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.

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