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.
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 = 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 for the above formula:
(Example: For r enter 5.0% as 0.05, etc.)
