Question

Which of the following investments has the highest effective return? (All are of equal risk)

A bank CD which pays 10%, compounded monthly

A bank CD which pays 10.5%, compounded annually

A bank CD which pays 10%, compounded quarterly

A bank CD which pays 10.3%, compounded semiannually

A bank CD which pays 9.6%, compounded daily (on a 365-day basis)

Answer 1

A bank CD which pays 10.3%, compounded semiannually

Working:

Working:
a.	Effective return			=	((1+(i/n))^n)-1			Where,
	(mothly compounding)			=	((1+(0.10/12))^12)-1			i	10%
				=	10.47%			n	12
b.	Effective return			=	((1+(i/n))^n)-1			Where,
	(annually compounding)			=	((1+(0.105/1))^1)-1			i	10.5%
				=	10.50%			n	1
c.	Effective return			=	((1+(i/n))^n)-1			Where,
	(Quarterly compounding)			=	((1+(0.10/4))^4)-1			i	10.0%
				=	10.38%			n	4
d.	Effective return			=	((1+(i/n))^n)-1			Where,
	(Semi annual compounding)			=	((1+(0.103/2))^2)-1			i	10.3%
				=	10.57%			n	2
e.	Effective return			=	((1+(i/n))^n)-1			Where,
	(Semi annual compounding)			=	((1+(0.096/365))^365)-1			i	9.6%
				=	10.07%			n	365
Thus,
	CD which pays 10.3%. Compounding semi annually has the highest effective return.