You have just won the lottery and will receive a lump sum payment of $22.57 million after taxes. Instead of immediately spending your money, you plan to deposit all of the money into an account that will earn 4.84 percent. If you make equal annual withdrawals for the next 30 years, how much can you withdraw each year starting exactly one year from now?

Question

Cordell Grimes

Business

21 December, 06:29

You have just won the lottery and will receive a lump sum payment of $22.57 million after taxes. Instead of immediately spending your money, you plan to deposit all of the money into an account that will earn 4.84 percent. If you make equal annual withdrawals for the next 30 years, how much can you withdraw each year starting exactly one year from now?

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Answers (1)

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Dominique Choi · Answer 1

I will withdraw $1,441,542.

Explanation:

Wquivalent annual annuity is the amount equally received or paid with investment on a specified rate including interest and its compouding effect as well.

PV of Annuity (NPV) = Payment (EAA) * [ (1 - (1 + r) - n / r ]

22,570,000 = EAA * [ (1 - (1 + 4.84%) ^-30 / 4.84% ]

22,570,000 = EAA * [ (1 - (1 + 0.0484) ^-30 / 0.0484 ]

22,570,000 = EAA * [ (1 - (1.0484) ^-30 / 0.0484 ]

22,570,000 = EAA * 15.65685

EAA = 22,570,000 / 15.65685

EAA = $1,441,541.56

EAA = $1,441,542