
)
Finite Mathematics
.
10
.
3 Interest Compounded
Continuously
Objective: To extend the notion of
compound interest discussed in Chapter 8
to the situation where interest is
compounded continuously. To develop
formulas for compound amount and
present value.
Continuous Compound Interest Formula:
Suppose a principal of
P
dollars is invested
for
t
years at an annual rate of
r
.
If interest
is compounded
k
times a year, then the
rate per conversion period is
r
/
k
,
and there
are
kt
periods. The compound amount is
given by
S
P
1
r
k
kt
.
If
k
,
the
number of conversion periods increases
indefinitely, and the length of each period
approaches
0.
We say that interest is
compounded continuously. The compound
amount is
S
k
lim
P
1
r
k
kt
which may
1
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View Full DocumentDr. Raja Latif.Finite Mathematics.Pg:2
be written
S
P
k
lim
1
r
k
k
/
r
rt
.
By
letting
x
r
/
k
,
then as
k
,
we have
x
0.
Thus
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 Spring '09
 Dr.RajaLatif
 Math

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