Continuous Interest

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Explanation

Continuous interest is a form of compound interest. With continuous interest the length of the compounding period is reasoned to be infinitely small. The interest, therefore, is compounded continuously.

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Formula

S	Final value of investment
P	Initial value of investment
r	Annual percentage rate (APR)
t	Number of years

Value of investment after t years:

S = Pe^rt

Where e is the transcendental number 2.7182818285...

Notice that the output, S, is an exponential function of t. That is, if we consider the final value of the investment as a function of the length of time for the investment, then t, the length of time for the investment, is in the exponent position, and this makes S an exponential function of t.

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Example calculation

If $4000 is invested at an annual rate of 6.0% compounded continuously, what will be the final value of the investment after 10 years?

S = Pe^rt

S = 4000e^(0.06)(10)

S = 4000e^0.6

S = 4000(1.822188)

S = $7288.48

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Calculator for continuous interest:

S = Pe^rt

S	Final value of investment
P	Initial value of investment
r	APR, Annual percentage rate
t	Number of years

Enter values for the above formula:

(Example: For r enter 5.0% as 0.05, etc.)

P: r: t:

After entering values into the above input areas, click the following 'Calculate' button to get S, the final value of the investment.

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