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Continuous interest is when interest is
continuously reinvested.
The
formula for calculating the accumulated value via continuous interest
is as follows:
A
=
Pert
where
A is
the accumulated value,
P
is Principal, r
is the annual interest rate,
t
is time in years.
Example 1
Calculate the interest earned from a $4,500 loan compounded
continuously at 5% for
6 years.
Here,
P = $4,500,
r = 5% = .05, and
m = 4 (quarterly).
Over 6-years, 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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Amortization
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