Question

You are saving $2,000 a year for retirement at the end of each year and plan to retire in 20 years. If you are planning for a 25-year retirement, what annual payment can you expect to receive at the end of each year during your 25-year retirement if your investments are earning 10% over your entire life?

$4,582

$8,426

$12,620

$13,880

Answer 1

Before retirement:

Annual saving = $2,000
Interest rate = 10%
Period = 20 years

Accumulated sum = $2,000*1.10^19 + $2,000*1.10^18 + ... + $2,000*1.10 + $2,000
Accumulated sum = $2,000 * (1.10^20 - 1) / 0.10
Accumulated sum = $2,000 * 57.2750
Accumulated sum = $114,550

After retirement:

Amount saved at the time of retirement = $114,550
Interest rate = 10%
Period = 25 years

Let annual withdrawal be $x

$114,550 = $x/1.10 + $x/1.10^2 + ... + $x/1.10^24 + $x/1.10^25
$114,550 = $x * (1 - (1/1.10)^25) / 0.10
$114,550 = $x * 9.07704
$x = $12,620

So, you can expect to receive $12,620 at the end of each year during your retirement.