Question

Joe plans to deposit $200 at the end of each month into a bank account for a period of 2 years, after which he plans to deposit $300 at the end of each month into the same account for another 3 years. If the bank pays interest at the rate of 3.5%/year compounded monthly, how much will Joe have in his account by the end of 5 years? (Assume that no withdrawals are made during the 5-year period.)

Answer 1

Joe will have in his account by the end of 5 years $ 16,883.35

Step-1:Future value of monthly deposit of first 2 years
Future Value	=	Monthly deposit	*	Future value of annuity of 1	*	Future value of 1
	=	$       200.00	*	24.8225808	*	1.110554
	=	$   5,513.36
Working:
Future value of annuity of 1	=	(((1+i)^n)-1)/i		Where,
	=	(((1+0.002917)^24)-1)/0.002917		i	=	3.5%/12	=	0.002917
	=	24.8225808		n	=	2*12	=	24
Future value of 1	=	(1+i)^n		Where,
	=	(1+0.002917)^36		i	=	3.5%/12	=	0.002917
	=	1.11055416		n	=	3*12	=	36
Step-2:Future value of monthly deposit of next 3 years
Future Value	=	Monthly deposit	*	Future value of annuity of 1
	=	$       300.00	*	37.8999532
	=	$ 11,369.99
Working:
Future value of annuity of 1	=	(((1+i)^n)-1)/i		Where,
	=	(((1+0.002917)^36)-1)/0.002917		i	=	3.5%/12	=	0.002917
	=	37.8999532		n	=	3*12	=	36
Step-3:Future value of deposit at the end of 5 years
Future value of deposit	=	$   5,513.36	+	$ 11,369.99
	=	$ 16,883.35