Question

You fell that you can retire, if you have the equivalent of $2 million of today’s purchasing power in your retirement account when you retire. Currently, you have $50,000 in this account and you anticipate that your investments will earn an average return of 6% per year (APR with monthly compounding). You expect to inflation to average 2% per year (also APR with monthly compounding). You want to retire exactly 30 years from today. You plan to start putting the same amount of money (the same number of dollars bills) into your retirement account each month starting one month from today. How much do you need your retirement account to have in it on the day you retire to meet your goal: how much do you need to contribute to your retirement account each month to meet that goal? (you want to have enough to retire immediately after you make your monthly contribution to the account exactly 30 years from today)

Answer 1

FIRST PART: Amount of money in retirement account to meet the goal in 30 years is $3,642,418.

Calculations as given below:

FutureValue = CurrentValue *(1 + r)"

r= rate at which things change, in this case annual inflation of 2% APR = 2%/12 = 0.167%. (Monthly compounding).

n= time period = 30 years*12 = 360.

Current Value	$        2,000,000
Inflation Rate per Annum	0.167%
Time Line - Years	360
Future Value of $2M in 30 Years	$        3,642,418

SECOND PART: Contribution per month to meet the target given above.

Monthly Investment Amount (A) formula

A = Futurevalue* i (1 + i)" - 1)

In this case, Future Value = $3,642,418.

r = 6%/12 = 0.5% per annum

n= 360

So Monthly Investment = $3,626 to meet the Goal.