Question

1. You have 35 years until your retirement. You currently have $50,000 in your 401(k) account. You can contribute $10 thousand per year and your company will match 50 percent of your contribution. You expect an average return of 8% over the life of your 401(k) investments.
2. a. What is your future value of your 401(k) in 35 years?
3. b. What is your future value of your 401(k) if the average return drops to 5%?
4. c. Given the original information above (35 years until retirement, average return of 8%, and $50,000 currently in your 401(k)), how much would you have to start saving per year if you wanted your 401(k)’s future value to be $1,500,000 by the time you want to retire?  

Answer 1

Answer

a) Calculation of future value

Future value of annuity =	Present value of annuity *Future value factor at 8% for 35 years
	=$10,000*172.317
	$       1,723,170
Future value of current balance=	Present value *Future value factor at 8% for 35 years
	=50,000*14.785
	$          739,250
So ,Total future value of 401(k)	$       2,462,420 (1,723,170+739,250)

b)

Future value of annuity=	Present value of annuity *Future value factor at 5% for 35 years
	=$10,000*90.320
	$          903,200
Future value of current balance=	Present value *Future value factor at 5% for 35 years
	=50,000*5.5160
	$          275,800
So ,Total future value of 401(k)	$       1,179,000 (903,200+275,800)

c)

Total future value	$       1,500,000
Future value of current balance=	Present value *Future value factor at 8% for 35 years
	=50,000*14.785
	$          739,250
Future value of annuity=	Present value of annuity *Future value factor at 8% for 35 years
$        760,750	=Present savings*172.317
So Present savings	$               4,415

So $4,415 should save per year to get a future value of $1,500,000 .