# Continuously Compounded Interest

Formula for Continuously Compounded Interest

To calculate continuously compounded interest use the formula below. In the formula, A represents the final amount in the account that starts with an initial (principal) P using interest rate r for t years. This formula makes use of the mathemetical constant e .

Continuously Compounded Interest is a great thing when you are earning it! Continuously compounded interest means that your principal is constantly earning interest and the interest keeps earning on the interest earned!

## Practice Problems

$$ A = Pe^{rt} \\ A = 2,000\cdot e^{.13 \cdot 20} \\ A = \boxed{ \$26,927.47} $$

## Further Reading

- How compound Interest Really Works - an in depth look at how the math works and examples of how banks use compound interest.
- FHA Mortgage Calculator
- Continuously Compounded Interest
- Exponential Growth
- How credit card companies use compound interest
- real world compound interest stories