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### Interest: Definitions

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Date: 9/25/96 at 23:12:48
From: Jake Taylor
Subject: math help

What does the term compound interest mean? What does continuous
compounding mean?
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Date: 10/29/96 at 20:15:14
From: Doctor Mason
Subject: Re: math help

Hi Jake!

Let's begin with simple interest.  Simple interest is computed only
once for the duration of the loan or investment.  Therefore, if you
plan to invest \$1000 for 3 years, the bank will figure the interest
only once at the end of the three years and then give it to you.
Let's say the account pays 5 percent interest.  At the end of three
years, the bank will calculate  \$1000 x .05 x 3 = \$150 and pay you
\$150 in interest.  If you add that to what you started with, you will
end up with \$1150.

Compound interest is calculated more often, and as soon as it is
calculated, the interest in added to your account. That way the next
time the interest is computed, you have MORE in your account than the
money you put there. Let's suppose your \$1000 is in an account paying
5 percent compounded semi-annually (twice a year) for three years.
We can use the Simple Interest formula over and over to figure your
interest. This formula is I = PRT, where I = the interest you get,
P = the amount you invest, R = the interest rate written as a decimal,
and T = the time in years. (For us our time is 1/2 since we're
figuring the interest twice each year.):

\$1000.00 x .05 x (1/2) = \$25 for the first 6 months.
\$1025.00 x .05 x (1/2) = \$25.63 for the second 6 months.
\$1050.63 x .05 x (1/2) = \$26.27 for the third 6 months.
\$1076.90 x .05 x (1/2) = \$26.92 for the fourth 6 months.
\$1103.82 x .05 x (1/2) = \$27.60 for the fifth 6 months.
\$1131.42 x .05 x (1/2) = \$28.29  for the last 6 months.

This makes for a total of \$1159.71 in your account!

As you can see, you end up with \$9.71 more if they calculate the
interest multiple times during the time the money is invested rather
than just at the end. You make more money because they are paying
you interest on the money they paid you earlier! Pretty neat, isn't
it? The more often the interest is compounded, the more interest you
earn. (By the way, banks don't do it by writing it all out the way we
did in our example above. They have charts and formulas that help
them calculate the compound interest quickly.)

Interest compounded continuously uses a formula that involves the
number "e".  "e" is like "pi" in that it's an irrational number that
people just found as they calculated things like growth and decay.
Continuous compounding is growth of money, so it fits the "e"
situation. Anyway, if you find an account that compounds continuously,
you would earn even more interest.  The formula for continuous
compounding is A = Pe^(rt) where the rate x time is the
exponent on the constant "e" (which is about 2.7).

Hope this helps.

-Doctor Mason,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Associated Topics:
High School Interest

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