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Exponential and Logarithmic Functions Homework
Solutions
STOR 112
Throughout, we use
r
to be the interest rate,
n
to be the number of compoundings
per time period, and
t
to be the number of time periods.
The general formula for compound interest is
P
±
1 +
r
n
²
nt
where
P
is the amount of money we start with.
The general formula for continuously compounded interest is
Pe
rt
where
P
is the amount of money we start with.
1. You invest a dollar in a stock. Suppose that
(a) the stock appreciates 20%
,
then depreciates
x
%
,
and as a result, you will
have your money back exactly, i.e. 1$. What is the value of
x
?
First, remember that if the rate is
x
% then
r
= 0
.
01
x
(for example, when
the rate is 20% then
r
= 0
.
20).
Then after the appreciation we will have 1
.
20, and after the depreciation
we will have 1
.
20(1

0
.
01
x
). But this is exactly 1, so solve for
x
:
1
.
20(1

0
.
01
x
) = 1
which gives
x
= 16
.
6667%.
(b) the stock depreciates
x
%
,
then appreciates 20%
,
and as a result, you will
have your money back exactly, i.e. 1$. What is the value of
x
?
Here, we will have (1
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 Fall '06
 RUBIN,David

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