Compound interest is when interest is
calculated on principal and any previously earned interest.
Let's
consider an example. You invest $500 at a 5% annual interest
rate. After the first year, the account would earn
interest of:
I
=
Prt
= 500 * .05 * 1 = $25
If
you reinvest this $25 in earned interest, then at the beginning of
the 2nd year, the account would have $525 as principal. During
the 2nd year, the account would earn interest of:
I
= Prt =
525 * .05 * 1 = $26.25
which
is $1.25 more than what was earned in the first year. Compound
interest has the property that earned interest is automatically
reinvested to earn additional interest.
The
formula for calculating the accumulated value via compound interest
is as follows:
A
= P(1 + r/m)^{n}
where
A is
the accumulated value,
P
is Principal, r
is the annual interest rate,
m
is compounding frequency, and
n
is the total number of periods.
Example 1
Calculate the interest earned from a $4,500 loan compounded
quarterly at 5% for
6 years.
Here,
P = $4,500, r = 5% = .05, and m = 4 (quarterly). Over 6years,
there are n = 4*6 = 24 quarters. The accumulated value is:
A
= (4500)[1 + .05/4]^{24} = 6063.08
I
= A 
P =
6063.08  4500 = 1563.08
Example 2
A savings account pays 4% interest and is compounded daily (365
days). When will the accumulated value be twice the original
principal?
We
are solving for n:
2P
= P( 1 + .04/365 )n
log 2
= n log (1 + .04/365)
n =
log 2 / log (1 + .04/365) = 6325.32
n is the number of periods which for
this example, is in days. It will take 6325 days to double the
principal, which is roughly 6325/365 = 17.32 years.
The online calculator below calculates simple interest.
Change the loan amount
to the right and then click Calculate. 


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