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Estimate the money in the retirement account

Case Scenario:

Your client just turned 75 years old and plans on retiring in exactly 10 years (on her 85th birthday). She is saving money today for her retirement and is establishing a retirement account with your office. She would like to withdraw money from her retirement account on her birthday each year until her death. She would ideally like to withdraw $50,000 on her 85th birthday and increase her withdrawals by 10% a year through her 89th birthday (she would like to withdraw $73,205 on her 89th birthday). She is planning anticipating that she will die on her 90th birthday, at which time she would like to leave $200,000 to her children. Your client currently has $100,000. You estimate that the money in the retirement account will earn 8% a year over the next 15 years.

Your client plans to contribute an equal amount of money each year until her retirement. Her first contribution will come in exactly 1 year; her 10th and final contribution will come in 10 years (on her 85th birthday). How much should she contribute each year to meet her objectives?

Possible answers:

a) 12,998.63

b) 13,243.18

c) 13,759.44

d) 14,021.53

e) 11,943.34

f) 11,532,65

g) 11,004.59

h) 10,187.45

i) 11,875.34

j) 12,401.59

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