Question

You deposit $4,000 in the bank at the end of each year for 30 years. If the bank pays interest of 5.25% per annum, what amount will you have accumulated if interest is compounded:

a. Annually

b. Semi-Annually

c. Quarterly

d. Monthly

e. Daily

Please show all your work and explain your answers.

Answer 1

	Future Value of Annuity =	P ( (1 + r)n - 1 ) / r
	EAR =	( 1 + r )^n - 1
a)	Future Value of Annuity =	4000* ((1 + 5.25%)^30 - 1) / (5.25%)
		277451.51
b)	EAR=	( 1 + 5.25%/2)^2 - 1
	EAR=	5.31890625000002%
	Future Value of Annuity =	4000* ((1 + 5.31890625%)^30 - 1) / (5.31890625%)
		280778.43
c)	EAR=	( 1 + 5.25%/4)^4 - 1
	EAR=	5.35426673707584%
	Future Value of Annuity =	4000* ((1 + 5.35426673707584%)^30 - 1) / (5.35426673707584%)
		282503.43
d)	EAR=	( 1 + 5.25%/12)^12 - 1
	EAR=	5.37818867274622%
	Future Value of Annuity =	4000* ((1 + 5.37818867274622%)^30 - 1) / (5.37818867274622%)
		283677.30
d)	EAR=	( 1 + 5.25%/365)^365 - 1
	EAR=	5.38985832635162%
	Future Value of Annuity =	4000* ((1 + 5.38985832635162%)^30 - 1) / (5.38985832635162%)
		284251.96