Question

You are celebrating your 22^nd birthday today. You have decided to start investing toward your retirement beginning one month from today. For the first twenty years, you will invest $500 every month. During the next ten years, you will increase your contributions to $900 per month. For the remainder of your working life until you retire at age 67, you plan to invest $1,500 every month. If your investments earn a rate of return of 8.4 percent throughout your working life, how much will be in your retirement account on the day you retire?

	A.	$1,885,411
	B.	$4,352,744
	C.	$2,900,421
	D.	$3,638,580

Answer 1

D.

$3,638,580

Working:

The question is based upon time value of money.
There are three cash flows are involved here.
First $ 500 for next 20 years
Second $ 900 for next 10 years and
Thirst $ 1500 for last 15 years.
In other words, we can say that $ 500 is invested for next 45(20+10+15) years.
Additional $ 400 is invested for 25 years (10+15) and
and further additional $ 600 is invested for 15 years (15).
Now future value of these cash flows are calculated as follows:
Step-1:Calculation of future value of $ 500 invested for 45 years.
Future value	=	Monthly investment	*	Future value of annuity of 1
	=	$                   500	*	6034.6899
	=	$       30,17,345
Working;
Future value of annuity of 1	=	(((1+i)^n)-1)/i		Where,
	=	(((1+0.007)^540)-1)/0.007		i	=	8.4%/12	=	0.007
	=	6034.689866		n	=	45*12	=	540
Step-2:Calculation of future value of $ 400 invested for 25 years.
Future value	=	Monthly investment	*	Future value of annuity of 1
	=	$                   400	*	1015.235
	=	$          4,06,094
Working;
Future value of annuity of 1	=	(((1+i)^n)-1)/i		Where,
	=	(((1+0.007)^300)-1)/0.007		i	=	8.4%/12	=	0.007
	=	1015.235029		n	=	25*12	=	300
Step-3:Calculation of future value of $ 600 invested for 15 years.
Future value	=	Monthly investment	*	Future value of annuity of 1
	=	$                   600	*	358.56864
	=	$          2,15,141
Working;
Future value of annuity of 1	=	(((1+i)^n)-1)/i		Where,
	=	(((1+0.007)^180)-1)/0.007		i	=	8.4%/12	=	0.007
	=	358.5686382		n	=	15*12	=	180
Step-4:Calculation of balance in retirement account on the day of retirement
Balance in retirement account	=	Sum of future value of all cash flows
	=	$       30,17,345	+	$ 4,06,094	+	$ 2,15,141
	=	$       36,38,580