1
Summer Lesson 28
MA 15200, Appendix I Sections 5.5 and 5.6
You are familiar with the simple interest formula,
I
prt
=
.
However, in many accounts
the interest is left in the account and earns interest also.
We say the account earns
compound interest.
For example:
Suppose Bob invests $100 at 10% simple interest.
At the end of 1 year,
Bob has earned
100(.10)(1)
$10
I
==
.
He now has $110.
(
A = P + Prt
or
A =
P(1
+rt
))
At the end of the 2
nd
year, Bob has earned
110(.10)(1)
$11
I
=
=
.
He now has $121.
At the end of the 3
rd
year, Bob has earned
121(.10)(1)
$12.10
I
=
=
.
He has a total of
$143.10.
I’m sure you get the idea of what is happening.
Formula for Compound Interest
with
Annual
compound interest:
(1
) , where
is the initial investment (principal),
is the number of years,
is the annual interest rate, and
is the future value or final value.
t
SP r
P
tr
S
=+
Ex 1:
Assume that $1500 is deposited in an account in which interest is compounded
annually at a rate of 6%.
Find the accumulated amount after 5 years.
Ex 2:
Assume that $1500 is deposited in an account in which interest is compounded
annually for 5 years.
Find the accumulated amount, if the interest rate is 8 ½ %.
Many banks or financial institutions figure interest more often than once a year; quarterly
monthly, semiannually, daily, etc.
For example, if the annual rate or
nominal rate
is
12% and interest is compounded quarterly, that is equivalent to 3% every 3 months.
3%
is called the
periodic rate
.
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Formula for Periodic Rate:
Periodic Rate =
annual rate
number of periods per year
, where
is annual interest rate,
is the number of times
interest is paid each year, and
is the periodic rate.
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 Summer '09
 Future Value, Annual rate

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