Effective to Nominal

Given an effective interest rate we can calculate the equivalent nominal interest rate.

n - is the number of compounding periods in a year

Effective to Annual Compounding

These are the same because all effective interest rates have annual compounding.

Effective to Semi-Annual Compounding

We have an effective interest rate of 10%.
What is the equivalent nominal interest rate with semi-annual compounding.

Effective to Quarterly Compounding

We have an effective interest rate of 10%.
What is the equivalent nominal interest rate with quarterly compounding.

Effective to Monthly Compounding

We have an effective interest rate of 10%.
What is the equivalent nominal interest rate with monthly compounding.

Effective to Daily Compounding

We have an effective interest rate of 10%.
What is the equivalent nominal interest rate with daily compounding.

Effective to Continously Compounded

The compounding frequency could be increased indefinitely to become continous
Taking the limits we get

ln - is the natural logarithm function