Question

Which one of the following has the highest effective annual rate? 6 percent compounded annually 6 percent compounded semiannually 6 percent compounded quarterly 6 percent compounded daily

Answer 1

Solution:
	Answer is 4th option 6 percent compounded daily
Working Notes:
	6 percent compounded daily has the highest effective annual rate
	Effective Annual rate (EAR) = (1+r/m)^m -1
	m is the number of compounding periods per year
	r is the interest rate APR
1st	6 percent compounded annually
	m = 1    annually
	r= 6%
	Effective Annual rate (EAR) = (1+r/m)^m -1
	=(1+ 0.06/1)^1 - 1
	=0.06
	=6%
2nd	6 percent compounded semiannually
	m = 2    for semi-annually
	r= 6%
	Effective Annual rate (EAR) = (1+r/m)^m -1
	=(1+ 0.06/2)^2 - 1
	=0.0609
	=6.09 %
3rd	6 percent compounded quarterly
	m = 4    for quarterly
	r= 6%
	Effective Annual rate (EAR) = (1+r/m)^m -1
	=(1+ 0.06/4)^4 - 1
	=0.06136
	=6.136 %
4th	6 percent compounded daily
	m = 365    for daily
	r= 6%
	Effective Annual rate (EAR) = (1+r/m)^m -1
	=(1+ 0.06/365)^365 - 1
	=0.061831
	=6.1831 %
Hence,	6 percent compounded daily have the highest effective annual rate that is 6.1831%
Please feel free to ask if anything about above solution in comment section of the question.