Force of interest

Force of interest refers to a nominal interest rate or a discount rate compounded infinite number of times (or continuously) per time period.

Consider a nominal interest rate(or even a discount rate) compounded half-yearly and another rate compounded quarterly, another rate compounded monthly, compounded weekly, compounded daily, compounded every second and so on until you can imagine an interest rate that is compounded every smallest fraction of a second(continuously). This interest rate compounded continuously is the force of interest.

If i^p  is the interest rate compounded p times a year, then the limit of i^(p)  as p tends to infinity, would be the force of interest.

Mathematically: