#### Overview of this book

Python for Finance
Credits
Acknowledgments
www.PacktPub.com
Preface
Free Chapter
Introduction and Installation of Python
13 Lines of Python to Price a Call Option
Introduction to Modules
Statistical Analysis of Time Series
Index

## Continuously compounded interest rate

In the previous section, our compounding frequency could be annual (`m=1`), semiannual (`2`), quarterly (`4`), monthly (`12`), or daily (`365`). If the compounding frequency increases further and further, such as by the hour, minute, and second, the limit is called continuously compounded. The following is the conversion formula:

Here, Rc is the continuously compounded rate, ln() is a natural log function, APR is the annual percentage rate, and m is the compounding frequency per year. For the natural log function, refer to the following code:

```>>>import math
>>>math.e
2.718281828459045
>>>math.log(math.e)
1.0
```

For example, if a given APR of 5 percent is compounded semiannually, its corresponding continuously compounded rate will be 4.9385225 percent, as shown in the following code:

```>>>import math
>>>2*math.log(1+0.05/2)
0.04938522518074283
```

In the next chapter, for a call option, the risk-free rate used is continuously...