Question

Your client is 25 years old and wishes to retire at age 65. At that time, your client wishes to have saved $2,000,000. You advise the client to set aside money every year for the next 40 years. This money will be invested in a fund that you believe will average 10% each year for the next 40 years.

Required:

1. How much will your client need to set aside for each payment into the fund in order to accumulate the $2,000,000 total?
2. If your client’s life expectancy is age 80, how much can your client withdraw each year for the 15 years of retirement? The cost of money is 10%.

Answer 1

Answer a.

Desired sum at retirement = $2,000,000
Time to retirement = 40 years
Interest rate = 10%

Let annual deposit be $x

$x*1.10^39 + $x*1.10^38 + … + $x*1.10 + $x = $2,000,000
$x * (1.10^40 - 1) / 0.10 = $2,000,000
$x * 442.592556 = $2,000,000
$x = $4,518.83

Annual deposit = $4,518.83

Answer b.

Saving at retirement = $2,000,000
Period after retirement = 15 years
Interest rate = 10%

Let annual withdrawals be $x

$2,000,000 = $x/1.10 + $x/1.10^2 + … + $x/1.10^14 + $x/1.10^15
$2,000,000 = $x * (1 - (1/1.10)^15) / 0.10
$2,000,000 = $x * 7.606080
$x = $262,947.55

Annual withdrawal = $262,947.55