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 Amortization Software > FREE > Mortgage Calculators
Continuous Interest
Consumer Mathematics with FREE Online Calculator
 

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.

 

 

 

 

 

 

Compound Interest
Principal
Annual Interest Rate  %
Time (in years) 

Interest earned 
Accumulated Value

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