Question

Which one of the following investments provides the highest effective annual rate of return (i.e., which of the following investments is the BEST = the largest EAR) over an investment horizon of 10 years)?

a. An investment which has a 3.0 percent nominal rate with annual compounding.

b. An investment which has a 2.98 percent nominal rate with semi-annual compounding.

c. An investment which has a 2.965 percent nominal rate with quarterly compounding.

d. An investment which has a 2.9575 percent nominal rate with monthly compounding.

e. An investment which has a 2.955 percent nominal rate and daily (365) compounding

Answer 1

b. An investment which has a 2.98 percent nominal rate with semi-annual compounding.

a.	Effective annual rate of return	=	((1+i)^n)-1			Where,
	(EAR)	=	((1+0.03)^1)-1			i	Nominal rate of return		0.03
		=	3.000%			n	Number of times compounding in a year		1
b.	Effective annual rate of return	=	((1+(i/n))^n)-1			Where,
	(EAR)	=	((1+(0.0298/2))^2)-1			i	0.0298
		=	3.002%			n	2
c.	Effective annual rate of return	=	((1+(i/n))^n)-1			Where,
	(EAR)	=	((1+(0.02965/4))^4)-1			i	0.02965
		=	2.998%			n	4
d.	Effective annual rate of return	=	((1+(i/n))^n)-1			Where,
	(EAR)	=	((1+(0.029575/12))^12)-1			i	0.029575
		=	2.998%			n	12
e.	Effective annual rate of return	=	((1+(i/n))^n)-1			Where,
	(EAR)	=	((1+(0.02955/365))^365)-1			i	0.02955
		=	2.999%			n	365
So,
b. An investment which has a 2.98 percent nominal rate with semi-annual compounding has highest effective annual rate of return.