Your client just turned 75 years old and plans on retiring in 10 years on her 85
ID: 2663698 • Letter: Y
Question
Your client just turned 75 years old and plans on retiring in 10 years on her 85th birthday. She is saving money today for her retirement and is establishing a retirement account with you office. She wants to withdraw money from her retirement account on her birthday each year until she dies. She would ideally like to withdraw $50,000 of her 85th birthday, and increase her withdrawals 10% a year through her 89th birthday (i.e. $73,205 on her 89th birthday). She plans to die on her 90th birthday, at which time she would like to leave $200,000 to her descendants. 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 one year, her tenth and final contribution will come in ten years (on her 85th birthday). How much should she contribute each year in order to meet her objectives?Explanation / Answer
Step 1 Calculate the amount of withdrawls for each of the 4 years which would come to 50,000 55000 60500 66550 73205 Step 2 - Calculate the Present Value of these Cash Flows Cash Flow PVF N N 50000 $2.16 10 8% $23,159.67 55000 $2.33 11 8% $23,588.56 60500 $2.52 12 8% $24,025.38 66550 $2.72 13 8% $24,470.30 73205 $2.94 14 8% $24,923.45 Present Value of withdrawls $120,167.36 Step -3 Present Value of withdrawls 120,167.36 Present Value of 200,000 63,048.34 ( 200,000 * 0.52 ) Amount she requires 183,215.70 Amount currently with her 100,000.00 Hence she needs 83,215.70 step-4 Calculate the annuities whose Present Value is 83215.70 PVF-OA (10,8%) = 14.48 Hence PMT = 83215.7 / 14.48 = 5744.29 Hence she needs to make annual contributions of $5744.29
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