Continuous interest is when interest is
continuously reinvested.
The
formula for calculating the accumulated value via continuous interest
is as follows:
A
=
Pe^{rt}
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 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. 


We ask that if you like this software,
that you add one of the following links to your website:
Amortization
Software
Generate fixed, variable or
interestonly amortization schedules.
Mortgage Calculators
Track
loans with ease. Add, edit, or delete to manage irregular payments.
RELATED LINKS
