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
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. How much money will you have, if
(a) The stock appreciates 20%
,
then depreciates 20% ?
First the stock appreciates 20%. So
n
= 1 and
r
= 0
.
20. Then we will
have
1(1 + 0
.
20) = 1
.
20 dollars
Next the stock depreciates 20%
.
So
n
= 1 and
r
=

0
.
20. Then we will
have
1
.
20(1

0
.
20) = 1
.
20
·
0
.
80 = 0
.
96 dollars
(b) The stock depreciates 20%
,
then apppreciates 20% ?
First, the depreciation:
1(1

0
.
20) = 0
.
80 dollars
Then, the appreciation:
0
.
80(1 + 0
.
20) = 0
.
80
·
1
.
20 = 0
.
96 dollars
(c) The stock appreciates 20%
,
for each of 5 consecutive years, then depre
ciates 20% for each of 5 consecutive years ?
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 Fall '06
 RUBIN,David
 ﬁrst equation

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