Continuous compound interest refers to the mathematical concept where interest is added to the principal balance of an investment continuously, rather than at discrete intervals (e.g., annually, semi-annually, quarterly, etc.).
In continuous compounding, the number of compounding periods becomes infinitely large while the time between periods becomes infinitesimally small.
continuous compound interest formula
The formula for continuous compounding is given by:
A = Pert
A is the future value of the investment/loan, including interest.
P is the principal investment amount (initial deposit or loan amount).
r is the annual interest rate (as a decimal).
t is the number of years that the money is invested or borrowed for.
e is the base of the natural logarithm, approximately equal to 2.71828.
Example Demonstrating Continuous Compound Interest
To understand what continuous compound interest is, let’s use a practical example involving bank accounts:
Imagine two banks:
Bank A: Offers to give you interest on your money once a year (annual compounding).
Bank B: Has a special account that continuously gives you interest all the time, every second of every day (continuous compounding).
Suppose you have $1,000 to deposit, and both banks offer a 5% interest rate. After one year, here’s what happens:
Bank A: At the end of the year, they give you 5% of $1,000, which is $50. So, you have $1,050 in total.
Bank B: Instead of waiting until the end of the year to give you the interest, they’re adding a tiny bit of interest every moment. By the end of the year, due to the magic of continuous compounding, you end up with a bit more than $1,050. It’s a small difference, but it’s more than Bank A.
Do you have different figures in mind? You can use this compound interest calculator.
Also Read: The Power of Compound Interest.
Conclusion
In the real world, no bank truly offers continuous compounding because it would be incredibly complex to track interest down to every tiny fraction of a second. However, some financial products or accounts might compound interest on a daily basis, which can make it feel almost like continuous compounding.
Do you want to explore the commonly used compounding frequency? Read this article on “What is Compound Interest Frequency“. Here you will know the 5 commonly used compounding intervals.
The concept is more of a mathematical ideal rather than a standard banking practice, but understanding it helps in fields like finance and economics.
