MAC1105: Compound Interest and Continuous Exponential Models
If
$P
o
is invested at
R%
interest compounded once per year, the formula is
t
0
P
P (1 r)
=
+
.
Interest does not have to be compounded once per year.
For example, if the number of annual compound periods
increases to
2
, then instead of getting
R%
interest annually, the interest would be (
R/2)%
applied twice a year.
So
as we divide the interest rate by the number of compound periods, we multiply the number of time intervals by that
same number in a slightly adjusted formula.
If we denote the number of compound periods as n, the formula
becomes
nt
0
r
P
P 1
n
=
+
=
+
.
Now suppose we let the number of compound periods increase to
∞
.
The formula
becomes
rt
0
P
P e
=
.
In these formulas
R
is called the
nominal interest rate.
# compound
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 Fall '08
 Algebra, Effective Interest Rate, Nominal Interest Rate, #, $100, $106

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