# Continuous Interest

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.

Formula symbols:

 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 = Pert

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.

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 = Pert

S = 4000e(0.06)(10)

S = 4000e0.6

S = 4000(1.822188...)

S = \$7288.48

Calculator for continuous interest

S = Pert

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

Enter values below for the above formula. When this page loads the values are set to an initial investment of \$100, an annual percentage rate of 5.0% (0.05), and an investment period of 2 years.

(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.

Click the following 'Code' button to see the actual JavaScript code that executes in the above calculator. Click on this button to see exactly how the above calculator arrives at its result.

Here's the code that runs when you click the above 'Calculate' button. It is shown here as an aid for your study and understanding.

You can change the code, if you like, and then click the following 'Reevaluate code' button. The program will then work as per your changes when you click the 'Calculate' button on the above calculator. Of course, your changes, especially random changes, can introduce errors, miscalculations, and browser crashes. If you need to get things back to their original condition, just reload this page using your browser's reload button.

Again, the intention here is to conveniently show you the inner workings of this program so that you understand how the program arrives at the result. Click the 'Code' button again to close this section.

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