Question

You are saving \$2,000 a year for retirement at the end of each year and plan...

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

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.