I deposited $10,000 in a savings account that paid 1% interst each
month. What is the effective annual rate of interest?

Hi!!


I = Nominal Rate = Periodic Rate x Number of Compounding Periods ==>

==> i = Periodic rate = Nominal rate/Number of Compounding Periods = I/n

Where:
n = the number of compounding periods 
I = the nominal interest rate 


Effective Annual Rate = (1 + I/n)^n - 1 = (1 + i)^n - 1


For this problem:
i = 1% = 0.01
n = 12
I = 0.01 * 12 = 0.12 = 12%


Effective Annual Rate = (1+ i)^n - 1 
                      = (1 + 0.01)^12 - 1 
                      = (1.01)^12 - 1 
                      = (1.1268) - 1 
                      = 0.1268

The Effective Annual Rate is 12.68% .


I hope that this helps you.


Regards.
livioflores-ga