SOLUTION: What interest rate compounded monthly will yield an effective interest rate of 8​%?

The problem asks which NOMINAL annual interest compounded monthly is equivalent to the annual interest of 8% compounded annually.


Let x be the nominal interest rate  under the question.


Then the account grows from month to month with the effective growing coefficient .


Thus the equation to find x is THIS


     = 1 + 0.08,   or

     = 1.08.


From the equation


     = 1.08^(1/12) = 1.006434.


and finally you get


     = 1.006434 - 1 = 0.006434.


Therefore,  x = 12*0.006434 = 0.0772.


Thus the equivalent (or effective) nominal annual interest rate is 7.72%.


ANSWER.  NOMINAL annual interest compounded monthly, equivalent to the annual interest of 8% compounded annually, is 7.72%.


         Or, in more compact form,  8% annual interest compound annually, is equivalent to 7.72% annual interest compound monthly.