A man is planning to retire in 15 years. Money can be deposited at 4% interest...

A man is planning to retire in 15 years. Money can be deposited at 4% interest compounded quarterly, and it is also estimated that the future general inflation rate will be 6% compounded annually. What amount of end-of quarter deposit must be made each quarter until the man retires so that he can make annual withdrawals of $80,000 in terms of today's dollars over the 20 years following his retirement? (Assume that his first withdrawal occurs at the end of the first six months after his retirement.)

Solutions

Expert Solution

Effective Annual rate of 4% interest compounded quarterly =(1+4%/4)^4-1 = 4.060401%

With inflation of 6% per year, first withdrawal (after 15 years and 6 months) at today’s Dollar

=$80,000*(1+6%)^15.5= $ 197,392.61

Present value of retirement withdrawals, as on commencement of payment (6 months after retirement)= $4,731,665.70 as follows:

PV of the above amount, as on date of retirement= $4,731,665.70/(1+4.060401%)^0.5

=$4,638,433.19

Amount to be deposited each quarter= $56,795.05 as follows

jeff jeffy answered 1 year ago

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